RU2806353C1 - Method and device for processing brittle transparent and semi-transparent materials - Google Patents

Abstract

FIELD: cutting devices.

SUBSTANCE: present invention is related to a method and device for controlled separation (cutting) of solid transparent and semi-transparent brittle materials, including hardened and super-hard ones, using the laser filamentation separation (LFS) process, and can be used in production of smartphones, tablets, wearable electronics, as well as in the automotive industry, construction and instrument making. The method includes the quantitative determination of radiation parameters that completely determine the LFS process. A laser device is also proposed in which the irradiation parameters for cutting are set according to their values found in accordance with the mentioned method, taking into account the properties of the material selected for LFS.

EFFECT: improved smoothness of the resulting side walls of separation is achieved, increasing the energy efficiency of LFS, obtaining a high speed of LFS or the ability to perform LFS with a laser beam of very low average laser power (from tenths of a W) obtaining a considerable separation speed acceptable for applications.

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Description

TECHNICAL FIELD

The present invention relates to a method and device for controlled separation (cutting) of solid transparent and translucent brittle materials, including hardened and superhard materials, using the laser filamentation separation (LFR) process, and can be used in the production of smartphones, tablets, wearable electronics , as well as in the automotive industry, construction and instrument making.

The objective of this invention is posed as an improvement of the specified LPR process in the form of achieving for a wide variety of materials such technical results as improved smoothness of the resulting side walls of separation, increased energy efficiency of LPR, high (record high) LPR speed, or the ability to perform LPR with a laser beam at a very low average laser power (from fractions of W) while obtaining, nevertheless, a considerable separation rate acceptable for applications. Obtaining cut side walls with improved smoothness for transparent and translucent materials would generally make it possible to significantly simplify and reduce the cost of the cutting process and increase its productivity, i.e. spend less time to obtain a final product of acceptable quality, since in this case there is no need to perform labor-intensive additional post-laser processing in the form of grinding, polishing or chemical etching of the separation walls to remove roughness on them, which is a source of unwanted crack nuclei and therefore reduces the impact resistance of the product during its further use.

LIST OF ABBREVIATIONS

LFR - laser filamentation separation,

OPE - volumetric energy density, measured in J/cm ³ ,

SFOI - creation of filament in one impulse,

SFCI - creation of a filament by a train of pulses,

DOL (short for “depth of layer”) - the depth of the near-surface tempered layer on the front and back sides of a chemically tempered glass plate.

LIST OF PARAMETER DESIGNATIONS

1. A _LP is the nonlinear absorption capacity of the filament, taken from the available experimental data; for the case of filaments considered here without radial overlap, its value is taken close to the maximum, about 0.8±0.05,

2. A _PH - conversion coefficient describing the fraction of thermal energy from the filament plasma E _TW actually converted into heat Q. Under the conditions of optimal choice w A _PH ≈0.9 or more, which corresponds to the loss of a fraction of energy (about 1-A _PH ≈0.1) to plasma radiation in the region of transparency of the material surrounding the filament, leaving the modification zone over long distances and thus not taking part in the formation and expansion of this zone,

3. C ₂ - some average value of specific heat capacity in the temperature range from T _i = 20 ° C to T _mod ,

4. C _HT - specific heat capacity of the material at high temperatures (>2500-3000 K),

5. c _s - speed of sound in the material,

6. d - distance in depth between sets of filaments located in the thickness of the material at different depths,

7. E ₀ - the energy of an individual train pulse in the material for the case when the energies of the individual train pulses are the same,

8. E _0i - energies of individual train pulses in the material, i=1,2,… N _p ,

9. E ₁ - laser pulse energy in the material for the SFOI mode,

10. E _burst - energy of a pulse train in the material,

11. E _dis - energy spent on dissociation,

12. E _p - filament plasma pumping energy,

13. - filament plasma energy minus energy losses E _dis due to dissociation,

14. E _S+T - energy of losses due to scattering and passage of the beam through the material,

15. E _sw is the energy component carried away from the filament by the shock wave,

16. E _trad - loss of filament energy due to its thermal radiation in the spectral transparency band of the cold transparent material around it,

17. E _tw - energy carried away from the filament by a thermal wave,

18. f ₁ and f ₂ - limits for the repetition rate of pulse trains,

19. f _burst - repetition rate of pulse trains,

20. f _burst ≥f ₁ - high-frequency range of train repetition frequencies,

21. f _burst ≤f ₂ - low-frequency range of train repetition frequencies,

22. H - filament length,

23. K _tw - coefficient of conversion of filament energy E _p' into thermal wave energy E _tw ,

24. K _sw - coefficient of conversion of filament energy into a shock wave. It is assumed that K _sw <<1 and K _tw ≈1, if the energy release occurs slowly, that is, t _E >t _P1 , t _P2 . Or they assume K _sw ≈0.5 for “fast” energy release, that is, t _E <t _P1 , t _P2 ,

25. L - material thickness,

26. M ² - beam quality parameter,

27. NA - focusing numerical aperture,

28. N _at - number of atoms in one molecule of material,

29. N _p - number of pulses in a train,

30. N _p0 is the lower limit for N _p to reduce the radius of shock wave action in the material around the filament to a level acceptable to obtain a smooth separation,

31. N _p1 - lower limit for the number of pulses in a train N _p in order to reduce the OPE of an individual train pulse to a level acceptable for obtaining a filament with a uniform diameter along the length,

32. P is the average power of pulse-periodic laser radiation in the material,

33. P ₁ - power of a single laser pulse in the material,

34. Р _с (λ) - power critical for self-focusing in an individual pulse, depending on λ,

35. Q - heat released in the material as a result of relaxation of the filament plasma created by one pulse,

36. q is a dimensionless coefficient in the relation r _f =qr ₀ , which can depend on w and τ, i.e. q=q(w,τ). Within the range w we are interested in, we assume that q≈1,

37. R=8.31 J/(mol⋅K) - universal gas constant,

38. R ₁ , R ₂ - local radii of curvature of the curvilinear cutting path in the cross-sectional plane of the filaments,

39. R _c - radius of curvature of the curvilinear cutting path,

40. r _f - filament radius,

41. R _sw - radius of the shock wave impact zone around the filament,

42. R _T - radius of the cylindrical impact zone around the filament axis due to the thermal conductivity mechanism,

43. R _TD - radius of the cylindrical impact zone around the filament axis due to the thermal deformation mechanism,

44. s ₁ - step of following filaments in the material,

45. s _1max - the maximum permissible step of filaments to obtain a smooth separation,

46. T ₀ - the maximum time heating temperature of the filament on its axis,

47. T ₁ and T ₂ - temperature limits for the filament temperature, corresponding to the OPE limits w ₁ and w ₂ and defining the “window” of unfavorable temperatures T ₁ < T < T ₂ , in which the share of filament energy losses due to thermal radiation is significant. However, outside this window, i.e. at T≤T ₁ and T≥T ₂ we consider losses due to thermal radiation to be insignificant,

48. _Тс - temperature critical for cracking of the material for the thermal deformation modification mechanism,

49. T _i (=20°С) - initial (room) temperature,

50. T _melt - melting point (for crystalline material),

51. T _mod - minimum threshold temperature in the zone around the filament critical for separation during the thermal modification mechanism,

52. T _strain - glass transition point (for an amorphous material),

53. t _E is the effective time of release of absorbed radiation energy from one filament in the material, during relaxation of the excitation of the material to the temperature of the equilibrium state. Depending on the laser pumping, the order of magnitude is estimated as the maximum t _E of two parameters: t _eh and t _ei ,

54. t _P1 - time of inertial pressure retention within the radius of the filament,

55. t _P2 - time of inertial pressure retention in the space between adjacent filaments,

56. t _T1 - heat retention time within the radius of the filament,

57. t _T2 - heat retention time within the radius R _T of the thermal impact zone,

58. t _r - beam position holding time,

59. t _rep - repetition time of pulse trains,

60. u is the speed of relative movement of the material and the laser beam,

61. V _f - filament volume,

62. w _dis - volumetric dissociation energy density of the material,

63. w is the volumetric energy density (VED) of the filament plasma,

64. w ₁ and w ₂ are the limits that define the “window” of unfavorable OPE, w ₁ <w<w ₂ , in which the share of filament energy losses due to thermal radiation is significant. However, outside this window, i.e. for w≤w ₁ and w≥w ₂ we consider losses due to thermal radiation to be insignificant,

65. w _mod - modification threshold for the thermal mechanism of formation of the impact zone around the filament,

66. xyz - coordinate system, selected so that the relative movement of the beam and material occurs in the xy plane, and the z axis is directed deep into the material,

67. Y [GPa] - Young's modulus of the material,

68. α[cm ^-1 ] - absorption coefficient of the material,

69. α _T [deg ^-1 ] coefficient of thermal expansion of the material,

70. β is the ratio of the energy flow from the filament due to thermal radiation to the energy flow from the filament due to thermal conductivity,

71. β _max - maximum permissible value B,

72. Г=1÷1.25 - dimensionless parameter, selected empirically,

73. δ - part (<1) of thermal energy E _tw released within the radius r _f of the filament in conditions when, during time t _E , if the condition t _E >t _T1 >>t _P1 is met, there is a significant transfer of thermal energy beyond r _{f ,}

74. Δt - time interval between pulses in a train,

75. η is the coefficient of thermal conductivity cooling of the material in the space between adjacent filaments from any pulse train to the moment the maximum heating of this gap is reached by the next in time and spatially adjacent pulse train,

76. Λ - thermal conductivity of the material,

77. λ - wavelength of laser radiation,

78. μ [g/mol] - molar mass of the material,

79. ρ - density of the material,

80. ρ ₂ - average value of the density of the material in the temperature range from T _i = 20°C to T _mod ,

81. - Stefan's constant,

82. σ _с - the compressive strength of the material under shock wave action,

83. τ - duration of an individual pulse, assumed to be the same for all pulses of the train,

84. τ _burst - duration of the train as a whole,

85. ϕ=R _T /R _sw - coefficient showing how many times it is desirable to reduce relative to R _T by using the number of pulses N _p0 in the train,

86. Ф ₁ - energy flow from the heated filament due to thermal conductivity,

87. Ф ₂ - energy flow from a heated filament due to its radiation as a black body,

88. χ - thermal diffusivity of the material,

89. Ω - energy efficiency of the LPR process.

Parameter designations used in clause 1 of the “Formula of the invention”:

r _f is the effective radius of the filament, which, for example, for a Gaussian distribution w(r) corresponds to the radius at the 1/e level of the decay of the dependence of w(r) on the beam axis, for a non-Gaussian distribution, in particular a Bessel beam, in the presence of an effective intensity concentration around filament axis with a dominant, clearly expressed distribution maximum, a similar effective radius can also be introduced for it,

χ - averaged value of the thermal diffusivity of the material in the temperature range from the initial T _i to the order of T _mod ,

- corresponding to the limit w _1, the limit of the filament plasma temperature (at T ₁ >>T _i , where T _i = 20°C is the initial temperature), which is calculated from the condition that the ratio β of the energy flow from the filament due to thermal radiation (considered as “ useless" losses) to the energy flow due to thermal conductivity (considered as useful energy losses of the filament, since it ensures the formation and propagation of a modification critical for zone separation during cooling of the filament plasma) does not exceed the maximum permissible value

_βmax ,

T _i =20°С, T _i (=20°С) - initial (room) temperature,

T _mod is the minimum (threshold) temperature to obtain a smooth separation, which for amorphous materials is assumed to be T _mod ≈T _strain , and for crystalline materials - T _mod =T _mel ,

T _strain is the glass transition point of an amorphous material,

_Tmelt is the melting point of the crystalline material,

С=C _HT - specific heat capacity of the material at temperatures above the dissociation temperature of the material (for example, for glasses >2500-3000 K), estimated as ≈3RN _at /μ, R=8.31 J/(mol⋅K) universal gas constant,

N _at - number of atoms in 1 molecule of material,

μ [g/mol] - molar mass of the material,

ρ is the density of the material,

- Stefan's constant,

w _dis - specific irreversible energy losses (in J/cm ³ ) for the dissociation of the material, which are not restored at the further stage of cooling the filament during the release of energy from it into the surrounding material,

- the so-called “inertial pressure retention time” in the filament,

c _s - speed of sound in the material,

t _E is the effective time of release in the material of the absorbed radiation energy from one filament during relaxation to the temperature of the equilibrium state of nonequilibrium energy excitation of the electronic levels of the material, excited both by multiphoton absorption of laser radiation and by high-energy photons of the thermal radiation spectrum of the filament plasma.

Parameter designations used in clause 2 of the “Formula of the invention”:

Рс (λ) is the power critical for self-focusing in a single pulse, depending on the wavelength of laser radiation,

λ is the wavelength of laser radiation,

ρ ₂ - average value of the material density in the temperature range from T _i = 20°C to T _mod ,

C ₂ - average value of specific heat capacity in the temperature range from T _i = 20°C to T _mod ,

σ _c is the compressive strength of the material when exposed to a shock wave,

Г - dimensionless parameter, selected empirically in the range 1÷1.25,

A _LP is the nonlinear absorption capacity of the filament, its value for the LPR conditions considered here with non-overlapping radially filaments in the SFCI mode is taken from the experimental data available in the literature as A _LP = 0.8 ± 0.05,

A _PH is the conversion coefficient describing the fraction of thermal energy from the filament plasma E _tw that is actually converted into heat Q. Under the conditions of the optimal choice of w, i.e. when w≤w ₁ , A _PH ≈0.9 or more is used to perform estimates,

t _P2 is the time of inertial pressure retention in the space between adjacent filaments, estimated as t _P2 ≈s ₁ /c _s ,

η is the coefficient of thermal conductive cooling of the material in the space between adjacent filaments from any pulse train to the moment the maximum heating of this interval is reached by the next in time and spatially adjacent pulse train, lies in the range η=0.76÷1 for the high-frequency range f _burst ≥1, and in the range η≤0.1 for the low-frequency range of train repetition frequencies, when f _burst ≤f ₂ ,

f ₁ and f ₂ - limits of repetition frequency f _burst of pulse trains, while f ₁ / f ₂ , and f _burst ≥f ₁ - high-frequency range of train repetition frequencies, af _burst ≤f ₂ - low-frequency range,

w _mod is the threshold for modification of the material by volumetric energy density for the thermal mechanism,

ϕ=R _T /R _sw - coefficient showing how many times it is desirable to reduce R _sw in relation to R _T by using the number of pulses N _p0 in the train,

R _sw is the radius of the cylindrical zone of shock wave action around the filament,

R _T is the radius of the cylindrical impact zone around the filament axis due to the thermal conductivity mechanism.

GLOSSARY

Filament In the text below, a filament is an extended thread-like object heated to a high temperature with a length from several tens of microns to several thousand microns, created inside the volume of an initially transparent material due to nonlinear absorption of a high-intensity beam of a femtosecond or picosecond laser - see Fig. 2, 5 and 7.

The filament can be created by one pulse (irradiation mode, abbreviated hereinafter as SFCI filament creation by one pulse), or by a train (group) of pulses closely spaced in time (hereinafter abbreviated as SFCI - filament creation by a train of pulses) - see Fig. . 4a, b.

To create a focusing area of extended length in the volume of the material, i.e. filament, use the nonlinear optical phenomenon of self-focusing, or a Gaussian-Bessel beam formed by conical lenses, or some other methods, using a femtosecond or picosecond laser beam emitting at a radiation wavelength at which the material is transparent at low laser intensity in an unfocused beam. To perform the laser filament cutting (LFR) process, one or more sets of filaments are created in the thickness of the material, where these sets differ from each other by their different positions in depth in the material, see Fig. 2.

Effective radius r _f and filament length H

A simplifying approximation of the model used here is to consider an individual filament as a cylinder of length H (see Figs. 2, 5 and 7). In this case, the volumetric energy density (VED) w of the filament is considered to be uniform along the length of the filament H, but with an initially Gaussian distribution along the radius.

The parameter r _f used in the text below denotes the radius of the filament at the level of 1/e decline of the OPE from the beam axis. In this case, we assume that r _f <<H, since r _f in the cases considered below is of the order of 1 μm or less, while H is a much larger value - from tens of μm to several thousand μm.

Another radius, also mentioned in the text below, r _1/2 , can be determined in a similar way, denoting the radius of the filament at the level of the OPE falling halfway from the maximum on the filament axis. In the method proposed here, we consider below a scheme with the creation of filaments that do not overlap in radii, when the pitch of the filaments in the volume of the material s ₁ is many times greater those. s ₁ >> - see Fig. 2.

Note that the filament radius r _f should be distinguished from other characteristic radii: R _sw - the radius of the shock wave (sw) impact zone around the filament, R _T - the radius of the cylindrical impact zone around the filament axis by the thermal conduction mechanism (T ) transfer and R _TD - the radius of the cylindrical impact zone around the filament axis due to the thermally-induced deformation (TD) mechanism. These characteristic radii usually exceed r _f and arise at the stage of relaxation of electronic excitation and cooling of the heated filament, when predominantly radial energy transfer occurs from it to the surrounding volume of the material.

Filament plasma energy

The parameters r _f and H introduced in this way make it possible to express the energy E _{p of} the filament plasma in a simple form

Parameter here there is an obvious meaning of the effective volume of the mentioned cylindrical filament, aw is the maximum value of the OPE on the axis of the filament.

Volumetric filament energy density

To properly describe laser filament heating and associated effects, a parameter such as filament OPE w measured in J/cm ³ is used instead of the usual energy density measured in J/cm ² or laser pulse intensity measured in W/cm ² . This choice of parameter w is explained by the fact that it is directly related to the filament temperature. Since many processes associated with LPR, such as softening of glass, its cracking, dissociation, ionization, are temperature-activated in nature, this approach makes it possible to most easily estimate the temperature of the filament through the OPE and thereby, from the value of the OPE, obtain an indication of the mechanisms and nature of those or other phenomena causing laser-induced separation of the material.

According to relation (1*), the quantitative OPE of the filament w is determined as

i.e., as the ratio of the filament plasma energy E _p to its effective volume ( ).

For a non-Gaussian distribution w(r) in the presence of a dominant pronounced maximum of the intensity distribution with an effective concentration around the filament axis, in particular, for the central maximum of the spatial distribution of the Gaussian-Bessel beam considered below, a similar effective radius r _eff can also be introduced. To perform estimates, it can be determined from an expression similar to (1*)

In this relation, w _max is the maximum value of the OPE in this non-Gaussian distribution, ar _eff is the effective radius of the said central maximum of the non-Gaussian distribution. The parameter r _eff is not as obvious as the above-mentioned (1/e)-radius r _f of the Gaussian distribution. As follows from (3*), r _eff can be estimated as

However, such a calculation requires information about the dependence w(r), which in the general case is not always known.

Pulse trains

In FIG. Figure 4b shows a diagram of the temporal structure of irradiation, in which each of the filaments for performing LPR is created by a train (or group, package) of several (N _p ) pulses closely spaced in time. In this case, τ denotes the duration of an individual pulse, Δt is the repetition time of pulses in a train, τ _burst is the duration of a pulse train, and t _rep is the repetition time of pulse trains. Irradiation by pulse trains is abbreviated as SFCI (creation of filament by a train of pulses) and is considered in the proposed method, in contrast to another previously discussed and described in the “State of the Art” and shown in Fig. 4a SFOI mode (filament creation with one pulse). Typically in practice, τ _burst is about 10-150 ns, while t _{rep is} many times larger - about 500-5000 ns.

To perform LPR, a moving laser beam is used, which during its movement creates not one filament, but a set of filaments in the thickness of the material. In this case, in order to localize the investment of the pulse energy of each train into approximately the same region of space in the form of a cylinder with a filament radius r _f (and thereby create a filament by a pulse train), it is important to choose the duration of the train τ _burst less or even much less than the time the beam travels along distance to the material is on the order of the filament radius those.

Where the speed of relative movement of the laser beam and the surface of the material.

BACKGROUND OF THE ART

The prior art is explained in FIG. 1-6, where:

Fig. 1 schematically shows in a generalized form the main elements of a device known from the prior art for separating transparent materials using LPR with the relative movement of a repetitively pulsed laser beam and the material (see, for example, [Vanagas et al Patent WO 2016/193786 A1]). 1 - laser source, 2 - supply channel, rigid or flexible (for example, using an optical fiber), for the beam emerging from laser 1 to focusing system 3. 3 - beam formation and focusing system, which may include beam-forming diaphragms , collimating lenses, spectral filters, beam expanders, polarizers, 1/4-wave plates, devices for changing the frequency of laser radiation, adjustable beam energy attenuator, rotating mirrors, diffraction optical elements, phase plates, focusing lens. System 3 can be stationary or movable (using an xyz-movement system) relative to the material being processed 5. 4 - laser beam formed and focused by system 3 and directed to the material being processed 5. 5 - transparent material being processed, in the thickness of which the focused beam 4 filaments or sets of filaments are created at one or another depth in the thickness of the material. 6 a system for fastening the material 5 under the beam 4, allowing you to adjust the tilt of the sample 5 and rotate it around the vertical axis z. 7 - three-coordinate xyz stage for adjusting the focus position along the z coordinate in the material 5, as well as for computer-controlled or otherwise moving the sample 5 in the xy plane at the required speed and along the required trajectory. The xyz coordinate system is chosen here and in subsequent figures so that the relative movement of the beam and material occurs in the xy plane, and the z axis is directed deep into the material.

Fig. 2 shows the scheme used for LPR for creating one or several sets 11 of filaments 10 inside the material. These sets are located in the plane 12. 8 - direction of relative movement of the focused laser beam 4 and material 5. 9 - trace of the movement of the laser beam 4 on the surface of the material 5. L - thickness of the material, H - length of the filaments 10 and at the same time the width of one set 11 of filaments, s ₁ - pitch of the filaments in the material with relative movement of the laser beam 4 and material 5 at speed u, d - distance between sets 11 of filaments 10 along the depth of their location in the material if there are several of these sets. Various schemes for the relative movement of the laser beam and the material are possible: (a) when, using a computer-controlled or otherwise controlled three-coordinate xyz-table in the xy plane, the material itself moves with the required speed and along the required trajectory, and the beam 4 is stationary, and/or (b) when, also with the help of a three-coordinate xyz stage, the beam 4 moves, while the system 3, with a flexible radiation supply 2, can be movable relative to the material being processed 5.

Fig. 3 shows (a) 2 photos showing the LPR production of both a non-smooth and a fairly smooth lateral surface of separation 13 for chemically tempered Corning Gorilla® glass with a thickness of 0.7 mm when creating filaments with single pulses of 6 ps duration and an energy of each 220 μJ [M. Kumkar, L. Bauer, S. Russ, M. Wendel, J. Kleiner, D. Grossmann, K. Bergner, S. Nolte. Proc. SPIE, Vol.8972, p. 897214-1 (2014)]; (b) Photo demonstrating the ability to obtain a smooth side separation surface 13 with a roughness R _a <0.1 µm without post-laser processing when cutting chemically tempered Corning Gorilla® glass with a thickness of 0.55 mm and a hardened layer depth of 20 µm using the ClearShape™ process, announced by Spectra-Physics® [V.Matylitsky, F. Hendricks, R.Patel. "Process can machine glasses and sapphire with high quality", http://www.industrial-lasers.com/articles/print/volume-30/issue-3/features/femtosecond-laser-processing-of-brittle-materials. html1. [F. Hendricks, V.V. Matylitsky. "Femtosecond Lasers for Machining of Transparent, Brittle Materials: Ablative vs. Non-Ablative Femtosecond Laser Processing." Proc. SPIE, Vol.9740, 97400Z-1 (2016)]. The details and physical basis of this process are not disclosed by the company.

Fig. 4 also relates to the prior art, (a) The time structure of the irradiation power used in the LPR modeling is shown, in which each of the filaments is created by one pulse [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)]. τ - duration of one pulse, t _rep - pulse repetition time; (b) Temporal structure of irradiation, in which each of the filaments for performing LPR is created by a train of several (N _p ) pulses closely spaced in time, r denotes the duration of an individual pulse, Δt is the repetition time of pulses in the train, τ _burst is the duration of the pulse train, and t _rep is the repetition time of pulse trains. This irradiation structure in the form of trains is considered in the method described below.

Fig. 5 shows a scheme for creating an extended focusing area 10 inside a transparent material using conical lenses (axics) 15 and a Gaussian-Bessel beam [Chebbi B, Minko S, Al-Akwaa N and Golub I 2010 Opt. Comm. 283, 1678]. 1 - laser radiation source, 2 - laser beam and its supply channel, rigid or flexible (for example, using optical fiber), from laser 1 to focusing system 3. 3 - system for beam formation and focusing from beam expander 14 and conical lenses 15, 5 - irradiated material, 10 - filament.

Fig. 6 also relates to the prior art. One of the necessary conditions for obtaining a smooth separation is explained and why it is possible for some materials and impossible for others [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)]. a) Shown is the virtual plane π 16 of the cross section of a set of 11 filaments located in the thickness of the material 5 in the plane 12. 8 - direction of movement of the laser beam relative to the material. Of several competing mechanisms for the formation of the impact zone (see the text for more details), we consider the thermal mechanism to be dominant in this case, that is, R _T >R _TD , where R _T is the radius of the cylindrical impact zone 17 around the filament axis due to the thermal mechanism, and R _TD - similar radius of the impact zone 18 due to the thermal deformation mechanism. 10 - locations of the filament axes, we assume that their radius r _f <<R _T , R _TD - The values of R _T and R _TD are determined for the indicated mechanisms, as shown in the figure, by the position of the isotherms in the material, respectively and T=T _s , where - the glass transition point of the material, above which, as is known, the increase in volume with temperature increases sharply (for a crystalline material T _strain coincides with the melting point T _m ), and T _c is the temperature critical for cracking and damage to the material for the thermal deformation mechanism, when heated to which deformation reaches the fracture threshold. Although the thermal deformation mechanism, when irradiated, leads to cracking of the material directly inside the zone r≤R _TD , the boundary of which is conventionally indicated by a zigzag contour, this entire zone, as can be seen from the figure, is located inside the zone of influence of the thermal mechanism r≤R _TD . Therefore, the cracked material in the zone of radius r≤R _TD undergoes annealing, and this cracking does not appear after separation is completed. 19 - possible straight and smooth line of separation during subsequent mechanical splitting in this case, b) Shows the cross section of 16 zones of influence of successive filaments in the form of the above-mentioned π plane in the opposite case, when the thermal deformation mechanism dominates, that is, R _TD >R _T . In this case, at intermediate radii r, such that R _T <r≤R _TD , there is, as can be seen from the figure, a region of damage and cracking of the material directly during irradiation, characteristic of the thermal deformation mechanism. Therefore, after irradiation is performed at the subsequent stage of mechanical splitting of the material weakened by irradiation, the line (surface) of separation 19 can be zigzag, randomly changing direction, since it passes along random microcracks and boundaries between pieces of material formed as a result of cracking in the specified area of damage to the material, which corresponds rough, non-smooth separation of material. Moreover, on both halves of the subsequent separation after irradiation there will be a damaged cracked near-surface layer, corresponding in this figure to the area of damage to the material on both sides of this rough separation surface 20, which adversely affects the strength of the material during its further operation after the separation. A comparison of cases (a) and (b) demonstrates that the condition for a smooth separation corresponding to figure (a) is the dominance of the thermal mechanism in the formation of the impact zone over the alternative thermal deformation mechanism, which corresponds to the fulfillment of the inequality T _strain < T _c , which, in turn, , is determined by the material parameters. More detailed description in the text [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)] shows that in the SFOI mode there is a certain class of materials for which this inequality is satisfied, namely chemically tempered glasses. For the situation where thermal and shock wave modification mechanisms are compared, it was similarly shown that a prerequisite for obtaining a smooth separation is also the dominance of the thermal mechanism, and this condition is also satisfied for tempered glasses.

TECHNICAL PROBLEM

In the modern world of technology, glass and other optically transparent materials are among the most important; they are used to create a wide variety of structures in construction, architecture, medicine, automotive industry, the production of mobile phone and tablet displays, electronics, electric power and many other industries. The global market for such products amounts to billions of units per year. It is important to note that precision cutting is required to produce virtually any glass or other transparent material into the desired shape and size. Therefore, for the production of such products on a large industrial scale, the development of new high-performance, energy-efficient and environmentally friendly cutting technologies is extremely important. In this regard, the development of laser cutting technologies is promising due to the prospects for obtaining a higher quality surface finish, tens and hundreds of times higher separation speeds, as well as a higher environmental friendliness of the process compared to traditional cutting processes.

For comparison with previous results, we point out that a method of laser cutting due to controlled crack propagation is known [RM Lumley, American Ceramic Society Bulletin, 48(4), 850 854 (1969)], also [S. Nisar, L. Li and M. A. Sheikh, J. Las. Appl. 25, 042010-1 - 042010-11 (2013)]. It is based on the possibility of creating a mechanical stress profile in a material when laser radiation is absorbed on its surface or in the volume. Continuous infrared emitters are used - CO ₂ lasers, ND:YAG lasers, or CO laser. Under certain conditions, temperature stresses cause the initiation of a crack propagating in depth from top to bottom, which also propagates along the trajectory of the laser beam along the surface of the material being processed. Parts are cut out without any auxiliary mechanical action, while the cut walls are smooth and do not contain any defects or chips. However, these advantages are provided by continuous CO ₂ lasers for straight cuts. The disadvantages of these continuous lasers include the fact that they do not work for curved cuts necessary to obtain rounded corners, slots and internal holes in a product (for example, smartphone glass) (including those with a small diameter of several millimeters or less). At high processing speeds, the propagation of a crack in glass for such lasers turns out to be difficult to control - it can begin to propagate in an arbitrary direction, which leads to too many defects in the form of unusable parts. Disadvantages also include the need to use significant laser power from continuous sources of hundreds and thousands of watts [AA Abramov, MW Kemmerer, Y. Sun, N. Zhou, “Laser separation of glass sheets.” Patent US 20100078417 A1 (2010)], which, with a typical low speed of movement of the beam relative to the part (less than 0.1 m/s), leads to a high energy release per unit length of the cut, thereby creating an overly extended zone of thermal influence from the side separation surfaces, with correspondingly high residual thermal stresses and deformations. Such effects are unacceptable for a number of applications when the material being cut already contains some functional working layers that are sensitive to heat or mechanical stress - for example, a layer of light-emitting organics in the case of cutting display glass.

Other methods are also known in which significant efforts have been made to improve the accuracy and quality of the cut - for example, by irradiation with two laser sources [S.-N. Tsai and H.-W. Chen, J. Mater. Proces. Techn. 136, 166 173 (2003)], by absorbing one laser in a glass volume [L.J. Yang, Y. Wang, Z. G. Tian, and N. Cai, Int. J. Mach. Tool. Manu. 50, 849 (2010)], by registering a trajectory with another laser [S.-N. Tsai and J.-S. Shiu. J. Laser Applications, 21, 57 (2013)]. Efforts have also been made to increase cutting speed through the use of additional ultrasonic wave action [D.J. Garibotti, "Dicing of micro-semiconductors", US Patent 3,112,850 (1963)], or jets of cold water or air in addition to laser exposure [V. Kondratenko. "Method of splitting nonmetallic materials". US Patent 5,609,284 (1997)]. The disadvantages in these cases are that these improvements lead to increased cost and complexity of the process, but the question remains unresolved of how to make the cutting technology on the one hand fast, accurate, well-controlled, simple and universal for various materials at the same time. , and on the other hand, also with smooth side cutting surfaces that do not require further lengthy and labor-intensive post-laser grinding and polishing, mechanical or chemical, and, therefore, have higher productivity.

Another well-known approach is the use of repetitively pulsed lasers instead of continuous wave lasers. In this case, laser filamentation separation (LFS) of the material was considered, which included two stages, where

(a) at the first, preparatory stage, a plate of material is irradiated with a beam of pulse-periodic radiation from a femtosecond (or picosecond) laser when the beam and material move relative to each other and create one or more extended thread-like objects heated to a high temperature (the so-called filaments) with a length of several tens of microns to several thousand microns, non-overlapping with each other in their radii, use the creation of a filament with one pulse (hereinafter abbreviated as SFPI), or the creation of a filament by a train (group) of pulses closely spaced in time (hereinafter abbreviated as SFCI) , to create a focusing region of extended length in the volume of the material, the nonlinear optical phenomenon of self-focusing is used, or a Gaussian-Bessel beam formed by conical lenses, or any other methods for a femtosecond or picosecond laser beam emitting at a radiation wavelength of in which a given material is transparent at low laser intensity in an unfocused beam, one or more sets of filaments are created in the thickness of the material, where these sets differ from each other by their different positions in depth in the material;

(b) after the above irradiation, the next stage involves mechanical splitting of the plate, i.e. its division along the surface of the arrangement of the set (or sets) of filaments created by the laser beam. Such separation can occur spontaneously or by applying additional mechanical action on said plate being processed in the form of tensile mechanical stress in the area where said sets of filaments are located in the material.

The generalized basic elements of a device known in the art for separating transparent materials using the relative movement of a focused pulsed laser beam and a material, as well as details of creating filaments within the material, are shown in FIG. 1 and Fig. 2 (see, for example, [E. Vanagas, D. Kimbaras, L. Veselis, "Method of laser scribing of semiconductor workpiece using divide laser beams", International application WO 2016/193786 A1]) and are explained in the captions to the indicated drawings.

The famous work [M. Kumkar, L. Bauer, S. Russ, M. Wendel, J. Kleiner, D. Grossmann, K. Bergner, S. Nolte. Proc. SPIE 8972, 897214-1 (2014)], in which the so-called “multifocusing” was used to create several sets of filaments in the thickness of the material, when the original laser beam is divided into several beams (two or more) using a special optical circuit, each of these is focused at a certain depth in the material, and the positions of the foci are different for different beams. The vicinity of each of the focal points ensures that the filament is created and the filaments from each focal area are aligned with each other. In this way, when the initial laser beam moves across the material in one pass, several sets of filaments are created at once, with each set differing from the others in the depth of its location in the thickness of the plate, see Fig. 2 and Fig. 3b, which demonstrates the possibility of obtaining both non-smooth and highly smooth separations for chemically tempered Corning Gorilla® glass with a thickness of 0.7 mm when creating filaments with single pulses of 6 ps duration and an energy of each 220 μJ. Other irradiation parameters: in the first photo Fig. 3a - repetition frequency 50 kHz, movement speed 0.2 m/s; in the second photo Fig. 3a - repetition frequency 25 kHz, moving speed 0.1 m/s. As can be seen in the second photo, it is possible to achieve high smoothness of the lateral surface of the separation. However, the disadvantage in this case is the extremely low speed of movement (0.1 m/s) of the material relative to the laser beam; the physical mechanism and control factors for obtaining smooth separation have not been clarified.

Known patent US 20130126573 A1 [S.A. Hosseini, P.R. Herman, “Method of material processing by laser filamentation”, where each of the filaments was created not by a single pulse, but by a train of pulses closely spaced in time (see Fig. 4), which, according to the authors, makes it possible to create longer filaments. The disadvantage in this case is that a smooth separation was not obtained within the set of filaments.

Close to the technical solution we propose in terms of such technical results as speed and improved smoothness (which in the experiment is expressed in a significant reduction in the amplitudes of roughness harmonics both within each set of filaments in the space between the nearest adjacent filaments, and along the rest of the lateral surface of the cut 13, including the unirradiated areas between the specified sets of filaments), apparently is to obtain a smooth surface without laser processing with a roughness R _a <0.1 μm on the side wall 13 of the separation when cutting chemically tempered Corning Gorilla® glass 0.55 mm thick and deep 20 µm hardened layer (Fig. 3b) using the ClearShape™ process announced by Spectra-Physics® (a division of Newport Company) [V. Matylitsky, F. Hendricks, R. Patel. "Process can machine glasses and sapphire with high quality." http://www.industrial-lasers.com/articles/print/volume-30/issue-3/features/femtosecond-laser-processing-of-brittle-materials.html]. [F. Hendricks, V.V. Matylitsky. Proc. SPIE 9740, 97400Z-1 (2016)]. The company does not indicate the physical basis of this process in these publications; it only reports that with its help it is possible to quickly cut chemically tempered and non-tempered glass, as well as sapphire at speeds of about 1 m/s with a manifold improvement in cut quality compared to other laser processes - without peeling of flakes, with cut edge roughness R _a <0.1 µm and bending strength >650 MPa for chemically tempered glass.

There is a known patent by the same authors [F. Hendricks and V.V. Matylitsky. Processing of material using non-circular laser beams. Patent WO 2016/005455 A1], which is close to the technical solution we propose. In this patent, when creating filaments used in LPR of a transparent or translucent material with a pulsed laser, irradiation is used not with a round laser beam, but with an oval one (in a section perpendicular to the axis of the filament at the focal point), with the long axis of this spot oriented along the tangent to the trajectory of the laser beam relative to the material, or at a small specified angle to it (no more than 20°). According to these authors, this makes it possible to obtain microcracks in the vicinity of each filament not in many different directions, but only a certain main microcrack in the direction of the specified long axis of the spot and, thereby, improve the quality of separation. The specified method is proposed to be used both in the SFDI mode and in the SFCI mode. To implement this separation method, the patent proposes a laser system using femto- and picosecond pulses, the distinctive feature of which is the possibility of forming an oval laser focusing spot in it and thereby obtaining a microcrack from the filament in the material with an orientation in the direction of the long axis of this spot .

The disadvantages of this patent include:

The problem of obtaining a smoother separation, as well as determining the conditions for obtaining maximum energy efficiency and high speed of relative movement of the beam and material, posed and solved in the method proposed here in our method, was not posed or considered in the specified patent, although the mode of more directional splitting proposed in the specified patent has some similarities with obtaining improved separation in our method proposed here.

The very possibility of a splitting mode directed along the long axis of the oval focusing spot is not substantiated in the text of the patent either by describing any experiments from the “State of the Art” or by our own experimental testing of the presence of such a mode. Also, the said patent does not quantitatively indicate the irradiation parameters at which the mode proposed in it operates, but only proposes to find these parameters by “blind” selection. However, such a selection, without a theoretical model of the phenomenon used as a “guiding thread” for the search, is an extremely difficult task with a large number of selected irradiation parameters, of which, as we will see below, there are 14 for the SFCI mode. This makes the practical use of the said laser separation device extremely difficult. In addition, with such a blind selection, there is no certainty that one or another set of parameters found is actually the most optimal.

Also, the authors do not indicate how their cutting method implements operational control of the orientation of the elongated spot, when when performing curved cuts, a constant change in the orientation of the long axis of this spot is required from filament to filament in accordance with the variable direction of the above-mentioned tangent to the trajectory of movement. Without disclosing information about the control of the orientation of the elongated spot in the device proposed by the authors, the specified method does not work.

The technical solution we propose uses not an elongated, but a round laser spot. In this case, directional cleavage is also achieved, but in a different way - not due to an elongated laser spot, the orientation of which is unclear how to operationally control, but due to other factors, when at a high frequency of filament creation, an elongated heating region to temperatures not lower than a certain critical one is not ensured in the material by one filament, but by the combined action of several filaments. In addition, our invention solves the problem of strictly grounded quantitative determination of irradiation parameters at which the desired technical results formulated in our method are achieved - higher smoothness of separation, high speed and high energy efficiency of the process.

In addition to glass, other materials were also studied. For example, the company "Evana Technologies" [http://www.evanatech.com/technologies/sapphire-wafer-scribing-dicing] demonstrated non-smooth filamentation laser cutting of sapphire using the company's patented (or pending) laser cutting technology ICICLE sapphire. This technology, according to the company, uses internal damage in sapphire with ultrashort laser pulses to easily and accurately cleave the material and is suitable for sapphire wafers up to 330 microns thick. The disadvantages in this case are that the separation speed is relatively low, no more than 0.3 m/s, and a smooth separation of this material was not obtained.

There are also works that show that filaments (or similar extended plasma objects) in the volume of a material can, in a more general case, be created not only through the use of the well-known phenomenon of self-focusing, in which a high-intensity laser beam is spontaneously compressed due to nonlinear optical effects in the material into an extended thin thread of micron or submicron diameter, but also through the use of any other methods that lengthen the beam focus area along the optical axis and are used both along with self-focusing and in addition to it. This effect was achieved through the use of special optical elements - axicons (conical lenses) to create a so-called Gaussian-Bessel beam in the processed plate - see, for example, [Chebbi B, Minko S, Al-Akwaa N and Golub I 2010 Opt. Comm. 283 1678]. The scheme for creating a Gaussian-Bessel beam in the material is shown in Fig. 5. The disadvantage of this work is that it did not study LPR at all.

A similar approach to the creation of filaments was used in the work of [K. Mishchik, V. Chassagne, , et al. Proc. of SPIE Vol.9740, 97400W1-16 (2016)]. It is also known to create filaments by using diffraction-optical elements, see, for example, [E. Vanagas, D. Kimbaras, L. Veselis, "Method of laser processing for substrate cleaving or dicing through forming "spike-like" shaped damage structures", International patent application WO 2016/059449 A1]. A smooth separation was not obtained.

Also from RF patent 2551043 C1 S.K., Vartapetov, A.F. Obidin, D.V. Ganina, “Method and device for forming precision holes in an optically transparent film using an ultrashort pulse of laser radiation,” the use of intentionally astigmatic focusing optics or placing the plate to be cut under a layer of liquid or solid transparent material is known. The disadvantage of this invention is that it has a smooth separation for LPR has not been studied.

It is also known to create filaments using diffractive optical elements to create fields from many holes in a transparent material [S.A. Hosseini. US2015246415 Method and apparatus for material processing using multiple flamementation of burst ultrafast laser pulses]. Each filament was created not by one pulse, but by a train (packet) of several pulses, the laser source had a wavelength of less than 5 μm, a pulse repetition rate of the laser beam from 1 Hz to 2 MHz, a number of pulses in the train from 1 to 50, and pulse energy from 5 to 500 µJ. The disadvantage of this work is that it focused only on obtaining holes in the material, but neither LPR, nor, especially, smooth LPR were studied at all.

There is a well-known experiment [K. Bergner, M. Muller, R. Klas, J. Limpert, S. Nolte and A. Ttinnerman, Appl. Opt. 57, 5941 (2018)], in which a thick, about 8 mm thick, quartz glass plate was cut by a Gaussian-Bessel beam, with each filament created by a train of N _p = 4 or 8 pulses. A wide range of energies of the Eburst pulse train was used, and it was found that the best smoothness (although not high) of the side walls of the cut is provided by the value Eburst = 0.9-1.0 mJ, which corresponds to obtaining a filament with a length H of about 7.4 mm. The disadvantage of the work is that a smooth separation was not obtained.

The advantage of the approach to creating filaments using a Gaussian-Bessel beam in these works is, in some cases, the possibility of obtaining filaments of significantly greater length (up to 10-20 mm or more), which is of practical interest for LPR of very thick materials with a thickness of not a fraction of a millimeter, but one or even several centimeters.

CLOSEST ANALOGUES

The closest in technical essence to the proposed invention regarding the obtained speed and smoothness of the LPR is the work of [V.N. Tokarev and I.V. Melnikov, Appl. Sci. 11, 1732 (2021)], which is accepted as the closest analogue. It describes the possibilities of obtaining smooth separation (at least with improved smoothness) during LPR based on a model that allows us to understand the mechanism and controlling factors of the process; a wide variety of materials and a wide range of changes in radiation parameters are considered. In this work, the irradiation mode was considered when the filaments do not overlap each other and the SFOI mode is used, shown in Fig. 4a. In this work, it was shown that, depending on the choice of irradiation parameters (their coordination with each other in a certain way), one or more of the following technical results of LPR are achieved:

(1) Obtaining smooth side walls of the separation, or at least with improved smoothness, which is expressed in a significant reduction in the amplitudes of the roughness harmonics both within each of the sets of filaments in the space between the nearest adjacent filaments, and along the remaining side surface of the cut, including non-irradiated areas between the specified sets of filaments;

(2) Highly efficient conversion of laser pulse energy into highly localized heat release in the space between adjacent filaments;

(3) Achieving high (and record high) cutting speeds, for example, about 1-4 m/s or more for glass and about 0.3-11 m/s or more for sapphire, which is tens and hundreds of times higher than the speeds of other known methods ;

(4) The possibility of separation under certain conditions at a very low average power of pulse-periodic laser radiation, starting from only about a hundred milliwatts, while achieving, although not a record high, but nevertheless acceptable for practical applications, material separation rate .

The listed technical results were achieved through the use of certain radiation parameters and material parameters, to find which a targeted search strategy was used, consisting of the following 6 parts:

1. A complex of several necessary physical conditions was formulated to obtain cutting with improved smoothness:

- Obtaining high energy efficiency of the separation process by eliminating filament energy losses due to thermal radiation. To do this, the pulse energy E ₁ in the material is selected in such a way that the filament plasma is pumped to a volumetric energy density (VED) w that satisfies the condition w≤w ₁ or w≥w ₂ . The limits w ₁ and W ₂ , for which usually w ₁ <w ₂ , are determined in the model by the thermophysical and optical properties of the material and are numerically of the order of one or several hundred kJ/cm ³ ;

- Ensuring increased uniformity of the diameter of each emerging filament along its length. To do this, the pulse duration r is coordinated with the pulse energy E1 in such a way that the power of a single laser pulse P ₁ ≈ E ₁ /τ is approximately equal to the critical power P _c for creating self-focusing power, i.e. P ₁ =GR _c , where Г=1÷2;

- Creation in the volume of the material of a continuous modified layer from filament to filament with the value of the volumetric energy density released in it (in [J/cm ³ ]) not lower than the minimum required (threshold) to obtain a smooth separation w _mod . To do this, the step of following s ₁ filaments in the material is coordinated with the radius R of the cylindrical zone critical for separating the modification as s ₁ ≤2R, which ensures closure, or even overlap with each other in the material of the indicated zones from neighboring filaments, and thereby the above-mentioned continuous modified layer from filament to filament - see Fig. 4c and Fig. 4d compared to Fig. 4b in the cited work. In this case, the radius R of the specified modification zone is calculated in the model depending on the modification mechanism and irradiation parameters:

- Formation of straight filaments of regular shape in each of their sets by minimizing their influence on each other, i.e. minimizing heating and temperature gradient from the previous filament at the location and at the moment of emergence of the next, new filament. To do this, the repetition frequency f of laser pulses is selected in one of two ranges found in the model, conventionally called high-frequency, f≥f ₁ , and low-frequency, f≤f ₂ , where the limits f ₁ and f ₂ differ by several tens of times and f ₁ >f ₂ ,

- Formation of an impact zone from the filament without destruction in the form of scattered cracking in the solid material directly during irradiation. For this, as is simplified in the model, the dominance of the thermal mechanism in the formation of the zone of influence is required, and not the alternative shock wave or thermal deformation mechanisms, which lead to scattered cracking in the solid material, which precludes smooth separation after irradiation. In this case, the dominance of one or another mechanism (thermal, thermal deformation, or shock wave) is defined as the dominance of the radius of the modification critical for separation determined by it over similar modification radii corresponding to two other alternative mechanisms - see Fig. 6. As the analysis shows, the dominance of the thermal mechanism over the above two alternative mechanisms occurs with the simultaneous fulfillment of two dimensionless criteria for the parameters of the material and radiation, which requires the use of a specific class of materials - tempered glasses. This theoretical conclusion is confirmed by obtaining smooth cutting for these materials in experiments. On the other hand, for sapphire and non-tempered glasses these criteria are not met, and in experiments smooth separation is indeed not observed for such materials.

2. The description of the above necessary conditions in the form of mathematical relationships between radiation parameters and material parameters made it possible to obtain a system of equations and inequalities.

3. A solution to this system of relationships was found, which is, in fact, an algorithm for a sequential step-by-step specific quantitative calculation using simple analytical formulas of all the necessary parameters for specifying the LDF with improved smoothness, as a function of a total of about 40 input parameters.

To be able to describe the complex nonlinear physical process of LPR, the model used a number of simplifying approximations based on experimental observations (for example, the approximation of the cylindrical shape of the filament). The so-called “semi-empirical approach” was also used, in which for a number of parameters their experimental values are used instead of the labor-intensive, cumbersome and unreliable calculation of these parameters (these include the length of the filament, its absorption capacity and energy transformation coefficients. In addition, the idea was used about the possibility of creating conditions (with a certain choice of irradiation parameters) for highly efficient conversion of laser pulse energy into heat release, localized within the space between adjacent filaments, which in turn is important for the above-mentioned dominance of the thermal mechanism over the other two alternatives.

4. A quantitatively found set of 4 radiation parameters from the indicated system of equations: the duration τ of the laser pulse and its energy E ₁ in the material, the pulse repetition rate f and the filament pitch in the material s ₁ , as well as the choice of material with suitable parameters completely determine the laser processing mode , preferred for obtaining a cut with improved smoothness. Three more practically important irradiation parameters - the speed of relative movement of the beam and the material and, the average power of the beam in the material P and the productivity of the LPR process Ω are determined through the indicated parameters s ₁ , f and E ₁ by the well-known expressions u=s ₁ f, P=E ₁ f and Q=2s ₁ H/E ₁ . The control parameters on which the resulting solutions depend in the form of sets (E ₁ , τ, f, s ₁ ) are, as the model shows, the volumetric energy density w of pumping the filament, its radius r _f and length H, which, in turn, may vary depending on focusing conditions, pulse energy, radiation wavelength, material thickness and its physicochemical properties.

5. Comparison of the proposed strategy and model for quantitatively finding the separation mode with improved smoothness with known experiments for sapphire, tempered and non-tempered glass for all specified parameters E ₁ , τ, f, s ₁ simultaneously, performed for both thin and thick plates - from very small thicknesses, approximately 50 μm, to large thicknesses, approximately 10 mm, showed good quantitative agreement.

6. After such successful testing, the solutions (E ₁ , τ, f, s ₁ ) found in the form of simple analytical expressions were further optimized by varying the specified control parameters w, r _f and H influencing them. As a result, a number of new LPR modes were found , providing in addition to improved smoothness the other positive results listed above - high energy efficiency and productivity of the LPR process Ω, and/or high (including record high) LPR speed u, and/or the possibility of LPR with a laser beam of very low average power P ( from one to several hundred milliwatts) obtaining, however, a considerable separation rate acceptable for practical applications.

The disadvantage of this work is that the analysis of the conditions for obtaining smooth separation was performed in detail for the SFOI mode. However, in practice, another mode is more widely used, when filament creation by a pulse train (PFTI) is used, and there is no overlap of filaments along the radii. This irradiation mode has the advantage that, due to the large number of pulses in the train, it makes it possible to provide significantly greater energy for creating a filament, which, in combination with the above methods for creating long filaments, makes it possible to optically pump a much longer (compared to the mentioned SFOI mode) filament , intermittent or continuous, until sufficient to separate the volumetric energy density. This difference between SFTSI and SFOI is important for cutting thick materials, for example, 7-10 mm thick or more. In this case, the SFCI mode is characterized not by four (as in the case of SFOI), but, as mentioned above, by a much larger number of radiation parameters, which include, for example, such new parameters as the energy E _burst of a pulse train in the material, the energy E _0i of individual pulses train (i=1,2,… N _p , where N _p is the number of pulses in the train), repetition rate f _burst of trains, repetition pitch s ₁ of filaments in the material, duration τ _burst of the train as a whole, time interval Δt between pulses in the train and their number N _p in the train. One of the ideas of the method proposed here is that a larger number of radiation parameters when using the SFCI mode allows one to obtain a greater number of degrees of freedom in controlling the LPR process and, due to this, may also improve the smoothness of the separation. Looking ahead, we note that, as will be shown below, the SFOI mode expands the class of materials for which it is possible to obtain separation with improved smoothness - these include not only tempered glass, as in the case of SFOI, but also non-tempered glass, as well as other materials.

There are also several known laser devices with variable irradiation parameters in order to select them to improve certain processing results. In this case, the closest device to the device proposed in this patent is the laser source "Monaco SmartCleave 1035-80-60" (www.coherent,com) offered by Coherent, which has a pulse energy of 80 μJ, a repetition rate of more than 188 kHz and a pulse duration of less than 350 fs to 10 ps. As can be judged from a very brief description [Industrial Laser Solutions, March-April 2018, www.industrial-lasers.com. and G. Oulundsen, J. van Nunen, and M. Laha. Industrial Laser Solutions, pp. 21-23, July/August 2019] the specified laser with a pulse duration of 350 fs and an average power of 40 W by creating filaments makes it possible to obtain separation of a layered system from a polyimide film with a thickness of 20 μm on glass with a thickness of 500 μm with a roughness of the side walls of the separation <0.35 μm. The type of glass, the speed of beam movement, the repetition rate of the trains and the pitch of the filaments, as well as the physical basis of the process and its other details are not indicated in the company’s message. The disadvantages of the described result, judging by the roughness parameters indicated in the example given and micrographs of the side walls of the cut, are their relatively low smoothness (>0.1 µm). It also remains unknown how irradiation parameters are selected to improve certain technical processing results. In addition, from the point of view of the method we propose here, other disadvantages include the fact that this laser operates only at one radiation wavelength (1.035 μm), the number of pulses in a train (4 pulses/train) is not enough to obtain cutting with improved smoothness of the display glass and sapphire, the average laser power (60 W) is insufficient to cut sapphire with a high repetition rate, as well as glasses with a thickness of more than 1 mm.

The fiber laser source "Antaus (Avesta) 10W-2μ/5M" from Avesta-Project LLC, Troitsk, Russian Federation, www.avesta.ru is also known. also having variable irradiation parameters. Here, the disadvantages include the fact that the method for selecting irradiation parameters to improve certain processing results (in the case we are discussing - LFR) is unknown, and data on the smoothness of the resulting separation walls is not reported. In addition, from the point of view of the proposed method, this laser has an extremely limited wavelength tuning (1.03-1.05 μm). Also, the average laser power (about 10 W), the energy of a pulse train (up to 12 μJ) and the energy of an individual train pulse (up to 2 μJ) are small and insufficient for high-speed cutting of sapphire, as well as glasses with a thickness of more than 1 mm.

SUMMARY OF THE INVENTION

The technical results of the claimed invention are:

1) Improved smoothness of the resulting side walls of separation, increased energy efficiency of LPR for a wide variety of materials;

2) High speed of LPR, or the possibility of performing LPR with a laser beam of very low average laser power (from fractions of a W) with obtaining a considerable separation speed acceptable for applications when using the mode of creating each filament in a pulse train (SFCI mode);

3) Devices that implement the specified process improvement, for materials with respectively small (50-750 microns) and large (about 7-10 mm) thicknesses, as well as for materials with surface curvature.

These technical results are achieved by the fact that the method proposed here discloses a sequence of actions for quantitatively finding 14 irradiation parameters that provide the specified technical results for LFR in the SFC mode. In this case, the principle of operation of the mentioned devices is based on adjusting the irradiation parameters in them according to the proposed method. The quantitative determination of the parameters is based on solving a system of 30 equations and inequalities that connects the desired irradiation parameters with a mathematical description of the set of numerous physical conditions necessary to obtain separation with improved smoothness. These conditions are described in detail below in the section “Justification of the conditions for achieving technical results.”

The difference between this method and the above-mentioned prototype [V.N. Tokarev and I.V. Melnikov, Appl. Sci. 11, 1732 (2021)] is that in this method, for the purpose of greater flexibility of the LPR process, the SFCI mode, which is widely used in practice, is used, but not the SFOI mode, as was the case in the specified prototype. This mode (SFCI) is characterized by a much larger number of radiation parameters (see Fig. 7), which requires the use of other methods for improving the LPR process. In addition, this mode creates the possibility of expanding the class of materials for which it is possible to obtain separation with improved smoothness - these are not only tempered glasses, as in the case of SFOI, but also non-tempered glasses, as well as other materials. Also, the SFOI mode creates the possibility of cutting much thicker materials than in the SFOI mode (for example, a thickness of 7-10 mm or more instead of thicknesses less than 1 mm for SFOI).

To achieve the specified technical results, a variety of amorphous or crystalline optically transparent materials (including hard or superhard materials, the cutting of which by traditional mechanical methods is extremely slow and labor-intensive) can be used as materials subjected to separation by this method - chemically tempered glass, display glass, sapphire, automotive glass, high and low pressure research chamber windows, planar light guides, transparent beakers and hollow cylinders, art objects, and materials such as diamond, glass-ceramics, ceramics, silicon carbide (SiC), gallium nitride (GaN), selenide zinc (ZnSe), zinc sulfide (ZnS), sodium chloride (KCl), potassium bromide (KBr), calcium fluoride (CaF ₂ ), barium fluoride (BaF ₂ ), magnesium fluoride (MgF ₂ ), lithium fluoride (LiF).

In this case, to achieve the specified technical results, pulse-periodic laser devices can be used, capable of generating trains of femtosecond or picosecond pulses closely spaced in time, with a radiation wavelength within the transparency region of the material, for example, for quartz glass in the range of 0.2-2.3 μm, preferably in the range of 0.5-1.1 microns, in order to obtain certain specified technical results, having the technical ability to independently adjust the following parameters characteristic of the pulse train irradiation mode: energy E _burst of a pulse train, energy E ₀ of individual pulses of a train, repetition rate of trains f _burst , step of repetition s ₁ of filaments in the material, duration τ _burst of the train as a whole, time interval of repetition of pulses in the train Δt, duration τ of an individual pulse of the train, number of pulses N _p in the train, speed and relative movement of the laser beam and material, average power of laser radiation in material P, as well as the wavelength of laser radiation λ, radius r _f and length H of the filament, in order to realize one or another of their coordination with each other depending on a particular material of one thickness or another according to the proposed method. Specific examples of using the method for adjusting irradiation parameters are described below in the section “Examples of the invention” for LPR of chemically tempered Corning Gorilla Glass of small (50-750 μm) and large (7-10 mm) thickness (see Table 3), and also for thin plates of display glass Eagle XG@Display Glass and sapphire (Table 4), when exposed to laser radiation with a wavelength of 0.52 µm or 1.04 µm. At the same time, specific values of all irradiation parameters necessary to set the LPR are indicated.

DESCRIPTION OF DRAWINGS

Fig. 1-6 are drawings illustrating the prior art (see section “BACKGROUND OF THE ART”).

Fig. 7 explains the designations of the parameters used in the description of the method and related to the individual filament 10 created by the pulse train. The filament is simplified in the model as a cylinder of radius r _f at the level 1/e in the approximation of a Gaussian distribution of the OPE w of the filament along the radius, but with a uniform distribution of w along the length H of this cylinder. E _burst - energy of a pulse train in the material, E ₀ - average energy of one pulse from a train in the material, E _p - filament plasma energy, λ - wavelength of laser radiation, time parameters of the pulse train τ, Δt, τ _burst , N _p , f _burst are explained in Fig. 4b. Irradiation schemes are possible when the material 5 is moved under the laser beam 4 using a three-coordinate xyz stage, and/or when the laser beam focusing system 3 is moved using a similar three-coordinate xyz stage.

Fig. 8 shows for the SFOI mode the sequence of decay in time of the laser pulse energy in the material E ₁ into 8 components with LPR of a transparent material: E _p - pumping energy of the filament plasma, E _{S + T} - energy of losses due to scattering and passage of the beam through the material, E' _p - filament plasma energy minus energy loss E _dis due to dissociation, E _tw - energy carried away from the filament by a thermal wave, E _sw - energy carried away by a shock wave, Q - heat released in the material, E _trad - filament energy loss due to its thermal radiation in the band of transparency of the cold material around it. The characteristic time scales t _E , t _P1 , t _P2 and t _T1 are defined in the “Notation List”. The case shown is t _E <t _P1 , t _P2 and t _T1 . A similar decay scheme is used for the SFCI mode.

Fig. 9 shows two energy flows due to thermal conductivity (Φ ₂ ) and thermal radiation (Φ ₂ ) that cause the flow shown in FIG. 8 decay of energy E _tw into components Q (due to Ф ₁ ) and E _trad (due to Ф ₂ ). For the exponential radius at which the comparison of Ф ₁ and Ф ₂ is performed, r=r _1/2 from the filament axis is selected, i.e. comparison of Ф ₁ (r=r _1/2 ) and Ф ₂ (r=r _1/2 ). At this radius, heating is halved compared to heating on the axis ΔT ₀ = (T ₀ -T _i ) and amounts to 0.5ΔT ₀ .

Fig. 10 shows the effect of the appearance in the plane 16 (π) of the cross section of a set of filaments of an elongated continuous oval region 21 inside the isotherm 22 T=T _strain (T _strain is the glass transition point of the material, above which, i.e. in region 21, the volume of the material increases with temperature , as is known, increases sharply). The influence of the pulse train repetition frequency f _burst on the shape and dimensions of this thermal wedge is also shown. In region 21, the material is heated to temperatures not less than T _strain . This region, like a wedge pushing the material apart, follows the movement of the beam relative to the material in direction 8 with a lag of one or several filament steps s ₁ . 10 indicates the locations of filaments with a following step s ₁ created by a beam moving along the x axis. L _hot denotes the length of the continuous region 21 in the direction of movement of the beam relative to the material within the isotherm 22 T= T _strain . Arrow 20 shows the arrival of the next pulse train and the creation of the last filament in time. 23 - a trace of material with a modification not lower than critical for obtaining separation, remaining after passing area 21 through the material. 24 - tensile stresses frozen in the material, remaining when the track 23 of the modified material is cooled and causing mechanical weakening of the material along it, as well as contributing to the mechanical splitting of the material along this track used after irradiation. Fig. 10a and Fig. 10b correspond to the use of different train repetition frequencies - accordingly (here f ₁ is the lower limit of the high-frequency range of train repetition frequencies f _burst >/f ₁ ). As can be seen, with increasing f _burst, the specified oval region 21 acquires a more elongated shape. For comparison, in the low-frequency range, f _burst ≤f ₂ , the specified oval region 21 does not appear (the dependence of the frequency limits f ₁ and f ₂ on the filament pitch, see below in the text). The highly elongated shape of such a singular area of influence in the material can, as is known from the literature, be a significant concentrator and amplifier of tensile stresses at the front and rear tapering tips of this area. Therefore, in this case, such a thermal wedge can cause, as shown in FIG. 10b, microcracks 25 in solid material near its front tip, predominantly in the direction of beam movement, or near this direction. As the repetition rate of trains increases from f _burst ≈f ₁ (Fig. 10a) to f _burst ≈3f ₁ (Fig. 10b) and higher f _bursts , this phenomenon can become dangerous due to the risk of microcracks at the front tip spreading to more numerous and more extended forward cracks 26, which can significantly deviate from the direction 8 of the beam movement and thereby lead to loss of controllability of the splitting direction. To avoid this phenomenon, it is preferable to limit the frequencies f _burst near f ₁ , i.e. for example, as f _burst ≈(1-3)f ₁ , when the aspect ratio of a given oval region 21, and with it the increase in tensile stresses in front of its anterior tip, are not excessively large.

Fig. 11 explains the limitation on the value of the local radii of curvature R ₁ and R ₂ of the curvilinear cutting path 27 in the plane 16 (π) of the cross section of the filaments. Several positions are shown along the path 27 mentioned in FIG. 10 oval area 21 critical for heat separation along this trajectory. L _hot is the length of this area. As follows from the figure, when the constraint R ₁ , R ₂ >>L _hot is met, the oval area 21 at each of its positions on the curved path 27, automatically, without any additional tricks, in contrast to the patent described in the “State of the Art” [F . Hendriks and VV Matylitsky. Processing of material using non-circular laser beams. Patent WO 2016/005455 A1], i.e. without forming an elongated each individual laser spot, follows the direction of the tangent to the specified curvilinear trajectory 27, thereby ensuring cracking directed along the tangent. The mechanism of origin of the oval heating region 21 is explained in FIG. 10.

Fig. 12 shows the sequence of quantitative determination of irradiation parameters preferable for obtaining LPR with improved smoothness of separation when using the SFCI mode. 5 consecutive stages (1-5) of executing this algorithm are indicated to find 12 unknown parameters of the FCI mode, the energy of the train as a whole E _burst , the filament repetition step s ₁ , the number of pulses in the train N _p , the average energy of a single pulse in the train E ₀ , the repetition frequency pulse trains f _burst , duration of an individual pulse in a train τ, duration of pulse trains as a whole Tburst, time interval between pulses in a train Δt, average laser power P in the material, speed u of the relative movement of the laser beam and material, energy efficiency Ω of the LPR process and volume density filament energy w. Together with 2 input parameters, radius r _f and filament length H, the indicated total of 14 parameters completely define the LPR process in the SFCI mode. The values of the remaining parameters in this diagram are indicated in the “List of Designations” in the text. The number of indicated stages and the boundaries between them in this scheme are quite arbitrary and are given only to give the vast array of input, freely selectable and calculated parameters a structure convenient for analysis.

Fig. 13 shows a diagram of a separation device using the proposed method for non-planar transparent and translucent materials in the form of rotation figures - a cylindrical tube, fiber, spheroid, ellipsoid, hyperboloid and other reliefs. Unlike the elements and modules mentioned above for the prior art in FIG. 1, 2 and 5, this device has the technical ability to rotate 31 of the specified non-flat part 5 relative to the laser beam 4 around its axis of symmetry 30 through the use of a module 29 for fastening and rotating the specified part with adjustable speed u, length H and radius r _f of the filament, the energy of the train in the material E _burst , the pitch of the filaments s ₁ , the number of pulses in the train N _p , the average energy of a single pulse in the train E ₀ , the repetition rate of the pulse trains τ _burst , the duration of an individual pulse in the train τ, the duration of the pulse trains as a whole Uurst and time interval between pulses in a train Δt, which are adjusted to the material parameters and are consistent with each other in accordance with the method proposed here. These parameters are calculated and set in the device “manually” and/or using a numerical program control unit 28 for various modules of the device, which include those mentioned in FIG. 1 and Fig. 2 laser source 1, system 3 for beam formation and focusing, mounting system 6 for material 5 under beam 4, which allows you to adjust the tilt of the sample 5 and rotate it around the vertical z-axis, three-coordinate xyz stage 7 for adjusting the focus position along the z coordinate in material 5 , as well as a module 29 for fastening and rotating the part subjected to laser processing at a specified speed.

When choosing irradiation parameters according to the proposed method for a wide variety of materials, technical results are achieved such as improved smoothness of the resulting side walls of separation, increased energy efficiency of LPR, high speed of LPR, or the ability to perform LPR with a laser beam of very low average laser power (from fractions of W) to obtain , however, the separation speed is acceptable for applications. In addition, the method proposes the principle of operation of devices for separating transparent and translucent materials with respectively small (50-750 μm) and large (about 7-10 mm) thicknesses, as well as materials with surface curvature.

IMPLEMENTATION OF THE INVENTION

The invention is carried out as follows. The sequence described below for the quantitative determination of irradiation parameters during LPR, which ensures the achievement of such technical results for a wide variety of materials as improved smoothness of the resulting side walls of separation, increased energy efficiency of LPR, high speed of LPR, or the ability to perform LPR with a laser beam of very low average laser power ( from fractions of W) obtaining, nevertheless, a considerable separation rate acceptable for applications.

The specified sequence of quantitative determination of irradiation parameters can be carried out as follows. The input (or input) parameters for performing the calculation are the radius r _f and the filament length H, which are set based on the experimental needs of performing LPR with improved smoothness for a particular material of a particular thickness. In this case, to carry out the actual process, the LPR r _f and H can be varied by the operator using a focusing system and selecting a particular wavelength of laser radiation using methods well known to specialists in this field. The parameters to be quantitatively determined are the volumetric energy density w of the filament, the energy of the pulse train in the material E _burst , the filament pitch in the material s ₁ , the number of pulses in the train N _p , the average energy of individual pulses in the train E ₀ , the repetition rate of the trains f _burst , energy efficiency of the LPR process Ω, average power of pulse-periodic laser radiation in the material P, speed of relative movement of the laser beam and material u, duration of the train τ _burst , time interval between adjacent pulses in the train Δt and duration of an individual pulse in the train τ. The indicated total of 14 parameters uniquely define the LPR process.

From the variety of possible solutions, it is preferable to use those for which the filament pitch s ₁ has a “small” value (i.e. in the range s ₁ ≈0.5-K3.5 μm instead of s ₁ ≈4÷7 μm known in the literature), since as s ₁ decreases, the roughness of the side walls also tends to decrease. For this, small radii r _f of the filament are used, which is achieved by using a larger numerical aperture of the focusing system, and/or a shorter wavelength of laser radiation (for example, λ in the range of 0.5-0.55 μm instead of 1-1.1 μm), and/or using OPE in limited range w≈(1.8÷2.5)w _dis .

The irradiation parameters found in this way are used for the practical implementation of the LPR process of a particular transparent material. The 2 devices proposed in this method for separating different materials with respectively small (50-750 microns) and large (about 7-10 mm) thicknesses are most suitable for this. A distinctive feature of these devices is that they have the technical ability to independently configure the above 14 parameters characteristic of the SFCI mode. In each device, the adjustment is carried out in such a way that it ensures the implementation of the optimal process parameters quantitatively found by this method and their coordination with each other to obtain the above-mentioned improvements in the LPR process for a particular material of a particular thickness. In more detail, all irradiation parameters and their specific coordination with each other for various materials are indicated for both devices below in Table. 3 and Table. 4 in the section “Examples of the invention”.

In practice, LPR with the adjustment of irradiation parameters proposed by this method is performed using two stages known from the prior art (see Figs. 1 and 2): - At the first, preparatory stage, the material plate is irradiated with a beam of pulse-periodic radiation from a femtosecond (or picosecond) laser at movement of the beam and material relative to each other and create one or several extended thread-like objects heated to a high temperature (so-called filaments) with a length from several tens to several thousand microns, non-overlapping with each other along their radii, using the creation of each filament by a train (group) of pulses , closely located in time, by using the nonlinear optical phenomenon of self-focusing, or through the use of a Bessel beam formed by conical lenses, or through any other methods of creating a focusing region of extended length (from several tens of microns to several thousand microns) in the volume of the material for a femtosecond or picosecond laser beam emitting at a radiation wavelength at which a given material is transparent at low laser intensity in an unfocused beam, one or more sets of filaments are created in the thickness of the material, where these sets differ from each other by their different positions in depth in material. What is important and new here is that to create filaments, the 14 irradiation parameters specified by the method proposed here are used: r _f , H, w, E _burst , E ₀ , N _p , f _burst , s ₁ , T _burst , Δt, τ, u , P and Ω;

- At the second, final stage, after the above-mentioned irradiation, mechanical splitting of the plate is performed (i.e., its division) along the surface of the arrangement of sets of extended plasma filaments created by the laser beam, which can occur spontaneously, or by applying additional mechanical impact on the said processed plate in the form of tensile mechanical stress in the zone of the material in which the above sets of filaments are located.

Adjustment of the total width H of sets of filaments in a device for separating plates with small (50-750 μm) thicknesses is carried out by using the known nonlinear process of spontaneous self-focusing in the material of a high-intensity laser beam, or by using laser beam focusing through the use of special optical elements, such as intentionally astigmatic focusing optics, axicons, etc. If it is necessary to increase H to approximately 700-750 μm, the well-known methods described above in the “State of the Art” are used - multifocusing or several repeated passes of the laser beam along the same track, or some other methods. At the same time, in a device for separating plates with large thicknesses (about 7-10 mm), which accordingly requires the creation of filaments of much greater length (several millimeters), for this purpose, laser beam focusing is used using conical lenses (axics) 16 and Gauss -Bessel beams.

Both of these devices, when using the specified method of quantitative determination of irradiation parameters, can include obtaining both rectilinear and curved cuts, or closed cuts, depending on the specified trajectory of the laser beam relative to the material, provided that the minimum radius of curvature R _c is not less than which is an order of magnitude greater than the length L _hot of the oval region 21, critical for the separation of the heating material, which occurs at high frequencies of repetition of the trains, i.e. R _c >>L _hot - see more details below in the section “Justification of the conditions for achieving technical results”, as well as Fig. eleven.

These devices, when using the proposed method for quantitatively determining irradiation parameters, may also include the technical ability to cut a part having a non-flat surface in the form of a figure of revolution by rotating this part relative to the laser beam around its axis of symmetry (see Fig. 13). In this case, the rotation speed is chosen so that the speed of relative movement of both the laser beam and the material coincides with its value according to the algorithm proposed in this patent for calculating parameters for a particular material of a particular thickness.

In addition, a device for thin materials, when using the specified method for quantitative determination of irradiation parameters, may also include the technical ability to separate extended flexible transparent materials when they move under a laser beam “from reel to reel” (“roll-to-roll manufacturing”).

LPR using the proposed method for quantitative selection of parameters can be performed using a multilayer composition, which consists of layers of the same transparent material located on top of each other, or includes layers of various transparent materials, solid and/or liquid, these layers can have different thicknesses, while the layer of material to be separated may be the first in the specified composition, i.e. facing the laser beam, or the last layer, i.e. on the back side of the specified multilayer composition, or enclosed between other layers.

The position of the filaments created in the thickness of the material for LPR using the proposed method for selecting parameters can be adjusted entirely within the volume of the material, i.e. without filaments coming out either on the front or back surfaces of the processed sample. Due to this, there is no release of material into the surrounding space in the form of vapors, drops or solid fragments, thereby realizing environmentally friendly non-ablative separation of material with zero cutting width.

If the use of the parameters proposed by this method, as well as the above practical measures, is still insufficient to obtain the desired level of smoothness of the side walls of the separation, then to increase the mechanical tensile strength of the material on the front (facing the incident laser beam) and/or rear surface material, and thus, as follows from the model, to artificially reduce the radius of the zone of unwanted chaotic or multidirectional cracking around each filament due to the action of the thermal deformation mechanism of forming an impact zone around each filament, they use the application of an additional auxiliary layer of transparent material with high rigidity (Young's modulus) and high tensile strength. For example, a transparent graphene film or a film made of a high-strength transparent polymer is used as such a material. The position of the filament in the thickness of the material plate is adjusted so that it does not extend beyond the processed sample into the area where the specified outer auxiliary layer is located.

Below is a physical justification of the conditions that ensure the achievement of the specified technical results.

1. LPR is a complex process that depends on many parameters, especially in the SFCI mode, when more than 80 parameters are used to describe the LPR process according to the “List of Designations” given in the text, and to set the irradiation mode, in which each filament is created by a pulse train, it is necessary to specify at least 12 of the above mentioned parameters - w, E _burst , E ₀ , N _p , f _burst , s ₁ , τ _burst , Δt, τ, u, P, Ω, as well as 2 more control input parameters - r _f and N Searching by trial and error in a multidimensional parameter space for a region that provides one or another desired positive result (improved smoothness, high performance, or the ability to use extremely low average power for LPR) is therefore extremely complex and time-consuming, and does not guarantee finding all possible, in including the best solutions to the problem and does not allow us to take a broad look at it beyond the parameters of the specific laser at our disposal, which are not always suitable and sufficient for solving the problem. In this regard, for such a search, it is important to create and use a model of the LPR process, which will be a kind of guiding thread in the complex multidimensional space of parameters for finding in it the area of parameters that are optimal for obtaining a particular result. Such an original model for the SFCI mode considered here is proposed and used in this method.

To be able to describe the complex nonlinear physical process of LPR, this model uses a number of simplifying approximations based on experimental observations - for example, the approximation of the cylindrical shape of the filament, as well as the so-called “semi-empirical approach”, in which for a number of parameters their experimental values are used instead of calculating these parameters, which, if possible at all, is time-consuming, cumbersome and unreliable in accuracy. These parameters include the length of the filament, its absorption capacity and the coefficients of transformation of laser energy into filament plasma energy, into a thermal wave, into a shock wave and heat release.

To understand the mechanism of smooth separation, the model is implemented previously formulated in the closest analogue [V.N. Tokarev and I.V. Melnikov, Appl. Sci. 11, 1732 (2021)] concept of various competing mechanisms of laser-induced modification and weakening of the material around each formed filament - thermal, thermal deformation and shock wave. With this approach, obtaining a separation with improved smoothness is considered as a result of the dominance (under certain conditions) of the thermal modification mechanism over the other two competing with it - thermal deformation and shock wave.

In addition, they use the idea of the possibility of creating conditions (with a certain choice of irradiation parameters) for highly efficient conversion of laser pulse energy into heat release localized within the space between adjacent filaments, which, in turn, is important for the above-mentioned dominance of the thermal mechanism, as well as for obtaining high energy efficiency of LFR.

Of key importance for understanding the mechanisms of the processes that make up the LPR is the sequence revealed in the model of the time decay of the laser pulse energy in the material into 8 components (see Fig. 8 for the SFOI mode). “Switching on” or “switching off” in time certain energy components and their effects on the material is determined by the above-mentioned characteristic time scales of this decay t _E , t _P1 , t _P2 , t _T1 , t _T2 , _tr , etc. (decoding of values For these parameters, see below when discussing formulas (1-30)). This systematic approach in this case of a cylindrical filament and radial energy transfer allowed, based on the energy balance and decay pattern in Fig. 8 find the following relationships for the components of the energy decay used in this method, the energy carried away by the shock wave E _sw , the energy carried away by the thermal wave E _tw , and the heat released in the material Q:

Here denotes the effective volume of the filament, A _PH is the coefficient of conversion of thermal energy from the filament plasma E _tw into heat Q. Under the conditions of the optimal choice of w, i.e. when the following condition (11) w≤w ₁ is met, the value A _PH ≈0.9 or more is used for calculations using the specified formulas.

2. To clarify the physical conditions for achieving better smoothness of separation of solid transparent materials, it is proposed to use the previously formulated in the prototype [V.N. Tokarev and I.V. Melnikov, Appl. Sci. 11, 1732 (2021)] the idea of creating conditions for the dominance of the thermal mechanism of material modification over the alternative shock wave and thermal deformation mechanisms. However, to implement such dominance for the considered SFOI mode, it is proposed to use new methods and other parameters than for the SFOI mode considered in the specified prototype.

2.1 The condition for reducing the influence of the shock wave mechanism in comparison with the thermal mechanism for the SFCI mode considered here is proposed to be fulfilled by appropriate selection of such new ones, not previously considered in the prototype [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)] radiation parameters inherent in the SFCI mode, such as the duration of the train as a whole τ _burst , the time interval Δt between pulses in the train, their number N _P in the train, as well as the repetition rate of the trains f _burst . For this purpose, for the duration of the train as a whole τ _burst , an appropriate characteristic time scale is chosen - less than the so-called “heat retention time” in the filament t _T1 , estimated as

those. The fulfillment of this inequality physically means that there are practically no thermal conductivity losses from the filament during the action of the train τ _burst . This leads to the effective summation of its heating by successive pulses of the train, thereby ensuring effective (without heat loss beyond the radius of the filament) heating of the filament by the train as a whole. Due to this, with the same OPE w for the SFCI mode as in the SFOI mode, the radius R _T of the modification zone due to the thermal mechanism remains the same.

In addition, for a moving laser beam it is also important to choose the train duration τ _burst much less than the time it takes the beam to travel through the material at a distance on the order of the filament radius, which can therefore also be called the beam position holding time:

Where

- speed of relative movement of the laser beam and the surface of the material, i.e. τ _burst <t _r . The fulfillment of this condition ensures the localization of the investment of the pulse energy of each train into approximately the same region of space in the form of a cylinder with a filament radius r _f , since when the beam moves at a speed relative to the material being processed, its displacement during the duration of the train τ _burst is small compared to r _f . Thus, τ _burst is chosen based on the final condition obtained by combining the indicated inequalities:

Simultaneously with constraint (4), the interval Δt between pulses in the train is chosen to be greater than the time of inertial pressure retention in the filament t _P1 and the time of inertial pressure retention in the space between adjacent filaments t _P2 , which are estimated as

those.

Also, with the specified choice of τ _burst and Δt according to (4) and (6), the obvious from Fig. 4b ratio

where N _p is the number of pulses in the train.

For a characteristic value of the speed of sound in a material c _s =6⋅10 ⁵ cm/s [S. Mauclair, A. Mermillod-Blondin, K. Mishchik, J. Bonse, A. Rosenfeld, J. Colombier and R. Stoian, High Power Las. Sci. Eng. 4, E46 (2016)], used in this method of submicron filament radius of the order r _f =0.25÷0.5 µm and, for example, filament step s ₁ ≈2÷6 µm, estimates of the indicated retention times are t _P1 =0.1÷0.2 ns and t _P2 =0.3÷1 ns.

From a physical point of view, limitation (6) means that, in contrast to the addition of heating amplitudes from individual train pulses, which occurs when condition (4) is met, for shock waves the addition and accumulation of their amplitudes induced by individual train pulses does not occur (at least , their transitional, quickly disappearing components), both within the radius r _f of the filament, and within the gap s ₁ between neighboring filaments, where the zone of influence of the filament on the surrounding material is formed. Therefore, the radius R _sw of modification of the material around the filament due to the shock wave mechanism from the train as a whole under such conditions becomes approximately equal to the corresponding modification radius from just one of the pulses of the train: R _sw ≈R _sw1 . But the energy of one pulse is many times, approximately one times less than the energy of the train as a whole. Accordingly, the OPE of a filament created by one pulse is N _p times less than the OPE of a filament w created by a train, i.e. is approximately w/N _p ). Therefore, for the SFCI mode with the same filament OPE as for the SFPI mode, the energy of the shock wave, taking into account the above expression for E _sw for one train pulse, takes the form: in this case, the corresponding modification radius during radial energy transfer into the material from the filament decreases from (1/N _p ) ^1/2 and has the form: R _sw1 ∞ (here σс _is the limit of mechanical strength of the material for shock wave exposure). At the same time, the modification radius R _T due to the thermal mechanism from the train as a whole, when constraint (4) is satisfied, does not depend on N _p and, as in the SFOI mode, according to those obtained earlier in the prototype [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)] estimates taking into account the above expression for Q and also with radial energy transfer from the filament to the surrounding material is:

Comparison of the obtained estimates for R _sw ≈R _sw1 and R _T for the SFCI mode shows that the use of a sufficiently large number of pulses in the train N _p makes it possible to reduce R _sw to such a level that the ratio R _sw /R _T becomes <1 (or even <<1), which corresponds to the dominance of the thermal mechanism over the shock wave and, thus, is favorable for obtaining a smooth separation. Moreover, by choosing a sufficiently large number of pulses in the train N _p, such dominance (and, accordingly, separation with improved smoothness) becomes possible not only for tempered glasses, as was shown earlier for the SFOI mode in the prototype [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)], but in the considered SFCI mode also for non-tempered materials - for example, display glasses, quartz glass and sapphire.

The number of pulses in the train N _p , which ensures the fulfillment of the corresponding condition R _sw /R _T <1, as follows from the above expressions for R _sw , and R _T , must not be lower than a certain minimum threshold value A _p0 :

Square brackets [] in (8) denote the integer part of the number in brackets, the coefficient ϕ=R _T /R _sw shows how many times it is desirable to reduce R _sw in relation to R _T by using the number of pulses N _p0 (for quantitative estimates, ( is used below ϕ=1.3-1.4), η is the coefficient of thermal conductive cooling of the material in the space between adjacent filaments from any pulse train by the time the maximum heating of this interval is reached by the next in time and spatially adjacent pulse train (for an explanation of the physical meaning of η, see Fig. 5 and in the caption to it in the prototype [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)]).

As shown below in Table. 3 and 4 specific examples of calculation of radiation parameters, estimates according to the obtained expressions (8, 9) are given for Corning Eagle XG™ display glass N _p0 = 5-7, and for sapphire, which is a crystalline material, N _p0 = 4-12 depending on OPE filament used. On the other hand, for chemically tempered glass (Corning Gorilla Glass 5) N _p0 has a smaller value: N _p0 ≈2-3.

Formula (8) for N _p0 in a transparent form shows that in the case of materials with a large value of N _p0 , it is possible to reduce this parameter (and thereby prevent N _p from being too large), for which the following factors are favorable:

- Maximization of the coefficient A _PH , which corresponds to minimizing energy losses due to thermal radiation of the filament, as a black body, in the region of transparency of the cold material surrounding the filament (see Fig. 9). Measures to eliminate filament energy losses due to thermal radiation will be indicated in more detail below;

- Maximization of the parameter η, which occurs in the “high-frequency” frequency range of repetition of trains f _burst ≥f ₁ , where η reaches maximum values in the range of 0.76÷1 (which corresponds to a significant accumulation of heat in the spaces between the filaments in this frequency range). For comparison, in the “low-frequency” range f _burst ≥≤f ₂ the parameter η is small - no more than 0.1, and the indicated heat accumulation in the spaces between the filaments is insignificant. The values of frequency limits f ₁ and f ₂ see below;

- Small coefficient K _sw (i.e. K _sw <<1). This leads to a corresponding decrease in the energy component E _sw carried away from the filament by the shock wave, which is responsible for the formation of the radius R _sw of the shock wave impact zone around the filament (see a more detailed explanation of the E _sw component in the caption to Fig. 8). Small values of K _sw (<<1) correspond to the inequality t _E >>t _P2 , i.e. materials with a sufficiently slow relaxation time t _E of the excitation of the filament plasma, in such materials the excitation of a shock wave is ineffective. For comparison, large K _sw (of the order of 0.5 or more) are typical for materials with rapid energy release, i.e. sufficiently small t _E : t _E <t _P2 . In this case, the excitation of the shock wave and its consideration are essential. In accordance with estimates of the time of inertial pressure retention t _P2 given above for the filament radius r _f =0.25÷0.5 µm and the filament pitch s ₁ ≈2÷6 µm, the above condition t _E >>t _P2 numerically corresponds to materials for which parameter t _E >>0.3-1 ns. Such a relatively long relaxation time t _E may be inherent in the material initially due to the presence of states with long-lived excitation in the structure of its electronic levels. It is known that long-lived excitation states can arise due to defects in the structure of the material and the formation of self-trapped excitons [S. Mauclair, A. Mermillod-Blondin, K. Mishchik, J. Bonse, A. Rosenfeld, J. Colombier and R. Stoian, High Power Las. Sci. Eng. 4, E46 (2016); P. Martin, S. Guizard, Ph. Daguzan, G. Petite, P. D'Oliveira, P. Meynadier and M. Perdrix, Phys. Rev. B 55, 5799 (1997)]. Therefore, it can be expected that, depending on the material in the SFC mode, long-lived states, even if they did not exist initially before irradiation, can develop directly during train irradiation, for example, due to the formation of numerous structural defects when the material in the filament is heated by successive pulses of the train to temperatures above the glass transition point or dissociation point, at which the structure of the material usually becomes disordered, promoting the formation of defects. In addition, structural defects and the long-lived states caused by them can also be created due to some other auxiliary irradiation source or instrument acting on the material in the zone of movement of the main laser beam through it before the passage of this beam.

2.2 To obtain a separation with improved smoothness, it is also necessary to reduce the undesirable effect of chaotic or multidirectional cracking from the filament due to another mechanism, thermal deformation. In this regard, we note the following: Firstly, as in previously discussed in [VN Tokarev and IV Melnikov. Appl. Sci. 11, 1732 (2021)] in the SFOI mode, to eliminate cracking from each filament in many directions, which is undesirable for smooth separation due to this mechanism, it is proposed to use materials with small α _T , Y, T _strain (for amorphous materials) or T _melt (for crystalline materials) materials), but with a greater limit of mechanical strength σ _c , which corresponds to the fulfillment of the condition on the material parameters The physical meaning of this condition is that in such materials, when locally heated in the zone of influence of the filament to the point T _strain (or T _melt ), thermally induced deformations turn out to be insufficient to destroy the material in the form of cracking. Such materials are, for example, tempered glass. However, for non-tempered glass and sapphire, this condition is not met, and to remove the harmful influence of this mechanism for such materials, a different solution to the problem is necessary.

Secondly, for materials other than tempered glass, in which the effect of chaotic or multidirectional cracking from the filament cannot be eliminated for this mechanism (which is the case for materials with a low limit of mechanical strength, which is characteristic, for example, for tensile stresses in mechanically fragile materials such as the above-mentioned non-tempered glasses, as well as sapphire), for the considered SFCI mode, it is proposed to replace chaotic or multidirectional cracking around each filament with highly directional cracking along the movement of the beam through the material, which is favorable for obtaining separation with improved smoothness. For this purpose, in the method proposed here, we use the frequency of repetition of bursts in the “high-frequency” range: f _burst ≥f ₁ (finding the value of the boundary f ₁ of this range and the physical meaning of the value f ₁ , see below). At such a sufficiently high repetition rate (usually from hundreds of kHz to several MHz), the time interval for the repetition of trains tr _rep =1/f _burst with which filaments are created turns out to be of the same order of magnitude or shorter than the time of characteristic cooling of the material in the space between adjacent filaments to temperature _Tmod . Due to this, when the condition also considered below is satisfied that the heat affected zones from neighboring filaments overlap with each other in the material, s ₁ /(2R _T )<1, several such heating zones adjacent in time to the creation of heating zones from different filaments merge with each other in the course of thermal conductivity spreading of these zones in space over time. Thus, even with a round laser spot of irradiation under such conditions in the volume of the material, by itself, as a result of heating by several filaments at once, a region of material 21 (see Fig. 10) is created, heated above the glass transition point T _strain , with an oval shape, elongated along the direction of velocity u, i.e. with the size of this area along the longer direction several times (3-5 or more) greater than the size along its short direction. With a further decrease in the specified ratio s ₁ /(2R _T ), i.e. With an increase in the degree of overlap of heating zones adjacent in time to creation from different filaments, this effect intensifies. This elongated continuous oval wedge-shaped region 21 occurs inside the T=T _strain isotherm 22 in the cross-sectional plane 16 (π) of the set of filaments, while inside the region 21 the material is heated to temperatures not less than T _strain . Let us recall that the T _strain point is characterized by the fact that when the material is heated to temperatures above this point, a significant (by an order of magnitude) increase in the coefficient of volumetric expansion of the material occurs. Therefore, in the specified region in which the temperature T≥T _strain , the material, due to its tendency to sharply expand at such temperatures, experiences significant mechanical compressive stress from the surrounding colder material outside this region. At the same time, with an elongated wedge-shaped shape, such a region of heated material tending to expand sharply occurs, as is known from the literature [AR Collins and GM O'Connor, Opt. Lett. 40 (20) (2015); CE biglis, SPIE Milestone Series, 137, 3-17 (1997)] concentration and amplification of tensile mechanical stresses outside this region immediately near its anterior and posterior tips. This creates directed cracking of the material on them, predominantly along the movement of the beam relative to the material. At the same time, mechanical stresses are weakened in other directions, which, as a consequence, leads to the absence of microcracks and, accordingly, the absence of their development in these other directions outside this heated area. Thus, under these conditions, although cracking of the material is not avoided, its highly directional nature along the beam movement (and not chaotic or multidirectional from each filament) is favorable for reducing the formation of cracks in other directions and obtaining the desired effect of reducing the roughness of the side walls of the separation, those. improving their smoothness. The specified thermal wedge and its two tips, splitting the material predominantly in front of the wedge in the direction of its movement along the entire length of the filament, move along the material following the laser beam, along the trajectory of the beam relative to the processed surface of the material in direction 8 with a lag from the beam position of one or several steps of following filaments s ₁ . 10 - locations of filaments with a following step s ₁ , created by a beam moving along the x axis. Arrow 20 shows the arrival of the next impulse and its creation of the latest (youngest) filament. 23 - a track of modified material remaining after passing through area 21 through the material. 24 - tensile stresses frozen in the material, remaining when the material is weakened along it, also contributing to the mechanical splitting of the material along this track used after irradiation, L _hot denotes the length of the continuous region 21 in the direction of movement of the beam relative to the material within the isotherm 22 T=T _strain .

Comparison Fig. 10a and Fig. 10b, corresponding to the use of different train repetition frequencies, f _burst ≈f ₁ and f _burst ≈3f ₁ (for the definition of parameter f ₁ , see below in the text), shows that with increasing f _burst , the specified wedge-shaped region 21 acquires a more elongated shape, which leads to to a corresponding increase in mechanical stress at the tip. Therefore, when in case (b) and at even higher frequencies f _burst , such a phenomenon can become dangerous due to too high amplification of stresses at this tip and, as a consequence, the propagation of too many microcracks 25 from it, which can already differ noticeably from the direction of beam motion . From these microcracks, larger cracks 26 can develop, which can deviate noticeably from the direction 8 of beam movement, due to which control over the direction of cracking only in the direction of beam movement can be lost. To avoid such an undesirable effect, it is preferable to use f _burst frequencies in a limited range around f ₁ , when the aspect ratio of this wedge-shaped region 21, as well as the increase in tensile stresses at its front tip, are not too large, i.e.

In the document cited above [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)] the specified restrictions (4,6,8,10) for the parameters τ _burst , Δt, N _p and f _burst characteristic of the SFCI mode have not been studied.

With the specified choice (10) of the train repetition frequency, not only rectilinear, but also curvilinear or self-closed cuts can be obtained, see Fig. 11. The characteristic radii of curvature R ₁ and R ₂ of the trajectory of the beam relative to the material in plane 16 (see Fig. 11) in practice are, as a rule, not less than about 500 μm. On the other hand, for the length L _hot of the mentioned oval region, which is f _burst depending on the magnitude of the repetition frequency of the trains, as follows from Fig. 10a and b, about (3-7)s ₁ , using specific values s ₁ = 1-11 µm, characteristic of this method according to calculations in Tables 3 and 4 below, we find L _hot = 3-77 µm. Therefore, with the indicated R ₁ , R ₂ ≥500 μm, the following relation is obviously satisfied:

R ₁ ,R ₂ >>L _hot .

When this condition is met, the oval region 21 is critical for the division of heat at each of its positions on the curvilinear trajectory of the beam relative to the material automatically, without any additional tricks, as was described in the document WO 2016/005455 A1, i.e. without forming an elongated each individual laser spot, follows the direction of the tangent to the specified curved path 27, thereby ensuring, as mentioned above, cracking directed each time along the tangent, see FIG. 11. The indicated inequality is thus a limitation on the magnitude of the radii of curvature of the trajectory. It can be seen that for its best performance, irradiation modes with small sizes of the oval region 21 are preferred, i.e. with a small length L _hot , which is achieved with a small filament pitch s ₁ - for example, on the order of 1-2 µm instead of 4-6 µm or more.

3. To obtain a separation with improved smoothness for the considered SFOI mode, a number of other effects are also used, which, on the one hand, are similar to those previously used to obtain improved smoothness in the SFOI mode in the document [V.N. Tokarev and I.V. Melnikov, Appl. Sci. 11, 1732 (2021)], but, on the other hand, they have significant differences specific to the SFCI regime considered here:

- When constraint (4) is satisfied on the duration of the train Xburst, which corresponds to heat retention within the radius of the filament during this time, the relative part of the filament plasma energy loss to thermal radiation becomes significant and even dominant in the “unfavorable window” of the OPE w: w ₁ <w<w ₂ . The limits w ₁ and w ₂ determine the boundaries of this “window”; they correspond to the filament plasma reaching certain temperature limits T ₁ and T ₂ , i.e. w ₁ =w(T ₁ ), w ₂ =w(T ₂ ) and are determined by the thermophysical and optical properties of the material. To obtain an energy-efficient LPR process and impart driving force and speed to it, it is important to eliminate unnecessary filament energy losses due to thermal radiation. To do this, the energy of not a single pulse, as previously in the SFOI mode, but a train of pulses E _burst in the material, is chosen such that the filament plasma is pumped to OPE w outside the specified “unfavorable window” of OPE, i.e. w≤w ₁ , or w≥w ₂ (for w ₁ <w ₂ ). However, in practice of LPR, of these two conditions it is advisable to use only one condition:

If we use another condition, w≥w ₂ , then at the stage of filament cooling and w decreasing in time, there is a possibility of w falling into the specified “unfavorable window” w ₁ <w<w ₂ , and, thus, the possibility of activating significant loss of filament energy due to thermal radiation in the spectral region of transparency of the material surrounding the filament, which is undesirable.

If the limits w ₁ and w ₂ are such that w ₁ ≥w ₂ , then this corresponds to the “closing” and disappearance of the specified “unfavorable window” of the OPE. Then the specified restriction (11) for w becomes meaningless, i.e. both w≤w ₁ and w≥w ₁ can be used.

The limits w ₁ and w ₂ depend, as the model shows, on the relaxation time t _E of the excitation energy of the filament to a state with an equilibrium temperature. The value of t _E can take values in a very wide range depending on the material, the method of its manufacture and pre-treatment. For several situations, conventionally designated below as A, B and C in increasing order of t _E , the limits w ₁ and w ₂ have the following form:

The parameter δ (which <1) used in (14) means that in the case indicated in (14) t _E >t _T1 >>t _P1 , when during the time t _E there is a significant transfer of thermal energy beyond the filament radius r _f , only part δ of the thermal energy released in the filament provides heating of the filament itself, and a significant, additional up to unity part (1-δ) of the energy E _tw is spent on heating the material outside the radius of the filament r _f . In (12-14) C is the high-temperature value of the specific heat capacity of C _NT , since T ₁ and T ₂ are several tens of thousands of K. C _NT is estimated using the formula:

where R=8.31 J/(mol×K) is the universal gas constant, N _at is the number of atoms in one molecule of the material, μ [g/mol] is the molar mass of the material. Since (1/δ)>1, a comparison of relations (12-14) shows that in the case of (13) the limits w ₁ and w _2B are the smallest, i.e. w _1B <w _1A , w _1C and w _2B <w _2A , w _2C . T ₁ is the filament plasma temperature limit corresponding to the OPE limit w ₁ . At T ₁ >>T _i , where T _i =20°C is the initial temperature, T ₁ is estimated from the condition that the ratio β = Ф ₂ /Ф ₁ of the energy flow Ф ₂ from the filament due to thermal radiation (considered as “useless” losses) to the energy flow F ₁ due to thermal conductivity (considered as useful energy losses of the filament, since it ensures the formation and propagation of a modification critical for zone separation during cooling of the filament plasma) (see Fig. 9) does not exceed the maximum permissible value β _max much less than 1 (for specific calculations we further assume β _max =0.12), which leads to the expression [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)]:

Table 1. Calculation of the limits T ₁ and w ₁ according to (12, 15, 16) for chemically tempered Corning Gorilla Glass 5, Eagle XG@Display Glass, quartz glass and sapphire, when the effective filament radius r _f is 0.25 μm, 0.5 µm or 1.5 µm, with the limiting fraction of losses due to thermal radiation β _max = 0.12 and the fraction of filament plasma energy losses due to excitation of the shock wave K _sw ≈0.5.

As an example, Table 1 shows calculations of the limits T ₁ and w ₁ according to (12, 15, 16) with the fraction of filament plasma energy loss due to shock wave excitation, taken as K _sw ≈0.5, for chemically tempered glass Corning Gorilla Glass 5, display glass Eagle XG@Display Glass, quartz glass and sapphire, when the effective filament radius r _f is 0.25 µm, 0.5 µm or 1.5 µm, and when choosing the limiting fraction of thermal radiation losses as β _max = 0.12. From Table. 1 it can be seen that the values of T ₁ for glasses with the same r _f are close to each other, but depending on g/ they vary from 29600 K to 55600 K. The limit w ₁ changes for glasses from approximately 230 kJ/cm ³ to 400 kJ /cm ³ . For sapphire, depending on r _f, T ₁ varies from 56700 K to 103000 K, aw ₁ - from 620 kJ/cm ³ to 1070 kJ/cm ³ , which is approximately 2-2.5 times higher than for glasses at similar r _f .

- They also ensure uniformity of the diameter of each emerging filament along its length. For this purpose the duration r; the i-th individual pulse of the train (i=1.2, ... N _P ) is matched with the energy E _0i of this pulse so that the power of a single laser pulse of the train P _0i ≈E _0i /τ _i ; was approximately equal to the critical power for creating self-focusing P _c , i.e. P _0i =GR _C , where the parameter Г is selected in the range 1÷1.25. From these expressions follows a relationship for matching the duration and energy of the pulse E _0i =GR _with τ _i similar to that previously used in [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)] for the SFOI mode. However, for the SFCI mode considered here, the difference is that since technically all pulses of the train have, as a rule, the same duration, i.e. τ _i =const=τ (where i is the number of the pulse in the train, i=1, 2, …N _p ), then, as follows from the last relation, it is preferable to use pulses in the train also with the same energy:

Or, in accordance with the specified range of 1÷1.25 values of the parameter Г of the pulse energy of the train, as follows from the formula may differ from each other by no more than 1.25 times.

In addition, to eliminate pulsations of the filament diameter along its length, OPE w _0i is used in train pulses (i = 1, 2,...NP) no more than approximately 0.8 w _dis , i.e. w _0i <0.8 w _dis . This inequality, taking into account the relation w _0i ≈w/N _p , gives, in addition to condition (8), another condition for the value of N _p :

Here, as in (8) above, square brackets [] denote the integer part of the number in these brackets. Combining inequalities (19) and (8) gives the final condition for choosing N _p :

where max (A, B) denotes the maximum of two values, 4 and B.

When the specified conditions (4, 6, 7, 17-20) are met to obtain a uniform diameter for each emerging filament along its length, the energy of the pulse train in the material has a simple form:

- In the volume of material, as in the specified prototype [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)], create a continuous modified layer from filament to filament with a value released in this OPE layer w (in [J/cm ³ ]) not lower than the minimum required (threshold) to obtain separation w _mod , i.e. e. w≥w _mod . To do this, the pitch s ¹ of the filaments in the material is coordinated with the radius R _T of the cylindrical zone critical for separating the modification due to the thermal mechanism:

which ensures that said zones from adjacent filaments are adjacent to each other, or even overlap each other in the material, and thereby forms the above continuous modified layer from filament to filament favorable for obtaining separation with improved smoothness. In relation to the parameters of the SFCI mode studied here, when condition (4) of heat retention is met, the radius R _T is calculated in the model depending on w, w _mod , f _burst and r _f following the same formula that was obtained earlier in [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)]:

where W _mod is given by expression (9). The designations of the parameters included in relations (22, 23) have already been explained above.

- To form straight filaments of a regular shape in each of their sets, their influence on each other is minimized, i.e. minimize heating and temperature gradient from the previous filament at the location and at the moment of emergence of the next, new filament. The solution to this problem for the SFOI mode was obtained earlier in the prototype [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)]. In relation to the SFCI mode considered here, the solution to the problem is similar - it is necessary to select the repetition frequency f _burst of laser pulse trains in one of two ranges, conventionally called “high-frequency”:

and "low frequency"

Depending on the attitude characterizing the degree of overlap with each other of the above critical zones of influence from neighboring filaments, as shown earlier in [VN Tokarev and IV Melnikov. Appl. Sci. 11, 1732 (2021)] when analyzing the SFOI mode, the limit f ₁ changes in the range where coefficient 12 corresponds to the maximum step size (when the impact zones are only adjacent to each other without overlap, see Fig. 4c in the indicated work [VN Tokarev and IV Melnikov. Appl. Sci. 11, 1732 (2021)]), and coefficient 18 - to the value s ₁ / s _1max = 0.6 (when the impact zones overlap significantly - see Fig. 4d in the same work). The limit f ₂ changes in the range f ₁ exceeds f ₂ by approximately 17 to 80 times, depending on the degree of overlap of adjacent impact zones s ₁ /s _max from 1 to 0.6. To make the assessments more specific, we select the following:

which corresponds to partial overlap of zones of influence from neighboring filaments. Then numerical estimates of the limits f ₁ and f ₂ give:

To get an idea of the order of magnitude of the limits f ₁ and f ₂ , we note that, for example, numerically for the filament pitch s ₁ = 6 μm and the thermal diffusivity of glass % at high temperatures, estimated according to reference data as (4÷5)10 ^{- 3} cm ² /s, these expressions give f ₁ =150÷190 kHz and f ₂ =6.1÷7.6 kHz. If s ₁ =2 µm, then with the same other parameters we find f ₁ =1350÷1700 kHz and f ₂ =55÷68 kHz. To achieve the above-mentioned effect of directional splitting for the thermal deformation mechanism (which is important mainly for non-hardened materials), it is preferable to select f _burst not in two ranges (24) and (25), but only in one, high-frequency range (24), and at this with an additional limitation of f _burst in this range, as indicated above in (10): f _burst =(l÷3)/f ₁ .

Finally, relationships are also written for two more parameters characterizing irradiation - the average power of the pulse-periodic laser beam in the material P and the energy efficiency of the LPR process Ω:

4. The relations (1-30) obtained in this way form a specific system of 30 mathematical equalities and inequalities; the solution of this system quantitatively determines the desired irradiation parameters, preferable for obtaining a separation with improved smoothness for the SFC mode. The proposed method is a sequence of finding all the necessary parameters one by one using simple analytical formulas - selecting (with some restrictions) some parameters and calculating a number of other parameters. In this case, shown in Fig. The 12 stages of calculations, the number of these stages and the boundaries between them are quite arbitrary and are given only to give the vast array of input, freely selectable and calculated parameters a structure convenient for reading and analysis.

Let us describe the practical application of the specified algorithm for quantitatively finding parameters consistent with each other to perform irradiation with improved smoothness using relations (1-30) and the calculation algorithm diagram presented in Fig. 12.

As already mentioned, each filament is created by a train of radiation pulses. The wavelength of the laser radiation λ, the thickness of the material L, the radius of the filaments r _f and their length H required to complete the process are set. Literary data on the parameters of the material in question are used: for an amorphous material (or T _mod =T _melt for a crystalline material) - for a description of the parameter values, see the text in the “List of parameter designations”. The initial temperature T _i =20°С and the parameter Г=1÷1.25 are assumed. It is believed, based on well-known experiments, that for the conditions considered here LPR with non-overlapping filaments in the SFC mode A _LP ≈0.8 and A _PH ≈0.9. It is assumed that K _tw ≈K _sw ≈0.5, which corresponds to a “fast” energy release (t _E <t _P1 , t _P2 ), at which the filament plasma energy losses associated with the excitation of the shock wave are significant. Or they assume K _sw <<1 and K _tw ≈1 if the energy release occurs slowly, i.e. t _E >t _P1 , t _P2 . All these data as shown in Fig. 12 circuit is used as input parameters.

At stage 1, for the above _rf, the high-temperature heat capacity is calculated temperature limit and the OPE limit w ₁ ≈2C _HT ρ(T ₁ -T _i )+w _dis , at w below which the proportion of filament energy losses due to thermal radiation is insignificant. The high-frequency range of train repetition frequencies is selected for irradiation, i.e. f _burst ≥f ₁ , for which the cooling coefficient η lies in the range of 0.76÷1. Or they choose the low-frequency range of train repetition frequencies, i.e. f _burst ≤f ₂ , for which η≤0.1. Accordingly, a specific value of η is selected from one or another of the specified ranges (in this case, specific values of the frequency limits f ₁ and f ₂ , as well as the value of f _burst itself will be quantitatively found below at stage 4). For LPR of tempered glasses, both frequency ranges can be selected, while for other materials it is preferable to choose only the high-frequency range, with the above-mentioned limitation f _burst in this range: f _burst = (1÷3)f ₁ .

At stage 2, the OPE of the filament plasma is chosen as w≤w ₁ , due to which the share of filament energy losses due to thermal radiation becomes insignificant. Also, from the specified input data C ₂ , ρ ₂ , T _mod , T _i and the value η selected above, the modification threshold for the thermal mechanism is calculated

At stage 3, according to the model, the energy of the pulse train in the material is calculated from the above parameters and the maximum allowable pitch of filaments in the material to obtain separation with improved smoothness

(with the above choice of the value of η in one or another, low- or high-frequency range). Select the filament pitch s ₁ , for example, for definiteness choose which, as noted above, ensures partial overlap of the impact zones along their radii. The parameters N _p0 and N _p1 are calculated according to the model for w, w _mod and the tensile strength of a given material defined above:

Square brackets [] in these expressions indicate the integer part of the number in these brackets. The number of pulses in the train N _p is selected according to the condition Np>N _p0 , N _p1 .

At stage 4, from the above data on s ₁ , H and E _burst , the energy efficiency of the LPR process Ω=2s ₁ H/E _burst is calculated, as well as the frequency limit f ₁ (or f ₂ ). In this case, for the specified ratio (s ₁ /s _1max ) = 0.9, the following expressions are used: In accordance with the previously selected value of η, the frequency of repetition of the trains is calculated quantitatively to obtain a separation with improved smoothness, in the high-frequency range, f _burst ≥f ₁ , or in the low-frequency range, f _burst ≥f ₂ . For the above s ₁ and c _s, the time of inertial pressure retention in the space between adjacent filaments is calculated: t _P2 ≈s ₁ /c ^s . The energy E ₀ of an individual pulse in the material is calculated, which, in accordance with the proposed method, is chosen to be the same for all pulses of the train, i.e. E ₀ = E _burst / N _p . For the input parameters r _f and χ given above, the heat retention time within the radius of the filament is calculated

At stage 5, the average power of pulsed-periodic laser radiation in the material is calculated and the speed of relative movement of the beam and material when substituting the above E _burst , fburst and s ₁ . If, in order to obtain separation with improved smoothness not only within each set of filaments, but also in the space between sets of filaments, it is necessary to create in the material not one, but simultaneously two or more specified sets of filaments, each of width H, for example, using the one mentioned above in “ Level of technology" of the multifocusing method, then the total energy of the pulse train and the average power in the material will be required, respectively, twice or more times higher than E _burst and P found above. Next, for a given r _f and defined above, the holding time of the beam position t _r ≈r _f is calculated /u. The duration of the train as a whole, τ _burst, is selected according to the constraint τ _burst <t _T1 ,t _r , and then the time interval between pulses in the train is found as Δt=τ _burst (N _p -1). In addition, with this choice of Δt, the condition Δt>t _P2 is met. The duration of an individual pulse is assumed to be the same for all pulses of the train and is calculated as τ = E ₀ /(GR _s ), which, taking into account the above relations for E ₀ and E _burst , makes it possible to quantitatively calculate τ through the parameters introduced above as well as

In this way, 12 radiation parameters are quantitatively found which, when taking into account two more input control parameters, r _f and H, amount to a total of 14 parameters. They completely and unambiguously quantify the LPR process in the SFC mode to obtain improved separation smoothness, and thus solve the problem of quantitatively finding the irradiation parameters necessary to obtain separation with improved smoothness.

5. Comparison of the proposed method for quantitatively finding the radiation parameters to obtain LPR with improved smoothness with the experiment known in the literature for tempered glass shows good quantitative agreement. On the other hand, for another experiment, where the LFR of untempered quartz glass was studied and a relatively low smoothness of the side walls of the separation was obtained, a comparison with the proposed method indicates those experimental parameters that differ significantly from those proposed by this method and therefore determine the indicated observed low smoothness of the separation. A detailed description of comparisons of these two experiments with the proposed method is given below in the section “Examples of the invention”.

6. After successful testing, the found parameters are optimized by varying the above freely selectable control parameters w, η, r _f and H that influence them to find a number of new LPR modes that provide, in addition to improved smoothness, other technical results:

- High energy efficiency of the LFR process Ω, determined according to (30). This parameter is important for large-scale industrial applications. Substituting expression (21) for E _burst into (30), as well as choosing the sequence step as s ₁ =Q.9s _max , where S _max is given by expressions (22,23), leads to the following expression:

It shows in transparent form that Ω is large if: (a) the ratio is maximum which, as can be easily determined from the position of the broad maximum of this dependence, occurs when (b) r _f is minimal, which occurs when using a shorter laser wavelength λ and a larger focusing numerical aperture NA; (c) minimum w _mod , for which, when the thermal conductivity mechanism of energy transfer dominates in the formation of the zone of influence, it is necessary to use the repetition frequency of trains in the high-frequency range, f _burst ≥f ₁ , and not in the low-frequency range, f _burst ≤f ₂ , since the accumulation factor increases heat η in the range f _burst ≥f ₁ leads, in accordance with estimate (9), to a decrease in the modification threshold w _mod by almost two times compared to the range f _burst ≥f ₂ ; (d) the coefficient of conversion of filament plasma energy into shock wave energy is minimal, K _sw <<1, which, as mentioned above, corresponds to materials with a sufficiently long energy release time t _E >t _P1 , t _P2 ; (e) the energy conversion coefficients A _LP and A _PH are maximum, which emphasizes the importance of using filaments for LPR with an OPE w that satisfies condition (11) w≤w ₁ , at which significant filament energy losses due to thermal radiation are eliminated.

High speed (3) relative movement of the laser beam and material. Substituting here expressions for f _burst in the form:

where, as follows from the above, a=13.3÷39.9 for the high-frequency frequency range (10,24,27), and a≤0.547 for the low-frequency range (25,28), gives an estimate

From this it becomes obvious that u is large when (i) a is large, i.e. when using the high-frequency range (10), (ii) when using a material with a higher thermal diffusivity χ, (iii) reducing the filament pitch s ₁ (which is achieved by reducing the filament radius r _f by reducing the laser wavelength λ and/or using a larger focusing numerical aperture NA, and/or with OPE in a limited range around w≈(1.8÷2.5)w _dis according to (22, 23, 26)). For example, the choice of the repetition rate of trains in the high-frequency range f _burst ≥f ₁ and, for example, the use of a laser radiation wavelength λ=0.52 µm twice shorter than λ=1.04 µm, allows one to obtain record high cutting speeds of about 1÷50 m/ s or more depending on the material - see for example below in Table 3 Example 1.3 for tempered glass, where u=11.5 m/s, and in Table 4 Examples 2.1 and 2.5 for display glass, where u=6.2 and 8.8 m/s s, as well as Example 3.1 for sapphire, where u=52 m/s. These speeds can be tens, hundreds and even thousands of times higher than the characteristic speeds of cutting glass, sapphire and other transparent materials using known mechanical methods and tens of times higher than the characteristic speeds of separation using known methods of laser-controlled thermal splitting using irradiation with continuous lasers. - The possibility of performing LPR with a beam of pulse-periodic laser radiation of very low average power P (from fractions of W) while obtaining, nevertheless, a considerable separation rate acceptable for practical applications. Substituting E ₁ from (21) and f _burst from (31) found above into expression (29) for P, as well as s ₁ according to (22, 23, 26) gives the expression:

From this formula it is clear that the main influence on the reduction of P is the use of the low-frequency range f _burst (28), which corresponds to a small value of the parameter a (≤0.547), which is many times (24-72 times or more) less than a = 13.3÷ 39.9 in the high frequency range (27). A number of other factors are also important: the use of shorter filaments, i.e. with H on the order of several tens of microns; large (i.e., close to 1) energy conversion coefficients A _LP and A _PH , which emphasizes the importance of using filaments with OPE w for LPR, satisfying condition (11) w≤w ₁ to eliminate significant filament energy losses due to thermal radiation; the minimum coefficient of conversion of filament plasma energy into shock wave energy, K _sw <<1, which, as mentioned above, occurs for materials with a sufficiently long energy release time: t _E >t _P1 , t _P2 . In this case, the speed in the indicated low-frequency range is maximum, as follows from (32), at maximum a in this range (i.e. a = 0.547), at f≈f ₂ , and also, as noted above, when using the material with a higher thermal diffusivity χ, a decrease in the filament pitch s ₁ (which is achieved by decreasing the laser wavelength X, and/or using a larger focusing numerical aperture NA, and/or according to (22, 23, 26) with an OPE of the order of Below in Table 3 is Example 1.4, in which the irradiation parameters are specifically calculated according to the specified scheme for thin tempered glass and the following values are obtained: P = 197 mW and u = 0.18 m/s.

7. It is possible to experimentally refine the radiation parameters proposed by the specified algorithm with some special choice of irradiation parameters, when: OPE w is chosen as w<w ₁ ; the parameter η is chosen corresponding to the high-frequency range; with an excess of at least several times over N _p0 , select the number of pulses in the train: N _P1 ; the frequency of repetition of the trains f _burst is chosen to be several times higher than f ₁ : the time interval Δt between pulses is chosen to be several times greater than t _P2 : Note that this choice of N _p , f _burst and Δt corresponds to the algorithm, i.e. does not conflict with obtaining a separation with improved smoothness. Then in the experiment for the parameters use their values found according to the proposed algorithm. At the same time, the value of the filament pitch _s1 is clarified by its experimental selection, comparing the results of cutting obtained in experiments at different _s1 : in this case, a suitable value of s\ is found, for which in the experiments a result with the best smoothness of the side walls of the separation is achieved. The lower and upper limits of the range of variation of s ₁ in these experiments are chosen to differ from the calculated value of s ₁ by no more than 1.4 times, respectively, downwards and upwards. The above significant excesses of N _p by several times over N _p0 , f _burst over f ₁ and Δt over t _P2 are necessary so that, with the indicated variation of si around the calculated value, not to go beyond the applicability of the conditions for using the high-frequency range f _burst ≥f ₁ , as well as the conditions N _p ≥N _p0 , N _p1 and Δt≥t _P2 , since the boundaries f ₁ , N _p0 and t _P2 change with varying s ₁ according to relations (27), (8) and (5), respectively. This procedure can also be performed for a different choice of OPE filament w, thereby expanding the number of experiments from which the result with the best separation smoothness is found.

8. If the application of the above measures is still insufficient to obtain the desired level of smoothness of the side walls of the separation, then an additional layer of transparent material with high tensile strength and high rigidity (Young’s modulus) is applied to the front and/or rear outer surface of the processed sample to increase the mechanical strength of these surfaces in relation to tensile thermally induced stresses. This leads to an artificial reduction on these surfaces of the radius of the zone of unwanted chaotic or multidirectional cracking around each filament due to the thermal deformation mechanism of the formation of the impact zone. As such an auxiliary material, for example, a transparent graphene film or a transparent film made of a high-strength polymer is used. In this case, the position of the filaments in the thickness of the material is adjusted so that they do not go out of the volume of the main processed material into the area where the specified additional outer auxiliary layer is located.

9. As follows from photographs of the side walls of the separation (see Fig. 3b), the main (or at least significant) contribution to the amplitude of their roughness is made by the relief with a period equal to the filament pitch s ₁ . Due to the fact that the aspect ratio for such a relief AR=R _a /s ₁ (where R _a is the average amplitude of its roughness over the separation surface) remains limited when varying s ₁ , then according to the relation R _a =s ₁ ⋅AR to obtain a reduced roughness (i.e. improved smoothness) from the variety of solutions found according to the above algorithm when varying the above control parameters w, r _f and H, it is preferable to use irradiation modes with reduced values of s ₁ , for example, in the range s ₁ ≈1÷3.5 µm compared to s ₁ ≈5÷7 µm in experiments known in the literature. To obtain such reduced s ₁ , as follows from the algorithm according to expressions (22, 23, 26), it is preferable to use small radii r _f of the filament (which is achieved by using a larger numerical aperture of the focusing system, and/or a shorter wavelength of laser radiation, for example, from the range λ=0.5-0.55 µm instead of 1-1.1 µm) and/or use OPE in a limited range: w≈(1.8÷2.5)w _dis .

10. To obtain separation with improved smoothness, in addition to the considered SFCI mode, it is preferable to use Gaussian-Bessel beams for irradiation, created by conical lenses (axics) 15, especially for cutting thick materials, with a thickness of about 7-10 mm or more - see Fig. . 5.

Indeed, along with the above factors for obtaining improved smoothness, the following conditions are also important:

(i) Straightness, determinism and repeatability of the direction of the axis of each filament and the axes of the filaments in the set;

(ii) Uniformity of the filament's OPE w along its axis and from filament to filament to eliminate variations in the radius of the impact zone in the material around each filament, both along the length of each filament and from filament to filament in their set, as well as the uniformity of filament pumping along its length from pulse to pulse in a train;

(iii) The ability, due to the large number of pulses in a train, to provide significantly more energy to create a filament, which makes it possible to optically pump a much longer filament to a volumetric energy density sufficient to separate it when using pulse trains compared to the above-mentioned SFOI mode. This difference and advantage of the SFCI mode is especially important for cutting thick materials, for example, with a thickness of 7-10 mm or more, when very long filaments of several mm are required to perform separation.

The use of irradiation with Gaussian-Bessel beams ensures that these conditions are met. In this case, the E _burst , E ₀ and P indicated in the paragraphs above mean the parameters corresponding to the central maximum of the spatial distribution of the beam intensity in the focusing region.

For comparison, the creation of filaments due to spontaneous self-focusing of a beam in a material allows one to obtain only short filaments of the order of several tens of micrometers, but not millimeters, and at the same time is more susceptible to various fluctuations - as in the position of the filament in the thickness of the material and its direction (in particular, its curvature ), and within the radius of the modification zone along the filament, which can lead to greater roughness of the separation walls obtained after irradiation.

11. The proposed method for quantitative selection of parameters for LPR can be used in combination with the known method, which uses a multilayer composition to perform LPR, consisting of layers of the same transparent material located on top of each other or including layers of various transparent materials, solid and/or or liquid, these layers can have different thicknesses, and the layer of material that is actually subject to LPR and in which the beam is focused can be the first in the specified composition and facing the laser beam, or the last layer, i.e. on the back side of this composition, or enclosed between other layers.

Note that for an alternative experimental design, when the material is irradiated in air, if it is necessary to create filaments directly at the front surface of the material facing the incident laser beam, the tapering part of the beam with high intensity is located at this surface. Therefore, there is a high probability of optical breakdown of air near this surface, which is an undesirable phenomenon for LPR, since it causes defocusing and screening for the laser beam incident on the material being processed, making processing impossible. The use of the specified multilayer composition allows one to avoid such an undesirable phenomenon.

12. Specific quantitative examples of the practical application of the specified separation method and the developed algorithm for chemically tempered Corning Gorilla Glass 5, Eagle XG@Display Glass and sapphire are given below in Tables 3 and 4 in the “Examples of the Invention” section. In this case, both thin plates with a thickness of less than 0.75 mm and thick ones, with a thickness of about 7-10 mm or more, are considered. All irradiation parameters necessary to set the SFCI mode to obtain improved smoothness of the separation walls are specifically indicated quantitatively -

It was found that the choice of repetition frequency in the high-frequency range, f≥f ₁ , and the use of a twice shorter wavelength of laser radiation, for example, 0.52 μm instead of 1.04 μm, make it possible to obtain higher, including record high cutting speeds - about 11 ÷52 m/s or more depending on the material. These speeds can be tens and hundreds of times higher than the characteristic speeds of cutting glass, sapphire and other transparent materials using known mechanical methods, and tens of times higher than the characteristic speeds of separation using known methods of laser-controlled thermal splitting using irradiation with continuous lasers.

On the other hand, it has been found that the choice of repetition frequency in the low frequency range, f≤f ₂ , and the use of a shorter wavelength of laser radiation (for example, λ = 0.52 μm instead of 1.04 μm) make LPR possible for tempered glasses, obtaining improved smoothness at extremely high temperatures. low average laser power (from fractions of W), which nevertheless provides, although not a record high, but acceptable for applications and considerable cutting speed of about 0.2 m/s.

LPR modes with improved smoothness have also been found, which make it possible to cut tempered and non-tempered glass, as well as sapphire, at a moderate average laser power with a relatively moderate moving speed of the order of 3-7 m/s and acceptable for implementation in applications.

The device, the operation of which is based on the practical implementation of the method proposed above, includes such well-known components as:

- Pulse-periodic laser;

- Beam formation and focusing unit with the ability to change the beam diameter, smoothly regulate the pulse energy, as well as focus the beam in the material using a focusing system with the ability to maintain the distance between it and the part;

- Block for precision fastening and tilting of the irradiated part under the laser beam with the possibility of its precision 3B movement relative to the laser beam:

(a) along the beam axis - to precisely adjust the position of the beam focusing area in the thickness of the sample in order to create one or more sets of filaments at different depths in the thickness of the material;

(b) in the focusing plane, using, if necessary, polygonal scanners to obtain a high scanning speed of several m/s, with cutting the processed material straight or along a curved path, or along a closed path, and/or “from reel to reel” for LPR of flexible transparent materials when they move under a laser beam, and/or in the form of rotation of the part relative to the laser beam around its axis of symmetry, when the part has a non-flat surface in the form of a figure of rotation;

- Irradiation capabilities that make it possible to create one or more sets of filaments in the thickness of the material using one or another method or their combinations:

(a) due to repeated passages of the beam along the same track in the material;

(b) due to multifocusing - the formation of two or more beams from the main beam for their simultaneous focusing in the material at different depths;

(c) due to the formation of filaments in the bulk of the material using a nonlinear process of spontaneous self-focusing, and/or the use of any other methods, used individually or in certain combinations and extending the beam focusing area along the optical axis, for example, due to the use of special optical elements, such as diffractive optical elements, either intentionally astigmatic focusing optics, or axicons, or through the use of some other focusing method;

(d) by creating each of the filaments with a train of pulses, i.e. a group of pulses closely spaced in time.

This device allows you to separate such relatively thin transparent materials as display glass with a thickness of 0.5÷0.75 mm, chemically tempered glass with a thickness of 0.3÷0.7 mm and sapphire with a thickness of 0.05÷0.3 mm, which are practically interesting for the manufacture of mobile devices - smartphones, tablets, wearable electronics, as well as for large-scale production of large-area glass panels to protect the photosensitive layer of solar cells from dust and precipitation.

- This device has the technical ability to independently vary irradiation parameters for the SFCI mode in the ranges listed below Table. 3 and 4: laser wavelength λ - from 0.3 µm to 1.1 µm, or at least in some part or parts of this range - for example, from 0.5 to 1.1 µm, or λ can take discrete values, for example, 0.52 µm and/or 1.04 µm; r _f from 0.2 µm to no more than 1.7 µm; H from 30 microns to no more than 700-750 microns; w from 115 kJ/cm ³ to no more than 900 kJ/cm ³ ; E _burst from 1 µJ to no more than 250 µJ; N _p from 2 to no more than 30; E ₀ from 0.1 μJ to at least 25 μJ; s ₁ from 0.5 µm to no more than 12 µm; P from 0.4 W to no more than 150 W; f _burst from 10 kHz to no more than 5 MHz; u from 0.05 m/s to 12 m/s, or at least in some part or parts of the specified ranges, depending on the material and the choice of irradiation parameters; in the case of the following LPR below with the rotation of a part having a non-flat surface in the form of a figure of rotation, relative to the laser beam around its axis of symmetry, the angular velocity of rotation is chosen so as to ensure the specified variation of u; τ _burst from 5 ns to at least 110 ns; Δt from 1 ns to no more than 30 ns; τ from 90 fs to at least 8 ps, while in the case of using a Gaussian-Bessel beam for focusing, the indicated E _burst , E ₀ and P mean the parameters corresponding to the central maximum of the spatial distribution of the beam intensity.

- In the device, by varying the specified irradiation parameters, such values are set that, according to the proposed method, provide certain technical results of LPR mentioned above (improved smoothness of separation, high speed and relative movement of the laser beam and material, high energy efficiency Ω of the LPR process, or implementation LFR with a laser beam of very low average power P (from fractions of W) obtaining, however, a considerable separation speed acceptable for practical applications), which is achieved by “manually” setting the optimal cutting parameters based on calculations according to the proposed method and/or using a block numerical program control of this device if it has a built-in program for calculating the specified parameters proposed in this method, as well as with their subsequent electronic installation in the device.

14. A similar device is also proposed for separating thick plates of transparent materials (7-10 mm thick or more), which is of practical interest in the automotive industry, construction, design, instrument making, manufacturing of decorative art products and other areas.

In this device for laser separation of thick plates, when it is necessary to create filaments of longer length, for example about 7-10 mm, for chemically tempered glasses, non-tempered display glasses and other materials, Gaussian-Bessel is preferably used as a focusing system for creating such long filaments bun. By E _burst and P then we mean the parameters corresponding to the central maximum of the spatial distribution of the intensity of such a beam.

For the practical implementation of various combinations of agreed irradiation parameters, the device has the technical ability to vary the specified parameters in the ranges following from those indicated below in Table. 3 and 4:

- Filament radius r _f - from 0.2 µm to no more than 0.5 µm;

- Length of filaments H - from 7 mm to 10 mm;

- Wavelength λ of laser radiation - in the range of approximately λ=0.5-1.1 μm, or λ can take discrete values, for example, 0.52 μm and/or 1.04 μm;

- OPE filament w - from 115 kJ/cm ³ to no more than 200 kJ/cm ³ ;

- Energy of the pulse train E _burst - from 230 μJ to no more than 2100 μJ;

- The energy of an individual pulse in a train E ₀ - from 40 μJ to at least 380 μJ or more;

- The pitch of filaments in the material s ₁ is from 1 µm to no more than 7 µm;

- Average laser power in material P - from 40 W to 1800 W or more;

- Repetition frequency f _burst - from 20 kHz to no more than 3.6 MHz;

- Speed of relative movement of the laser beam and material and - from 0.01 m/s to 9 m/s;

- Duration of the pulse train τ _burst - from 4 ns to at least 110 ns;

- Number of pulses in a train N _p - from 3 to 6 or more;

and, for example, when N _p =6, the time interval between pulses in a train Δt is used - from 1 ns to 24 ns and the duration of an individual pulse τ - from 17 ps to 75 ps.

Variation of the parameters in both of these devices, respectively for thin and thick materials, is achieved by methods known to specialists in the field who use lasers with variable radiation parameters to process materials. For example, the radius of the filament is varied by changing the apex angle of the 3 cone lenses 15 used in the focusing system, shown in FIG. 5. Changing the length of the filament when using the focusing system 3 with the formation of a Gaussian-Bessel beam is achieved by changing the diameter of the beam 2 through the use of a beam expander 14, as well as changing the angle at the apex of the cone lenses 15 used in the focusing system 3.

15. Both of these devices, respectively for thin and thick materials, may have the technical ability to cut using the proposed method not only flat, but also non-flat surfaces, in particular, cutting materials in the form of cylindrical tubes, fibers and other axisymmetric parts in the form of figures of rotation - spheroids, ellipsoids, hyperboloids and other reliefs with curvature. The relative movement of the laser beam and the material is ensured in this case by adding a degree of freedom in the relative movement of the laser beam and the workpiece in the form of its rotation under the beam around its axis of symmetry. Fig. 13 shows a block diagram of such a separation device. Unlike the elements and modules mentioned above for the prior art in FIG. 1 and 2, this device has the technical ability to rotate 29 the specified non-flat part 5 relative to the laser beam 4 around its axis of symmetry 28 through the use of a module 27 for fastening and rotating the specified part with adjustable speed and, length H and radius r _f of the filament, train energy in the material E _burst , filament pitch s ₁ , number of pulses in a train N _p , average energy of a single pulse in a train E ₀ , repetition rate of pulse trains f _burst , duration of an individual pulse in a train r, duration of pulse trains as a whole τ _burst and temporary the interval between pulses in the train Δt, which are adjusted to the material parameters and are consistent with each other in accordance with the method proposed here.

The proposed method and the device based on its use for separating thin plates make it possible to separate such relatively thin transparent materials as display glass with a thickness of 0.5÷0.75 mm, chemically tempered glass with a thickness of 0.3÷0.7 mm and sapphire with a thickness of 0.05÷0.3 mm, which are practically interesting for manufacturing displays and protective plates in mobile devices - smartphones, tablets, wearable electronics, the global production of which is about 1.5-2 billion products per year, as well as in all kinds of sensors, fitting bracelets, wristwatches, scientific and medical devices, in the manufacture sapphire heat-dissipating substrates for microprocessors and protective glass panels for solar batteries.

The device proposed for separating thick plates of several millimeters in thickness could have extensive applications in industries such as automotive, construction, architecture and instrumentation. The market for such products also amounts to billions of units per year.

The advantages of using the invention are described below. These include:

- Obtaining cut side walls for transparent and translucent materials with improved smoothness with proper selection of radiation parameters, due to which the cutting process as a whole is significantly simplified and cheaper, and its productivity increases, i.e. less time is spent to obtain a final product of acceptable quality, since in this case there is no need to perform labor-intensive additional post-laser processing in the form of grinding, polishing or chemical etching of the separation walls to remove roughness on them, which, as noted above, is a source of unwanted crack nuclei and therefore reducing the impact resistance of the product during its further operation. When using this method, there is thus an increase in the impact resistance of cut plates and other products made of transparent materials during their further practical operation;

- Unprecedentedly high cutting speed in this method (for example, from 0.05 m/s to 3÷52 m/s or more depending on the material and the choice of irradiation parameters), which is tens, hundreds and even thousands of times higher than the characteristic cutting speeds of hardened and non-tempered glasses, sapphire, as well as many other transparent and translucent materials by known mechanical methods, and tens and hundreds of times the characteristic separation rates by known methods of laser-induced controlled thermal splitting using irradiation with continuous and pulse-periodic lasers;

- Very small thickness (only a few microns) of the laser impact zone in the material along the side walls of the separation and the ability to avoid significant residual thermal stresses and deformations of the material due to the low energy release per unit area of the side walls of the cut compared to the use of continuous lasers to separate transparent materials, as well as the implementation of a sufficiently high speed of movement of the laser beam at a very low level of applied average laser power (in fractions of W). This effect is important for applications when the material being cut already contains some heat-sensitive functional working layers, for example, a layer of light-emitting organics in the case of cutting display glass;

- The applicability of the method, depending on the settings of irradiation and focusing parameters, for separating both thin (with a thickness of 0.05-0.75 mm) and thick materials (thickness, for example, 7-10 mm or more);

- The applicability of the proposed device (devices) for separating not only any one, but various optically transparent or translucent materials, including hard, super-hard and super-strong, the cutting of which by traditional mechanical methods is extremely slow and labor-intensive;

- The wavelength of the laser radiation can be selected within the range of transparency of the material, for example, for quartz glass in the range of 0.2-2.3 microns;

- The proposed devices, depending on the specified trajectory of the laser beam relative to the surface of the material, can include obtaining not only straight, but also curved or closed cuts with a sufficiently small radius of curvature - at least about 80 microns, as well as cuts for surfaces with curvature;

- With computer control of the process, cutting adjustment occurs by programmably setting the necessary parameters of laser radiation, beam focusing and the speed of relative movement of the laser beam and the material being processed; the trajectory of the relative movement of the beam and material is easily set, while the process itself has high flexibility, the possibility of high automation, high reproducibility, accuracy and quality of cutting results, including when used in large-scale production;

- The plate of transparent material to be cut by this method may be part of a multilayer composition in which the superimposed layers consist of the same or different transparent materials, solid and/or liquid, and may have different thicknesses. In this case, the solid plate to be cut may be the first of the layers, i.e. facing the laser beam, or the last layer, i.e. on the back side of said multilayer composition, or enclosed between other transparent layers;

- The proposed device for cutting thin materials may also include separation of flexible extended transparent materials when they move under a laser beam “from reel to reel”;

- The method indicates possible directions for targeted materials science design of the properties of transparent materials to give them such parameters for which the smoothest separation becomes possible;

- The method also indicates possible directions for the targeted design and creation of pulse-periodic lasers and laser systems with parameters that are most suitable for obtaining separation with improved smoothness, high speed and high energy efficiency;

- The proposed cutting method is environmentally friendly, since it is achieved without the use of oils or any technical liquids, abrasives, liquid or gaseous chemical etchants. In the case when the filaments created in the material do not reach the front and/or back surfaces of the processed plate, during the cutting process there is no release of vapors, drops or solid fragments of the material into the surrounding space, and the separation itself in the form of splitting has zero width. Thus, there is virtually no material removal and no environmental pollution occurs;

- In this method and devices there are no cutting mechanical tools (saws, drills, scribers) and their contact with the material being processed. In this regard, there is no mechanical wear of the tool, minimal stress and distortion in the material being processed, and the risk of mechanical damage is reduced.

APPROBATION OF THE METHOD

Experiment 1. LPR of thin tempered glass

In documents [V. Matylitsky and F. Hendricks, 9th hit. Conf. on Photonic Technol. LANE 2016, Industrial Paper. Published by Bayerisches Laserzentrum GmbH, 2016] and [V. Matylitsky, F. Hendricks, and R. Patel, http://www.industrial-lasers.com/articles/print/volume-30/issue-3/features/femtosecond-laser-processing-of-brittle-materials.html ] describes the experiments also mentioned above in the "Prior Art", in which laser cutting of chemically tempered Corning® Gorilla® Glass 5 with a thickness of 550 μm was observed with high smoothness of the side walls of the separation and at high speeds of up to 4 m/s - see FIG. 3b. The depth of the tempered DOL layer on the front and back sides of the glass plate was 20 µm. According to these authors, the laser source used was Spirit® HE laser (from Spectra Physics, Rankweil, Austria), which had a pulse energy of more than 120 μJ and an average laser output power of >16 W. The laser allows LPR to be performed at wavelengths of 520 nm and 1040 nm with programmable pulse energy, repetition rate and pulse duration between 340 fs and 10 ps. It is also possible to irradiate in the form of trains of femtosecond pulses with a controlled number of pulses in the train up to 20 and with a time interval between pulses in the train of about 13 ns. Using the ClearShape™ process from Spectra-Physics, flake-free separation walls were obtained with high laser cut quality corresponding to a low average roughness value of <0.1 µm. The mechanism of this process, as well as all radiation parameters for its implementation, are not disclosed in these publications.

The method proposed here allows us to quantitatively explain the radiation parameters used in these experiments, obtaining high smoothness and high separation speed. Below is the calculation of the parameters w, E _burst , f _burst , s ₁ , τ _burst , τ, Δt, N _p , P and u necessary for a smooth separation, following those shown in Fig. 12 diagram of their quantitative location:

- We create each filament with a train of radiation pulses. According to the literature data, we use the following reference parameters for this material: wdis=64 kJ/cm ³ , _RS (λ=1040 nm)=5 MW, ρ2=2.43 g/cm ³ , C ₂ ≈1.0 J/(g⋅K) , A _LP =0.8, A _Р-Н =0.9, T _mod =T _strain =571°С, χ=(4÷5)×10 ^-3 cm ² /s, c _s =6×10 ⁵ cm/s, μ=60 g/mol, N _at =3, σ _s =1.8-2.4 GPa (kJ/cm ³ ). We also use the initial temperature T _i =20°C and Г=1÷1.25. We assume, according to experiment, that the laser has a radiation wavelength λ = 1.04 μm, a beam factor M ² = 1.25 and a focusing numerical aperture NA = 0.6. For the glass thickness, we use the value L=550 µm indicated in this experiment. For calculations, we assume that the radius of the filaments is r _f =0.5 μm, which corresponds to the estimate of r _f using the formula when using the indicated λ, M ² and NA, as well as q≈1. [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)]. For calculations, we select the filament length H = 45 µm. We assume K _tw ≈K _sw ≈0.5, which corresponds to a “fast” energy release (t _E <t _P1 , t _P2 ), when the energy losses associated with the excitation of the shock wave are significant. All these data according to the calculation scheme shown in Fig. 12, we use as input parameters;

- At stage 1 for the above r _f according to the relation we calculate the temperature limit T ₁ =44100 K, according to the expression C _nt ≈3RN _at /μ we find the high-temperature heat capacity C _nt ≈1.25 J/(g⋅K) and from the relation w ₁ ≈2C _nt ρ(T ₁ -T _i )+w _dis let's find the OPE limit w ₁ ≈336 kJ/cm ³ . We select for irradiation the high-frequency range of train repetition frequencies, i.e. f _burst ≥f ₁ , namely, f _burst ≈f ₁ , which corresponds to the value of the cooling parameter η=0.76;

- At stage 2, we select the OPE of the filament plasma according to the condition w≤w ₁ , namely, as w=270 kJ/cm ³ . We also calculate the modification threshold for the thermal mechanism w _mod =0.76 kJ/cm ³ from the relation for the specified input data C ₂ , ρ ₂ , T _mod , T _i and the mentioned value η;

- At stage 3 of the indicated r _f , H, w, w _dis and w _mod and ratios we calculate E _burst =11.5 μJ, and also according to the relation

the maximum allowable pitch for obtaining smooth separation of filaments in the material is s _1max = 6.6 µm. We choose the filament step as s ₁ =0.9s _1max <s _1max , i.e. s ₁ =5.9 µm, which ensures partial overlap of heat-affected zones. We calculate the parameters N _p0 and N _p1 according to the expressions

for the above w, w _mod and σ _с . We get N _p0 =2 and N _p1 =6. Square brackets [] in the above expressions indicate the integer part of the number in these brackets. We select the number of pulses in the train N _p according to the condition N _p ≥max (N _p0 , N _p1 ), in this case, for the above N _p0 and N _p1 we select N _p =6;

- At stage 4, from the above s ₁ , H and E _burst, we calculate the energy efficiency of the LPR and find Ω≈46 µm ² /µJ. We calculate the frequency limit f ₁ . For the specified ratio (s ₁ /s _1max )=0.9 we use the expression that when using the above χ at high temperatures and s ₁ gives f ₁ =153÷191 kHz. We choose the repetition frequency of the bursts to obtain a separation with improved smoothness, as f _burst ≈f ₁ , i.e. f _burst =153÷191 kHz. For the above s ₁ and c _s, we calculate the pressure retention time in the space between adjacent filaments t _p2 ≈s ₁ /c _s , which gives t _p2 ≈1 ns. We calculate the energy of an individual pulse in a train, which we choose to be the same for all pulses in the train: E ₀ =E _burst /N _p =1.92 μJ. For the above r _f and χ, we calculate the heat retention time within the radius of the filament which gives t _T1 ≈120÷150 ns;

- At stage 5, we calculate the average power of pulse-periodic laser radiation in the material as P = 1.8-2.2 W according to the relation when substituting the above E _burst and f _burst . Also according to the relation for the s ₁ and f _burst found above, we calculate the speed of the relative movement of the beam and material u=0.9-1.13 m/s. Accordingly, when choosing a higher frequency, for example, f _burst =3f ₁ =3×191 kHz=573 kHz, and the same s ₁ =5.9 μm E _burst =11.5 μJ, the average power and speed of movement increase: P = 6.6 W and u =3.4 m/s. The resulting range u=0.90÷3.4 m/s is consistent with the velocities reported by the authors of the experiment: from 1 m/s to <4 m/s.

To actually separate chemically tempered glass, two sets of filaments are required - one usually near the back of the wafer, and one closer to the front of the wafer, facing the incident laser beam. Moreover, to obtain smooth separation as a whole, and not just between filaments of one set, it is important that at least one of these sets of filaments covers both the hardened layer itself and also extends into the area of the unhardened mass of the rest of the material [Bhuyan MK, Jedrkiewicz O, Sabonis V, Mikutis M, Recchia S, Aprea A, et al. High-speed laser-assisted cutting of strong transparent materials using picosecond Bessel beams. Appl. Phys. A 120(2), 443-446 (2015). https://doi.org/10.1007/s00339-015-9289-7]. With the filament length considered here (i.e., the width of the filament set) H = 45 μm, which exceeds the thickness of the hardened surface layer of 20 μm, this is possible. Therefore, when creating not one, but simultaneously two specified sets of filaments in a material, for example, due to the multifocusing method, at the specified f _burst = 153-191 kHz, the total energy of the pulse train and the average power are required, respectively, twice as high as those mentioned above, i.e. E _burst =23 µJ and Р=3.6÷4.4 W. This estimate closely corresponds to the average power reported by the authors of this experiment for separating a given plate: P < 4 W. And for the above f _burst =573 kHz, s ₁ =5.9 µm and E _burst =11.5 µJ for the simultaneous creation of two sets of filaments, the average power will also double compared to the above 6.6 W and will be P = 13.2 W.

Next, for the indicated r _f and u, we calculate the holding time of the beam position t _r ≈r _f /u, which for the u=0.90÷3.4 m/s found above gives t _r ≈120-500 ns. We choose the duration of the train as a whole τ _burst according to the condition τ _burst <min (t _T1 , t _r ), which for the above values t _T1 and t _r gives τ _burst <120÷150 ns. Considering that for N _p pulses in a train, the distance between them in time is estimated, as follows from Fig. 4b, by the obvious relation Δt=τ _burst /(N _p -1), for the above N _p =6 we will then find Δt<24÷30 ns. If we choose N _p =10, then we will accordingly find Δt<13÷17 ns. Both of these estimates of Δt are consistent with the interval Δt=13 ns between pulses in trains, which was used in the experiment under consideration. In addition, the indicated value Δt=13 ns actually satisfies the condition Δt>t _P2 , which is preferable for obtaining better smoothness of the side walls of the cut, since, as calculated above, t _P2 ≈1 ns. Based on the above data on Г, Р _с and Е ₀ (for N _p =6), we calculate the duration of an individual pulse, which we assume to be the same for all pulses of the train τ=Е ₀ /(ГР _с ), which gives τ≈307÷384 fs. This estimate is also consistent with the experiment discussed, where, as the authors point out, pulses with τ<400 fs were used.

Table 2 shows that the irradiation parameters predicted on the basis of this method are in good agreement with the values of τ, P, u and Δt reported in the experiment under discussion.

Experiment 2. LPR of thick quartz glass

It is interesting to check whether condition (11) on the OPE w≤w ₁ is fulfilled in the experiment to practically eliminate filament plasma energy losses due to thermal radiation. To do this, the OPE of the filament w must be found in the experiment and compared with the calculated limit w ₁ described above. As an experiment, we consider the data [Bergner K, Mǘller M, Klas R, Limpert J, Nolte S and Tunnerman A, Appl. Opt. 57, 5941 (2018)], where a quartz glass plate about 8 mm thick was cut by a Gaussian-Bessel beam. In this case, each filament was created in a train of N _p = 4 or 8 pulses, the train repetition frequency f _burst = 10 kHz, the filament step s ₁ = 10 μm, and the speed of relative movement of the material and the laser beam u = 10 cm/s were used. We believe that the filament radius of 0.61 µm, estimated and reported by the authors, is close to the radius Then the filament radius r _f (1/e) required for further analysis can be found as [VN Tokarev and IV Melnikov, Appl. Sci. 11, 1732 (2021)] and, therefore, is 0.43 µm. According to the experimental data of this work, from the wide range of train energies used to perform LPR, we take E _burst = 0.9-1.0 mJ, since it is reported that it is in this energy range of E _burst that the best smoothness of the side walls of the cut is achieved. Moreover, according to Figure 3 from the above work, such a train energy corresponds to a filament length H of about 7.4 mm.

According to (21), the energy of the train of laser pulses inside the material is determined by the dependence on the length H and radius r _f (1/e) of the filament, as However, if the energy E _burst , like r _f and H, is already known from experiment or from any other sources, then from this relationship one can estimate the practically important value of OPE as Substituting the indicated values of E _burst , r _f and H, as well as the above-mentioned filament absorption capacity A _LP ≈0.8 for non-overlapping filaments, then allows one to find the OPE from the last relation as w = 167-186 kJ/cm ³ . This value turns out to be less than the minimum of the 3 thresholds demonstrated by formulas (12-14), i.e. w<min (w _1A , w _1B , w _1C )=w _1B . In this case, w _1B =187 kJ/cm ³ for the indicated r _f =0.43 μm. This means that w<w _1A , w _1B , w _1C . Therefore, in this case, condition (11) w<w ₁ is satisfied regardless of the relaxation time t _E to the equilibrium state, which, as a rule, is unknown in advance. Thus, we can conclude that the energy losses due to thermal radiation of the filament plasma are indeed insignificant in the experiment under consideration, where the laser radiation, its focusing parameters and OPE w were experimentally selected by the authors so as to provide the best results in terms of the quality of the surface of the side walls of the separation.

Similar to the above calculation for Experiment 1, we will quantify other parameters, following the same scheme for their selection and calculation as for the discussion of Experiment 1, shown in Fig. 12.

According to the literature data, for this material we use w _dis =64 kJ/cm ³ , R _C (λ=1040 nm)=5 MW, ρ ₂ =2.2 g/cm ³ , C ₂ ≈1.09 J/(g⋅K), C _nt ≈1.25 J/(g⋅K), P _s (λ=1040 nm)=5 MW, A _LP =0.8, A _PH =0.9, T _mod =T _strain =775°С, χ=5×10 ^-3 cm ² /s, c _s =6×10 ⁵ cm/s, μ=60 g/mol, N _at =3, λ _ha =140 nm and σ _s =0.59 GPa (kJ/cm ³ ). We also use the initial temperature T _i =20°C, Г=1÷1.25 and the above values r _f (l/e)≈0.43 μm, w=0.9-1.0 mJ, H=7.4 mm and λ=1.04 μm. We assume K _tw ≈K _sw ≈0.5, which corresponds to a “fast” energy release (t _E <t _P1 , t _P2 ), when the energy losses associated with the excitation of the shock wave are significant. All this data according to the calculation algorithm shown in Fig. 12, we use as input parameters.

For the convenience of comparing the calculation with the experiment, we assume in the calculation the same parameters as those estimated above for this experiment: r _f ≈0.43 μm and H = 7.4 mm, as well as approximately the same value w = 170 kJ/cm ³ . In this case, we calculate the remaining parameters according to the algorithm similar to the above example for Experiment 1. We will then find the following values:

As the most favorable for this non-hardened material to obtain separation with improved smoothness, we select the high-frequency range of train repetition frequencies and the train repetition frequency f _burst ≈3f ₁ , for which the accumulation factor We further find w _mod = 0.90 kJ/cm ₃ , E _burst = 0.91 mJ, s _1max =3.80 µm, s ₁ =0.9s _1max =3.4 µm, N _p0 =6 and N _p1 =4. We choose N _p =8. Next we find Ω=55 µm ² /µJ, f _burst =1-73 MHz, /N _p ≈ 114 µJ, t _T1 =92 ns, P=1574 W, u=5.9 m/s, t _r ≈73 ns. We choose the duration of the train as a whole according to the condition τ _burst <t _T1 , _tr , which for the above t _T1 , t _r gives the estimate: τ _burst <73 ns. The parameter Δt, calculated according to Δt=τ _burst /(N _P -1), for the specified N _p =8 is estimated as Δt<10.4 ns. We choose according to this inequality Δt=9 ns. Comparison of this Δt with the above t _p2 =0.57 ns shows that the condition Δt>t _P2 is indeed satisfied. The duration τ of a single pulse in a train will be found from the relation (18)τ=E ₀ (GR _s ) as τ=18-23 ps for the indicated E ₀ ≈114 μJ and Г=1÷1.25. In this case, the value τ=18 ps (for Г≈1.25) practically coincides with the duration τ=19 ps of an individual pulse reported in this experiment.

The estimates performed show that the time parameters of the train (the duration of the entire train as a whole τ _burst , the time interval Δt between pulses in the train and the duration τ of an individual pulse of the train) are predicted in the proposed method in good agreement with the experiment under consideration. The number of pulses in the train N _p (=8) also coincides with the experiment.

However, this experiment demonstrates a number of parameters that are very different from those recommended by the method proposed here.

Firstly, at stage 1, based on the small value f _burst =10 kHz reported in the experiment, the authors of this work used f _burst in the low-frequency range of train repetition frequencies, f _burst ≤f ₂ , which, according to the proposed method, is not favorable for obtaining separation with improved smoothness for this material. In this case, in the experiment, the speed of the relative movement of the laser beam and the material, accordingly, turns out to be extremely small, u = 0.1 m/s, while the calculation suggests u = 5.9 m/s. As we noted, for this non-hardened material, obtaining improved smoothness and high speed requires the use of f _burst in a different, high-frequency range of repetition rates. In this case, f _burst is estimated to be 1.73 MHz, which is 173 times greater than the value of 10 kHz indicated in the experiment.

Secondly, the filament pitch used in the experiment, s ₁ =10 μm, is almost 3 times larger than the calculated s1 = 3.4 μm, which also does not contribute to obtaining improved smoothness of separation.

Thirdly, instead of the same energies of train pulses recommended by the proposed method, the first two pulses of the train in this experiment have approximately twice the amplitudes compared to the others, which, from the point of view of our model, is another factor responsible for the heterogeneity of the diameter of the filament impact zones observed in the experiment along their length.

Thus, the very low smoothness of the side walls of the separation observed in the indicated experiment can be explained by significant differences between this experiment and calculations according to the proposed method for the indicated three parameters s ₁ , f _burst and E _0i , with the value being especially large, by two orders of magnitude, the difference in the value of f _burst , as well as a threefold difference in the value of s ₁ .

EXAMPLES OF IMPLEMENTATION OF THE INVENTION

After successful testing of the method described above, we use it to calculate the parameters of the LPR with improved smoothness for various materials of different thicknesses, for which we use different input values _rf , N and the choice of different w in the calculation.

Example 1. LPR of chemically tempered glass

Table 3 shows the results of these calculations for chemically tempered glass. Examples 1.1-1.4 are given for thin plates (thickness from 50 to 750 µm), and Examples 1.5-1.7 for thick plates with a thickness of more than 10 mm, for which we assume the filament length required for separation H = 10000 µm = 10 mm. As Example 1.1, the calculation data obtained above is given to explain Experiment 1, which is noted in this table in the Note to the corresponding column 1.1.

Example 2. LPR of display glass

Table 4 shows the preferred irradiation parameters for obtaining improved smoothness for thin slabs of display glass for various r _f and w (Examples 2.1-2.5).

In the calculations for this material, according to literature sources, we use the following input data: the mechanical strength limit is taken equal to σ _c = 0.6 kJ/cm ³ (0.6 GPa), which is significantly inferior to the similar parameter σ _c = 2 kJ/cm ³ (2 GPa) discussed above tempered glass Corning Gorilla Glass 5. w _dis =64 kJ/cm ³ , as before μ=60 g/mol, N _at =3, λ _ha ≈220 nm. We also use the initial temperature T _i =20°C and Г=1÷1.5. λ=1.04 µm and r _f =0.5 µm in Examples 2.1-2.3 and λ=0.52 µm, r _f =0.25 µm in Example 2.4. Thin plates with a thickness of L=550 microns are considered, as above in Examples 1.1-1.4. For this material, we also select the filament length H = 45 µm for calculations. We assume, as before, K _tw ≈K _sw ≈0.5, which corresponds to a “fast” energy release (t _E <t _P1 , t _P2 ), when the energy losses associated with the excitation of the shock wave are significant. Since this material has a lower tensile strength than tempered glass (with very similar other material parameters), to obtain improved smoothness for it, as mentioned above, it is preferable to use the effect of directional splitting, which is realized in the range of high repetition frequencies of trains at f _burst = (1-3)f ₁ . Therefore, Table 4 shows calculation data only for f _burst =3f ₁ , and the range of low frequencies of repetition of trains f _burst ≤f ₂ , which is not preferable for this material, unlike tempered glass, is not considered.

Examples 2.1-2.3 in Table 4 for λ=1.04 µm were obtained for w=2w _dis , 3w _dis and 4w _dis respectively. At the same time, for separation with improved smoothness, movement speeds of 6.20 m/s, 4.38 m/s and 3.57 m/s and average powers of 11 W, 8.1 W and 7.2 W were obtained, respectively. From the point of view of obtaining not excessively high, but not excessively low speeds for a given material, the range w=(3÷5)w _dis , but not more than the limit w ₁ , seems preferable.

If it is necessary to create a longer filament for separation, for example, a length of 495 μm, which is 11 times longer than the length H = 45 μm used in the above calculations and practically (90%) covers the above-mentioned plate thickness L = 550 μm, the P values will also increase 11 times to 120 W, 89 W and 79 W, respectively. As a specific calculation of the parameters, Table 4 gives Example 2.4 for H=495 μm and w=4w _dis when P is 79 W.

For comparison, column 2.5 (Example 2.5) provides data for irradiation with half the wavelength λ=0.52 μm at OPE w=3w _dis . In this case, it increases by 2 times to 8.76 m/s compared to Example 2.2, where the same OPE was used. The average power turns out to be the same: P = 8.1 W.

Examples 2.1-2.3, 2.5 show that for H=45 µm pulses with a duration of approximately 90 fs to 380 fs are required. However, to create the aforementioned 11 times longer filaments at 495 µm in Example 2.4, the pulse duration increases to values from 2.75 to 4.14 ps. The number of pulses N _p in a train in the indicated modes is selected to be no less than 5-7.

Example 3. LPR of sapphire

Table 4 in columns 3.1-3.3 also discusses examples of calculating parameters for LPR of thin plates of sapphire, which is a crystalline material. We use a laser with a radiation wavelength of λ=1.04 microns. We believe that the filaments have the same characteristic length Н = 45 μm and radius about r _f = 0.5 μm as in the experiment [Mikalauskas S, Raciukaitis G. md Las Sol 5, 22-27 (2016)] on the separation of sapphire by radiation with the same λ. We are considering thin plates with a thickness L=150-550 microns, which is common in applications for mobile devices. According to the literature data, we use for this material P _s (λ = 1.04 μm) = 2.8 MW, w _dis = 78 kJ/cm ³ , ρ ₂ = 3.97 g/cm ³ , C _nt ≈1.22 J/(g⋅K), those same A _LP =0.8 and A _P-H =0.9, T _mod =T _melt =2050°C, χ=2×10 ^-2 cm ² /s, c _s =6×10 ⁵ cm/s, μ=102 g /mol, N _at =5, λ _ha =148 nm and σ _c =3.0 GPa (kJ/cm ³ ). We assume, as in the Examples above, the initial temperature T _i =20°С, Г=1÷1.25 and K _tw ≈K _sw ≈0.5, which corresponds to “fast” energy release (t _E <t _P1 , t _P2 ), when losses The energies associated with the excitation of the shock wave are significant. All this data according to the calculation algorithm shown in Fig. 21, we use as input parameters.

To obtain separation with improved smoothness for this material, it is preferable to use the effect of directional splitting, which is realized according to (10) in the range of high train repetition frequencies f _burst =(1÷3)f ₁ Therefore, calculation data are indicated only for f _burst =3f ₁ , and We do not consider the range of low repetition frequencies of trains f _burst <f ₂ .

In Example 3.1, when choosing w as w = 2w _dis = 156 kJ/cm ³ , the required speed of relative movement of the laser beam and material of about 52 m/s is too high, and therefore is hardly feasible at the current technical level.

Therefore, further in Example 3.2, a calculation is performed for a different value of filament OPE w = 800 kJ/cm ³ , which is 5 times higher than the value used above in Example 3.1 of 156 kJ/cm ³ . In this case, condition (11) is satisfied, i.e. w≤w ₁ =860 kJ/cm ³ , which, according to our method, provides significant suppression of filament energy losses due to radiation and thereby provides the driving force and efficiency of the LPR process. The speed of relative movement of the beam and material decreases in this case by 3 times to u=17.0 m/s. However, this value also seems too large for practical use.

To further reduce and in Example 3.3 with the same filament length H = 45 μm, we use relatively thick filaments with a radius r _f = 1.5 μm, which is 3 times larger than the radius r _f = 0.5 μm used above in Examples 3.1 and 3.2, and corresponds to less sharp focusing, i.e. with smaller numerical aperture. For such r _f, the limit on OPE is w ₁ = 620 kJ/cm ³ , therefore, to satisfy condition (11) w≤w ₁ , we select w = 550 kJ/cm ³ . The speed of relative movement of the beam and material then drops to a technically acceptable value of about u=7.0 m/s. In this case, the average power in the material is P = 135 W, the number of pulses in the train N _p = 10, the duration of individual train pulses τ = 5.2÷7.8 ps and the train repetition frequency f _burst of about 620 kHz (see more details in column 3.3 in the Table 4).

The specific examples obtained in Tables 3 and 4 allow us to draw the following conclusions.

The claimed method quantitatively finds the parameters necessary to set the SFCI mode with obtaining improved smoothness of the separation walls - this is the energy E _burst of a pulse train in the material, the number N _p of pulses in the train, the average energy of individual pulses of the train E ₀ , the repetition rate f _burst of trains, the repetition step s ₁ filaments in the material, the duration τ _burst of the train as a whole, the time interval Δt between pulses in the train and the duration r of an individual pulse in the train, as well as the average power of laser radiation P, the speed u of the relative movement of the laser beam and the material and the energy efficiency Ω of the LPR process. The values of all these parameters are consistent with each other through their dependence on the control parameters, which are the OPE w of the filament, its radius r _f and length H. The specified complex of a total of 14 parameters uniquely sets the irradiation mode preferable for cutting pulse trains with improved smoothness.

According to Tables 3 and 4, to separate thin plates, the duration of individual pulses τ is required from 90 fs to 8 ps, the number of pulses in a train from 3 to 15 or more and the average radiation power in the material from 0.4 W to 135 W depending on the material selected by the OPE w filament and one or another (high- or low-frequency) range of train repetition frequency.

If it is necessary to create a filament of great length, for example, H = 10 mm (which corresponds to the separation of thick glass plates with a thickness of more than 10 mm in Examples 1.5-1.7), then for glass the average laser radiation power in the material is 44-550 W or more, depending depending on the material and OPE w, the number of pulses in the train N _p is selected from 3 to 6 or more, and, for example, with Np = 6, the duration of individual pulses in the train t is in the range of 24-63 ps.

As noted above in the section “Justification of the conditions for achieving technical results”, as an additional factor for obtaining improved roughness, from calculations according to this method and algorithm, it is preferable to also use solutions (and the corresponding irradiation parameters) that provide a reduced filament step size s ₁ , for example, in the range s ₁ ≈0.5÷3.5 µm instead of s ₁ ≈4÷7 µm known in the literature. To do this, use: (a) focusing with a small radius r _f of the filament due to sharper focusing of the laser beam, and/or due to shortening the wavelength of laser radiation λ, and/or (b) a limited value of the OPE

These examples show that in addition to improved separation smoothness, it is also possible to achieve high energy efficiency Ω of the LPR process, estimated as and high speed relative movement of the laser beam and material (about 0.15÷52 m/s or more, depending on the material and irradiation parameters) when using one or more of the following factors: the preferred choice of OPE as (see Examples 1.2-1.4, 1.5-1.7, 2.1-2.4, 3.1), reducing the filament radius r _f by reducing the laser wavelength λ and/or using a larger numerical aperture of the focusing system (see Examples 1.3, 1.4, 1.5, 1.6, 2.4), the use of a material with a relatively low (no more than 600°C) temperature critical for the separation of the modification - T _strain or T _melt , the use of train repetition frequency in the high-frequency range, i.e. preferably f _burst >>f ₁ (see Examples 1.1.-1.3, 1.6, 1.7, 2.1-2.4, 3.1-3.3), and/or use for separation of material with a sufficiently long energy release time t _E >t _P2 , which corresponds to suppression to an insignificant fraction of Ksh of unwanted energy loss carried away by the shock wave. This makes it possible to obtain record high cutting speeds - about 11÷52 m/s or more depending on the material (Examples 1.3, 3.1, 3.2), which is tens and hundreds of times higher than the characteristic cutting speeds of glass, sapphire and other transparent materials using known mechanical methods and tens of times - the characteristic separation rates using known methods of laser-controlled thermal splitting using irradiation with continuous lasers. However, such high-speed modes have practical meaning as long as the resulting high speed does not exceed the technical capabilities of varying the speed of relative movement in a particular installation.

In addition, LPR modes have been found that make it possible, at a moderate average laser power, to cut tempered, non-tempered glass and sapphire with a relatively moderate and acceptable for application moving speed of the order of 3-7 m/s (see Examples 1.2, 2.1-2.3, 3.3).

On the other hand, it was found that the choice of repetition frequency in the low-frequency range, f≤f ₂ and the use of a short radiation wavelength (for example, λ = 0.52 μm instead of 1.04 μm) make LPR possible for tempered glasses at extremely low average laser power (from fractions W), providing, however, although not a record high, but a considerable cutting speed of about 0.2 m/s acceptable for applications (Examples 1.4 and 1.5).

According to the data given for chemically tempered glass Corning Gorilla Glass 5 (see Examples 1.1-1.7), it is preferable to choose a filament radius in the range r _f = 0.2-0.5 µm, OPE in the range preferably in the range number of pulses in a train

For Corning Eagle XG™ display glass (see Examples 2.1-2.5) or quartz glass, it is preferable to select the filament radius in the range r _f =0.2÷0.5 µm, w in the range preferably in the range but at the same time no more than the limit w ₁ , the number of pulses Np in the train is not less than a certain value, Where and the repetition rate of pulse trains is in the high-frequency range preferably in the range

At the same time, for sapphire, the filament radius is chosen for calculations, preferably in the range r _f = 1.3-1.7 μm, w in the range preferably in the range w=(7÷11)w _dis , but not more than the limit w ₁ , and the number of pulses in the train - from the condition Np≥ Where (See Example 3.3).

Note that the given specific calculations are only explanatory examples and by no means exhaust the variety of different cases of application of this method, including both the variety of transparent materials and the variety of methods used for creating filaments, as well as exposure to radiation not only with the considered wavelengths λ = 1.04 and 0.52 microns, but also with other λ, and therefore do not limit the scope of application of the method. The processed material can be display glasses used in liquid crystal displays (LCD), flat panel displays (FPD) and organic veto-emitting displays (OLED), or automotive glass, quartz glass, windows, biochips, optical sensors, planar light guides, clear glasses and hollow cylinders, art products, microelectronic chips, memory chips and cards, touch chips, light-emitting diodes (LEDs), laser diodes (LDs), and vertical cavity surface emitting lasers (VCSELs). Also, transparent and translucent materials other than the above glasses can be used as the separated material: sapphire, diamond, ceramics, polymers, conductors, semiconductors, glass ceramics, crystalline zirconium dioxide with varying levels of stabilizing additives, silicon carbide (SiC), nitride gallium (GaN), as well as selenides, sulfides, chlorides, bromides, fluorides, for example, zinc selenide (ZnSe), zinc sulfide (ZnS), sodium chloride (KCl), potassium bromide (KBr), calcium fluoride (CaF ₂ ), barium fluoride (BaF ₂ ), magnesium fluoride (MgF ₂ ), lithium fluoride (LiF).

The given specific examples give an idea of the characteristic orders of magnitude of radiation parameters, the ranges of their variation and their agreement with each other in various situations. For example, in the case when it is necessary to create a filament of a different length in the thickness of the material than that indicated in these tables, or the simultaneous creation of two or more sets of filaments with the length H = 45 μm indicated in the examples, then when creating them simultaneously (for example, using the multifocusing method) the required values of the average power and energy of the train will increase compared to those indicated in the given Examples and tables in proportion to the change in the total width of several such sets compared to the values of H indicated in the given Examples. The results of calculations of the required radiation parameters can also be easily recalculated for filament radii that differ from those indicated in the Examples given.

The set of essential features of the method and device is described by the claims below.

Claims (219)

1. A method of laser filamentation separation (LFR) of a brittle material, including the creation of a filament by a pulse train (SPTS), while the filaments do not overlap each other along their radii in the volume of the material, characterized in that the filament is created using the duration τ _burst [s] of a train with a limited value, i.e. τ _burst < t _r , t _T1 , t _r = r _f /u [s] - time of holding the laser beam within the radius of the filament r _f , taking into account the movement of the beam relative to the material with a speed u [cm/s]; r _f [cm] - radius of the filament at the level (1/e) of the decrease in volumetric energy density (VED) w [J/cm ³ ] from the filament axis along the radius r in the approximation of the Gaussian distribution w(r); t _T1 = r _f ² /(4χ) [s] - heat retention time within the filament radius r _f ; χ [cm ² /s] - average value of the thermal diffusivity of the material in the temperature range from the initial temperature T _i = 293 K to the order of T _mod ; T _mod [K] - temperature, which for amorphous materials is T _mod = T _strain , and for crystalline materials T _mod = T _melt ; T _strain [K] - glass transition point of an amorphous material; T _melt [K] - melting point of crystalline material; in this case, the OPE w [J/cm ³ ] of laser pumping of the filament on its axis is selected with a limited value, i.e. according to the condition w ≤ w ₁ , where the limiting limit w ₁ [J/cm ³ ] is numerically from 200 to 1000 kJ/cm ³ depending on the material and the radius r _f of the filament; the specified limit w ₁ is assessed taking into account the coefficient K _sw of converting filament energy into a shock wave: w ₁ = [1/(1-K _sw )]ρC _HT (T ₁ - T _i ) + w _dis , where ρ [g/cm ³ ] - density of the material; C _HT [J/(g×K)] - specific heat capacity of the material at temperatures above the dissociation temperature of the material, which for glasses is >2500-3000 K; T ₁ [K] - corresponding limit w ₁ filament plasma temperature limit; T _i = 293 K - initial temperature of the material before irradiation; w _dis [J/cm ³ ] - RPE of irreversible losses due to dissociation of the material during laser heating; C _HT is estimated as _CHT = 3RN _at /μ; R = 8.31 J/(mol×K) - universal gas constant; N _at - dimensionless parameter, the number of atoms in 1 molecule of material; μ [g/mol] - molar mass of the material; temperature limit T ₁ is estimated as T ₁ = [16(ln2) ^1/2 β _max C _HT ρχ /(σr _f )] ^1/3 ; β _max = 0.12; σ = 5.67 × 10 ^-12 W/(cm ² × K ⁴ ) - Stefan's constant; limit w ₁ according to OPE is calculated as w ₁ = 2ρC _HT (T ₁ – T _i ) + w _dis at K_sw = 0.5, when, accordingly, time t_E[c] energy release during relaxation of electronic levels of the material excited by a laser pulse relatively little, i.e. t _E << t _P1 ; t _P1 [s] is the time of inertial retention of the shock wave pressure in the filament, which is estimated as t _P1 = 2r _f /c _sw ; c _sw [cm/s] - shock wave speed in the material in the micron vicinity of the filament; or the limit w ₁ is calculated as w ₁ = ρC _HT (T ₁ – T _i ) + w _dis at K _sw << 1, when time t _E > t _P1 , i.e. t _P1 < t _E < t _T1 . 2. The method according to claim 1, characterized in that the parameters of laser irradiation are quantitatively determined, completely defining the LPR process in the SFC mode with the roughness value R _{a of} the side walls of the separation not exceeding 0.1 μm: energy E _burst [J] of the pulse train in the material , average energy E ₀ [J] of individual pulses of the train, repetition frequency f _burst [Hz] of trains, repetition pitch s ₁ [cm] of filaments in the material, duration τ _burst [s] of the train as a whole, duration τ [s] of an individual pulse in train, time interval Δt [s] between pulses in a train and their number N _p in a train, average power of pulse-periodic laser radiation in the material P [W], speed of relative movement of the laser beam and material u [cm/s], and also energy efficiency Ω [cm ² /J] of the LPR process based on setting control parameters - radius r _f , length H [cm] and OPE w of the filament; To do this, use the following sequence to find the specified irradiation parameters: at the initial stage: set the input parameters - laser radiation wavelength λ [cm], material thickness L [cm], filament radius r _f [cm] and their length H [cm], selected by the operator to perform the LPR process; use reference data on w _dis , P _c (λ), ρ ₂ , C ₂ , μ, χ, c _s , N _at , σ _c , as well as T _mod = T _strain for an amorphous material, or T _mod = T _melt for crystalline material; use the values T _i = 293 K, Γ = 1-1.25, ϕ = 1.4, A _LP = 0.8, A _PH = 0.9; where P _c (λ) [W] is the critical power for self-focusing in an individual pulse, depending on λ; ρ ₂ [g/cm ³ ] - average value of the density of the material in the temperature range from T _i = 293 K to T _mod ; C ₂ [J/(g×K)] - the average value of the specific heat capacity in the temperature range from the initial (room) T _i = 293 K to T _mod ; c _s [cm/s] - speed of sound in the material, which is used in the calculations below instead of c _sw ; σ _c [kJ/cm ³ ] - the compressive strength of the material under shock wave action; T _i [K] - initial (room) temperature; Γ is a dimensionless parameter, selected empirically in the range 1-1.25; ϕ = R _T /R _sw is a dimensionless parameter, a coefficient showing how many times it is desirable to reduce R _sw in relation to R _T by using the number of pulses N _p0 in the train; R _sw [cm] - radius of the cylindrical zone of shock wave action around the filament axis; R _T [cm] - radius of the cylindrical impact zone around the filament axis due to the thermal conductivity mechanism; A _LP - dimensionless parameter, nonlinear (depending on OPE w) absorption capacity of the filament; A _PH - dimensionless parameter, conversion coefficient, describing the fraction of thermal energy from the filament plasma E _tw [J] converted into heat Q [J]; at stage 1: calculate the time t _P1 of inertial retention of the pressure of the shock wave in the filament, as t _P1 = 2r _f /c _s ; calculate the heat retention time t _T1 within the filament radius using the above r _f and χ: t _T1 = r _f ² /(4χ); use K _sw = 0.5 if the energy release time t _E of the material is relatively short, i.e. t _E << t _P1 ; or use K _sw << 1, which, according to paragraph 1, corresponds to a time t _E exceeding time t _P1 , i.e. t _P1 < t _E < t _T1 ; calculate C _HT , T ₁ and w ₁ ; For irradiation, the “high-frequency” frequency range of pulse train repetition f _burst [Hz] is used, i.e. f _burst ≥ f ₁ , where f ₁ [Hz] is the lower limit of this range, in which η varies in the range η = 0.76-1, η is the dimensionless coefficient of thermal conductivity cooling of the material in the space between adjacent filaments from any pulse train by the time the maximum heating of this interval is reached by the next in time and adjacent in space pulse train; or use the “low-frequency” range of train repetition frequencies, i.e. f _burst ≤ f ₂ , where f ₂ [Hz] is the upper limit of this range, in which η ≤ 0.1; accordingly, select a specific value of η from one or another specified range; for chemically tempered glasses, the “high frequency” or “low frequency” range is used, and for non-tempered materials, it is preferable to use only the “high frequency” range, further limiting f _burst in this range, as f _burst = (1-3)f ₁ ; at stage 2: use the value of filament plasma OPE that satisfies the condition: w ≤ w ₁ ; calculated from the specified input data C ₂ , ρ ₂ , T _mod , T _i and the value η selected above, the modification threshold w _mod [J/cm ³ ] for the thermal mechanism w _mod = C ₂ ρ ₂ (T _mod -T _i )/(1+ η); at stage 3: From the above parameters, the energy of the pulse train in the material E _burst and the maximum permissible step of filaments in the material s _1max [cm] to obtain a smooth separation are calculated: E _burst = πr _f ² Hw/A _LP , s _1max = 2[(1/e)(1-K _sw )A _PH (ww _dis )/w _mod ] ^1/2 r _f ; use a limited step of filaments s ₁ according to the condition s ₁ ≤ s _1max , providing partial overlap of thermal impact zones from neighboring filaments; use s ₁ = 0.9s _1max ; for the above w, w _mod and the above σ _c and K _sw (= 0.5, or << 1) calculate the limits N _p0 and N _p1 : N _p1 = [w/ (0.8w _dis )] + 1; in this case, square brackets [ ] in these last two expressions denote the integer part of the number in these brackets; the number of pulses in the train N _p is chosen according to the condition Np ≥ max (N _p0 , N _p1 ); at stage 4: calculate the energy efficiency Ω [cm ² /J] of the LPR process Ω = 2s ₁ Н/E _burst , using the above s ₁ , H and E _burst ; calculate the frequency limits f ₁ and f ₂ depending on the degree of overlap of adjacent impact zones, characterized by the ratio (s ₁ /s _max ) from 0.6 to 1, as f ₁ = (12-18)χ/s ₁ ² , f ₂ = (0.22-0.70)χ/s ₁ ² ; for the above (s ₁ / s _1max ) = 0.9 use the relations f ₁ = 13.3 χ/s ₁ ² , f ₂ = 0.547χ/s ₁ ² ; in accordance with the previously selected value of η, the frequency of repetition of trains f _burst is used in the “high-frequency” range, i.e. f _burst ≥ f ₁ , or in the “low frequency” range, i.e. f _burst ≤ f ₂ ; calculate the time t _P2 [s] of inertial retention of the shock wave pressure in the space between adjacent filaments t _P2 = s ₁ /c _s ; the energy E _0i [J] (i = 1.2,..N _p ) of individual train pulses in the material is taken to be the same for all train pulses and is calculated for the E _burst and N _p found above as E _0i = const = E ₀ = E _burst /N _p ; at stage 5: calculate the average power P of pulse-periodic laser radiation in the material P = E _burst f _burst and speed u of the relative movement of the laser beam and material u = s ₁ f _burst when substituting the above E _burst , f _burst and s ₁ ; calculate the time t _r for holding the beam position for a given r _f and u found above: t _r = r _f /u; use the duration of the train as a whole τ _burst according to the condition of limiting its value τ _burst < t _T1 , t _r ; the time interval ∆t between pulses in a train is found as ∆t = τ _burst /(N _p - 1), in this case, between ∆t and t _P2 the following relation is observed: ∆t > t _P2 ; The duration τ of an individual pulse is taken to be the same for all pulses in the train and is calculated as τ = E ₀ /[ΓР _с (λ)]. 3. The method according to claim 2, characterized in that, in addition to obtaining the specified level of roughness, the energy efficiency Ω of the LPR process is increased, for which, when quantitatively determining the irradiation parameters, at least one of the following additional restrictions is applied: preferably choose w in the range (2-3)w _dis , but not more than w ₁ ; reduce the radius of the filament r _f by using a shorter wavelength λ of laser radiation than 1.03 μm and a larger focusing numerical aperture NA (more than 0.5); use a material with a modification temperature critical for separation, T _strain or T _melt , not more than 870 K; use the frequency of repetition of trains in the “high-frequency” range, i.e. f _burst ≥ f ₁ , preferably f _burst >> f ₁ ; use a material with energy release time t _E > t _P1 ; in addition to the indicated increase in Ω, with LPR, the speed u of the relative movement of the laser beam and the material is also 4-52 m/s, depending on the material and irradiation parameters, for which the above list of restrictions when quantitatively finding irradiation parameters is supplemented with two more restrictions that apply separately or together: they use a material with a higher χ value (for sapphire χ is 4-5 times higher than for quartz glass); use a reduction in the ratio s ₁ / s _1max to values less than 0.9, using a higher degree of overlap of the radii of thermal action of the filaments. 4. Method according to claim 2 or 3, characterized in that LPR is carried out with a low-power laser beam, i.e. with an average power P from tenths of W, while at least one of the following additional restrictions is used to find the irradiation parameters: use the frequency of repetition of trains f _burst in the “low-frequency” range, i.e. f _burst ≤ f ₂ ; use filaments with a length H of no more than several tens of microns; w is preferably chosen in the range (2-3)w _dis , but not more than w ₁ ; use a material with energy release time t _E > t _P1 ; they use material with a relatively small χ value, i.e. quartz or display glass instead of sapphire; In addition to the indicated low power P, LPR is performed at a speed u of the relative movement of the laser beam and material up to about 20-30 cm/s, for which, when quantitatively determining the irradiation parameters, the specified list of restrictions is supplemented with several more restrictions, which are applied separately or together: use f _burst = f ₂ ; they use filaments with radii r _f less than 0.5 µm, which is achieved through the use of a numerical aperture of the focusing system NA of more than 0.5 and due to the wavelength λ of laser radiation no more than 1.03 µm. 5. Method according to claim 3 or 4, characterized in that the material with energy release time t _E > t _P1 , t _P2 is used as: a material, when heated by a train of pulses, structural defects and the resulting long-lived states of electronic excitation with t _E of the specified value arise; a material for which structural defects and the long-lived states caused by them with the specified t _E are created due to: - composition of the material, its modification; - auxiliary influence on the material in the zone of movement of the LPR laser beam through it before its passage through the material. 6. The method according to claim 2, characterized in that chemically tempered Corning Gorilla Glass 5 is used as the material for LPR, and at least one of the following restrictions is used to quantitatively determine the irradiation parameters: the filament radius is chosen in the range r _f = 0.2-0.5 μm; The OPE of the filament is selected in the range w = (1.8-6)w _dis , but not more than the limit w ₁ ; the number of pulses in the train N _p is chosen to be no less than a certain minimum value, N _p ≥ N _p ^min , where N _p ^min = 3-6. 7. The method according to claim 2, characterized in that Corning Eagle XG™ display glass or quartz glass is used as the material, and at least one of the following restrictions is used to quantitatively determine the irradiation parameters: the filament radius is chosen in the range r _f = 0.2-0.5 μm; OPE w of the filament is selected in the range w = (1.8-6)w _dis , preferably in the range w = (3-4)w _dis , but not more than the limit w ₁ ; the number of pulses N _p in a train is chosen to be no less than a certain minimum value N _p ^min , i.e. N _p ≥ N _p ^min , where N _p ^min = 5-7; the frequency f _burst of repetition of pulse trains is chosen in the “high-frequency” range, where f _burst ≥ f ₁ , preferably in the range f _burst = (1-3) f ₁ . 8. The method according to claim 2, characterized in that sapphire is used as a material for LPR, and one or more restrictions are applied to quantitatively determine the irradiation parameters: the filament radius is preferably chosen in the range r _f = 1.3-1.7 μm; The OPE of the filament is selected in the range w = (2-11)w _dis , preferably in the range w = (7-11)w _dis , but not more than the limit w ₁ ; the number of pulses in the train N _p is chosen not less than the minimum value N _p ^min , i.e. N _p ≥ N _p ^min , where N _p ^min = 9-13; The repetition frequency f _burst of laser pulse trains is selected in the “high-frequency” range f _burst ≥ f ₁ , preferably in the range f _burst = (1-3) f ₁ . 9. The method according to claim 3 or 4, characterized in that in order to increase the energy efficiency of the LPR and obtain separation at a high speed of up to tens of m/s, as well as to achieve high speed in the irradiation mode with low laser power from tenths of a W, a laser with the radiation wavelength λ is less than 1.03 µm, and filaments with a radius r _f less than 0.5 µm and a repetition pitch s ₁ of less than 6 µm are used. 10. The method according to claim 2, characterized in that to perform LPR, the irradiation parameters E _burst , E ₀ , s ₁ , f _burst , τ, Δt, t _burst and N _p are used, of which one or more parameters differ, but not more than 2-3 times higher or lower than the corresponding values of these parameters calculated according to paragraph 2 with the same input parameters r _f , H and w. 11. The method according to claim 2, characterized in that in addition to the quantitative calculation of irradiation parameters for carrying out LPR, their values are experimentally clarified: OPE is chosen as w ≤ w ₁ ; with an excess of several times over N _p0 , the number of pulses in the train is selected, i.e. N _p ≥ (2-3)N _p0 , N _p1 ; the frequency of repetition of the trains f _burst is chosen in excess of f ₁ : f _burst = (2-3) f ₁ , and the parameter η is chosen corresponding to this range as 0.8-1; the time interval Δt between pulses is selected in excess of t _P2 : Δt ≥ (2-3)t _P2 ; for the parameters r _f , H, w, E _burst , E ₀ , f _burst , τ, Δt, t _burst , N _p and u their selected and calculated values are used, while the filament step size s ₁ is refined by its experimental selection, comparing the results of LPR obtained at different s ₁ , i.e. for different u=s ₁ f _burst for fixed f _burst ; the lower and upper limits of the range of variation in the experiment of the value of s ₁ are chosen to differ by no more than 1.4 times, respectively, on the smaller and larger sides of the calculated value of s ₁ ; find in the experiment the optimal value of s ₁ for which the result of LPR is achieved with the best smoothness of the side walls of the separation; preferably, the specified procedure is also performed for a different choice of OPE w, thereby expanding the number of experiments from which the result with the best separation smoothness is found. 12. Method according to any one of paragraphs. 1-11, characterized in that filaments in the volume of transparent material are created by laser irradiation due to the nonlinear optical process of self-focusing in the material of a high-intensity laser beam or the use of methods used along with self-focusing or without it, ensuring the creation in the material of an elongated focusing area of the laser beam along its axes; To perform LPR of materials with a thickness of 7-10 mm and more preferably, a combination of Gaussian-Bessel beams with the SFC mode is used, which makes it possible to create filaments with a length of more than 1 mm. 13. Method according to any one of paragraphs. 1-12, characterized in that they implement non-ablative separation of the material with zero cutting width, for which the position of the created filaments is chosen entirely within the volume of the material, and during laser irradiation they do not come out to either the front or rear surface of the processed sample, without creating an ejection material into the surrounding area in the form of vapors, drops or solid fragments. 14. Method according to any one of paragraphs. 1-13, characterized in that LPR is performed for a material that is part of a multilayer composition consisting of layers of the same transparent or translucent material located on top of each other, or including layers of various transparent and translucent materials, solid and/or liquid ; these layers may have different thicknesses, and the material layer subject to LFR may be the first in the specified composition, i.e. facing the laser beam, or the last layer, i.e. on the back side of the specified multilayer composition, or enclosed between other layers. 15. Method according to any one of paragraphs. 2-14, characterized in that for LPR they use parts with a non-flat surface containing, at least as an element, a surface section in the form of a figure of rotation, i.e. cylindrical tubes, optical fibers and other axisymmetric parts - spheroids, ellipsoids, hyperboloids, other reliefs with curvature, while the relative movement of the laser beam and the specified part, along with other possible types of movements, includes its rotation around the axis of symmetry of the above-mentioned figure of rotation; They use flexible materials for LPR using relative movement of the material and the laser beam according to the “reel to reel” scheme. 16. Method according to any one of paragraphs. 1-5, 9-15, characterized in that for LPR they use: display glasses used in liquid crystal displays (LCDs), flat panel displays (FPDs), and organic light-emitting displays (OLEDs); automotive glass, windows, biochips, optical sensors, planar light guides, transparent glasses and hollow cylinders, art products, heat-sinking substrates for microprocessors, memory cards, touch chips, light-emitting diodes (LEDs) and laser diodes (LDs); diamond, ceramics, polymers, transparent conductors, semiconductors, glass ceramics, crystalline zirconium dioxide with varying levels of stabilizing additives, silicon carbide (SiC), gallium nitride (GaN), as well as selenides, sulfides, chlorides, bromides, fluorides, for example, zinc selenide (ZnSe), zinc sulfide (ZnS), sodium chloride (KCl), potassium bromide (KBr), calcium fluoride (CaF ₂ ), barium fluoride (BaF ₂ ), magnesium fluoride (MgF ₂ ), lithium fluoride (LiF) . 17. A device for LPR of a fragile material, containing a pulse-periodic laser, a unit for forming and focusing the laser beam, a unit for creating the SCFI mode, a system for fastening and moving the material under the laser beam with adjustable focus position in depth, characterized in that it contains a numerical program control unit , made with the ability to set irradiation parameters for the SCFI mode: r _f , H, w, E _burst , E ₀ , f _burst , s ₁ , τ _burst , τ, Δt, N _p , P and u according to the values determined for the implementation of the method according to any one of paragraphs. 1-16. 18. The device according to claim 17, characterized in that when thin materials are used for LPR, including display glass with a thickness of 0.5-0.75 mm, chemically tempered glass with a thickness of 0.3-0.7 mm and sapphire with a thickness of 0.05 -0.3 mm, irradiation parameters are set in the following ranges: laser radiation wavelength λ - from 0.3 μm to 2 μm, or in part or parts of this range, or λ can take discrete values of 0.52 μm, 1.04 μm; filament radius r _f : 0.2-1.7 µm; filament length H: 30-750 µm; OPE filament w: 115-900 kJ/cm ³ ; pulse train energy E _burst : 1-250 µJ; number of pulses in a train N _p : 2-25; average energy of one train pulse E ₀ : 0.1-25 μJ; pitch of filaments in the material s ₁ : 1.2-13 µm; average laser power in material P: 0.4-150 W; train repetition frequency f _burst : 10 kHz-5 MHz; speed of relative movement of the laser beam and material u: 1-1200 cm/s; pulse train duration τ _burst : 5-130 ns; time interval between pulses in a train Δt: 1-30 ns; duration of an individual train pulse τ: 90 fs-9 ps. 19. The device according to claim 17 or 18, characterized in that when using transparent and translucent materials with a relatively large thickness (10-12 mm or more) for LPR, including chemically tempered glass and non-tempered display glass, the irradiation parameters are set in the following ranges : filament length H: 7-10 mm, and a Gaussian-Bessel beam is preferably used as a focusing system to create filaments of the specified length; filament radius r _f : 0.2-0.5 µm; wavelength λ of laser radiation in the range of 0.5-1.1 μm, or λ can take discrete values of 0.52 μm, 1.04 μm in the specified range; OPE filament w: 115-260 kJ/cm ³ ; pulse train energy E _burst : 230-2100 µJ; number of pulses in a train N _p : 3-7; average energy of an individual pulse in a train E ₀ : 40-380 μJ; pitch of filaments in the material s ₁ : 1-7 µm; average laser power in material P: 40-2000 W; train repetition frequency f _burst : 10 kHz-4.2 MHz; speed of relative movement of the laser beam and material u: 5-1000 cm/s; pulse train duration τ _burst : 4-110 ns; time interval between pulses in a train Δt: 1-24 ns; duration of an individual train pulse τ: 17-75 ps. 20. The device according to claim 18 or 19, characterized in that the installation of at least some of the specified calculated irradiation parameters is performed “manually”. 21. The device according to any one of paragraphs. 17-20, characterized in that it is configured to rotate a part having a non-flat surface in the form of a figure of revolution, relative to the laser beam around the axis of symmetry of said part; in this case, the angular velocity of said rotation is selected so as to ensure the required value of the speed u of the relative movement of the laser beam and the specified part at the depth of creation of filaments in the thickness of the material.