WO1999063633A1

WO1999063633A1 - Laser source and filtering method for obtaining a good optical quality from beams of annular section

Info

Publication number: WO1999063633A1
Application number: PCT/IT1999/000148
Authority: WO
Inventors: Antonio Lapucci
Original assignee: Istituto Nazionale Di Ottica
Priority date: 1998-06-01
Filing date: 1999-05-27
Publication date: 1999-12-09
Also published as: ITFI980130A1; JP2003524290A; EP1084526A1; AU4163799A

Abstract

For concentrating a laser beam (FR), there is provided a re-phasing at a distance (SF) of the beam emitted with an output having annular geometry, the ratio between the dimension (2) in the azimuthal (in other words tangential) direction of the apertures (13A) and the periodicity (d) of the apertures being less than 1; in particular, there is provided an annular laser with a periodic cavity filter (13) having a parameter (filling factor) Δ ≈0.7 0.95 and a re-phasing surface at a distance δF of the order of, for example, a few tens of cm, for a periodicity of a few mm and a wavelength of approximately 10 microns.

Description

lι ational Application No

PCT/IT 99/00148

A. CLASSIFICATION OF SUBJECT MATTER

IPC 6 H01S3/08 H01S3/085 H01S3/25

According to International Patent Classification (IPC) or to both national classification and IPC

B. FIELDS SEARCHED

Minimum documentation searched (classification system followed by classification symbols)

IPC 6 HOIS

Documentation searched other than minimum documentation to the extent that such documents are included in the fields searched

Electronic data base consulted during the international search (name of data base and where practical, search terms used)

C. DOCUMENTS CONSIDERED TO BE RELEVANT

Category Citation of document, with indication, where appropriate of the relevant passages Relevant to claim No

DE 43 25 063 A ( ROFIN-SINAR LASER ) 1 , 4 2 February 1995 ( 1995-02-02) ci ted i n the appl i cati on abstract ; cl ai ms 1-4 ; fi gures 1-10

LAPUCCI A ET AL : "OPTIMAL PHASE FILTERING 1 ,4

FOR HIGH-POWER LASER ARRAY FAR-FIELD

DISTRIBUTION"

OPTICS LETTERS , vol . 18 , no . 20 ,

15 October 1993 ( 1993-10-15 ) , pages

1694-1696 , XP000398567

ISSN : 0146-9592 ci ted i n the appl i cati on abstract page 1696 , ri ght-hand col umn , l i ne 1 - l i ne 13

D Further documents are listed in the continuation of box C Patent family members are listed in annex

^* Special categories of cited documents

T" later document published after the international filing date or priority date and not in conflict with the application but

"A' document defining the general state of the art which is not cited to understand the principle or theory underlying the considered to be of particular relevance invention

Ε" earlier document but published on or after the international 'X" document of particular relevance the claimed invention filing date cannot be considered novel or cannot be considered to

"L" document which may throw doubts on priority claιm(s) or involve an inventive step when the document is taken alone which is cited to establish the publication date of another Υ" document of particular relevance, the claimed invention citation or other special reason (as specified) cannot be considered to involve an inventive step when the

O" document referring to an oral disclosure use, exhibition or document is combined with one or more other such docuother means ments such combination being obvious to a person skilled P" document published prior to the international filing date but in the art later than the priority date claimed '&" document member of the same patent family

Date of the actual completion of the international search Date of mailing of the international search report

4 August 1999 11/08/1999

Name and mailing address of the ISA Authorized officer

European Patent Office P B 5818 Patentlaan 2 NL - 2280 HV Rijswijk Tel (+31-70) 3 0-20 0, Tx 31 651 epo nl, Fax (+31-70) 3 0-3016 Mal i c , K

Form PCT/ISA210 (second sheet) (July 1992) I lational Application No

Information on patent family members

PCT/IT 99/00148

Patent document Publication Patent family Publication cited in search report date member(s) date

DE 4325063 02-02-1995 NONE

Form PCT/ISA/210 (patent family annex) (July 1992) - 1 - LASER SOURCE AND FILTERING METHOD FOR OBTAINING A GOOD

OPTICAL QUALITY FROM BEAMS OF ANNULAR SECTION

DESCRIPTION

The use of capacitive discharges at radio frequency for exciting gas lasers cooled by heat diffusion has led to a completely new approach to the design and development of laser sources using gases (particularly CO and

CO₂). This is because these methods can be used to excite efficiently, by an electrical discharge, volumes of gas characterized by dimensions which are very large in two directions and very thin in the third direction, in such a way as to remove the heat in a very efficient way toward the largest surfaces. In this way it becomes possible to charge the gas with power densities ten times greater than those of the conventional continuous discharges.

This property, together with the possibility of sealed or semi-sealed operation, and the opportunity to pulse the discharge up to repetition frequencies of the order of 10 kHz, has made these sources extremely advantageous by comparison with other manufacturing technologies for medium- to high-powered lasers. This is because the shift toward high powers is achieved simply by increasing the discharge surface, in a much more economical way than in the case, for example, of sources with a fast gas flow. Sealed sources up to a mean power of the order of 500 W and semi-sealed sources up to a mean power of the order of 2 kW, which are consequently of interest for industrial applications, have now been constructed.

The advantages and properties of these sources are summarized in the paper by H. Baker and D.R. Hall, "Area sealing boosts CO₂-Laser performance", Laser Focus World, pp. 77-80, October 1989. The typical discharge diagrams for these systems use a planar geometry or an annular geometry. The method of constructing lasers of the planar type has been described in various patents, starting with J. Tulip, U.S. Pat. 4,719,649 and H.

Opower, EP Pat. 0 305 893 B1. On the other hand, annular lasers have been known since S. Yatsiv, U.S. Pat. No. 4,847,852.

However, other patents (J.A. Macken, U.S. Pat. No. 4,755,999 and J.A.

Macken et al., U.S. Pat. No. 5,528,613) have disclosed that, even with - 2 - electrical discharges based on a different technology, it is possible to make advantageous use planar or annular geometries of the optically active medium for the purpose of cooling the medium by heat diffusion. In Patent No.

4,755,999, a continuous discharge stabilized by a magnetic field is used in place of the capacitive discharge at radio frequency mentioned previously, while in Patent No. 5,528,613 the same geometries are used for an active gas medium excited by the combination of a continuous discharge and one at high frequency.

Finally, it should be noted that the removal of heat is a major problem even in the case of solid-state (or liquid) lasers. This is because high temperatures in the optically active material lead to deformations which reduce the quality of the extracted beam, or even cause fractures of the material. The solutions considered in this document are therefore of interest for both gas lasers and solid-state lasers. This is because, in order to obtain good results from these new geometries, it is necessary to solve unusual technical problems, such as the extraction of a beam with high optical quality from a region of active medium which is very thin, and therefore has a cross section which is very different from the conventional one. The use of the ordinary optical resonators (as described, for example, in the book by A.E. Siegmann, "Lasers", University Science Books, Mill Valley, California, 1986) therefore becomes impossible. The extraction of a beam of good optical quality (in other words, one that is easily focusable) is in fact extremely important, since in most applications the use of good focusing is considerably more effective than the use of higher overall power. Theoretically, annular lasers have advantages over planar lasers because of the containment of the overall dimensions and of the optical elements; however, the problem of the extraction of a beam of good optical quality is found to be even more complicated for these.

For example, the use of a stable-unstable hybrid resonator, usefully adopted in U.S. Pat. No. 4,719,639 and in EP No. 0 305 893 for planar geometry and applied in U.S. Pat. No. 5,353,299 for annular geometry, requires, in the latter case, the use of optical elements which are difficult to - 3 - manufacture and therefore highly expensive.

An advantageous solution to this problem consists in the use of a resonator in which the selection of the field distribution in the transverse direction with respect to the direction of propagation of the beam (the transverse mode of the resonator) is carried out by means of methods based on the Talbot effect. This approach is used, for example, in patent application DE No. 4,325,063.

According to the Talbot principle, periodic electromagnetic (e.m.) field distributions with a transverse spatial period equal to d are reconstructed (exactly, in theory, if the field has infinite transverse dimensions, and approximately in the real case) at distances which are integral multiples of what is called the Talbot distance (D_τ);

D_τ = 2 d² / λ (1) where λ is the wavelength of the e.m. field. Thus, by calculating a periodic aperture function in a cavity whose length is equal to half the Talbot distance, we obtain the reconstruction of the field in one resonator cycle, in other words selection with low diffraction losses of a transverse mode of the optical cavity. The periodic function in the resonator for the annular geometry can be obtained by means of a cavity filter with a set of apertures aligned on the ring. In particular, this structure can be produced directly by incision on the output mirror of the laser. The information given up to this point has already been disclosed in the aforesaid German patent application. This application, however, suggests that the apertures should be made with dimensions as close as possible to the periodicity of the filter, in other words that the areas of obstruction of the filter should be reduced to a minimum, in order to minimize the cavity losses.

However, it should be borne in mind that the teaching contained in the aforesaid German patent application does not in any way ensure the extraction of a beam of good optical quality. This is because, when cavities having a length of D_τ/2 are used, there is a possibility of extracting e.m. field modes with adjacent lobes in the same phase or in opposite phase. Typically, the counterphase mode (with adjacent lobes in opposite phases) is slightly - 4 - more likely to be present, but a change from one mode to another can be caused by small changes in the cavity parameters. Moreover, the mode in which the adjacent lobes are in counterphase has an intrinsically poor focusing quality, since it produces a ring-shaped remote field, in other words one which has a hole at the center.

It is possible to extract, with low losses, only the mode with adjacent lobes in counterphase for cavity lengths which are odd-numbered multiples of D_τ/4. In this case, use may be made of an optical element outside the cavity to re-phase the lobes, with the result that there is always one mode in phase. The cavity lengths (denoted henceforth by the symbol L) suggested by the aforesaid German patent application No. 4,325,063 are expressed by the following formula:

L = n-^- = n~ n = 1,2,... (2)

conversely, the cavities which are suggested here have lengths expressed by:

7") ^" L = (2n + 1) ^•-^***- = (2n + l) — n = 0,1 .... (3)

4 2Λ where the values have the same meaning as those given in equation (1).

It is also important to note that having a pure mode (in other words one with an azimuthal distribution very close to a sinusoidal variation), re-phased as stated previously or in general obtained by small periodic obscurations of the annular aperture as indicated in the aforesaid German patent application, enables only part of the energy to be concentrated in the central lobe of the field at a long distance from the source (in other words also in the focal plane of a focusing optical element). This is because only a fraction of the energy of the beam is transferred in this way into the fundamental mode of the ring (the mode with uniform azimuthal distribution). This fraction is typically of the order of 50-70%, with the remaining fraction of the energy contained in higher-order modes, owing to the high spatial frequencies still present in this field distribution.

Finally, it is known that the variation of the sinusoidal type in the azimuthal direction is an eigenfunction of the e.m. field, in other words a field - 5 - distribution which is propagated unchanged in this transverse direction.

However, in the case of nonharmonic periodic distributions (in other words those not of the sinusoidal type) in the azimuthal direction, the diffraction causes significant modifications in this direction as well (see A. Lapucci, F. Quercioli and D. Jafrancesco, Optimal phase filtering for high-power laser array far-field distribution", Opt. Lett., 18(20), pp. 1694-1696, 1993), producing greater field uniformity at certain specified distances. The re-phasing can then be carried out more advantageously at a distance from the output plane of the optical cavity, a distance where a certain degree of uniformity of the field has been achieved by means of the diffraction, as indicated in the text of 1993 cited above, as shown in Fig. 2, where in particular the difference is made clear in the comparison between the field F and the field B.

In the present invention, a method is provided for raising the optical quality of the beam extracted from a laser of annular section or from an array of lasers aligned on a circle.

The method consists in the use of a laser source characterized by an emission on to lobes arranged on the ring in such a way that the dark regions of the ring have a thickness which is not negligible in the tangential direction (called the azimuthal direction in the literature on laser beams), and in particular that said dark regions cover an area equal to approximately 10-30% of the ring. This emission can be obtained, for example, by using Talbot cavities with a means which obscures part of the cavity equivalent to the aforesaid fraction of 10-30%.

The method is also based on the placing of a re-phasing means at the distance at which the lobes have diffracted in such a way that they have covered the dark regions, in other words in such a way that they have made the illumination of the ring more uniform, particularly in the tangential direction. The re-phasing means will have a thickness variable in steps which provides a difference in optical path between adjacent lobes, in other words a phase delay between these lobes. This delay typically has a value close to π (corresponding to a difference of λ/2 in the optical path) if the source emits radiation with adjacent lobes in counterphase, and a value close to π/2 - 6 - (corresponding to a difference of λ/4 in the optical path) if the source initially emits with lobes all having the same phase. In fact, the optimal thickness, as well as the optimal distance at which the re-phasing means are to be located, has to be calculated by numerical methods with the aid of a computer, as a function of the dimensions of the source and in particular of the portion of annular section which is obscured. More generally, the re-phasing means will tend to cancel the phase modulation at the distance at which the propagation has minimized the amplitude modulation.

A first object of the invention is a method for processing a beam in order to obtain its concentration, in which there is provided a re-phasing at a distance of the beam emitted by the laser or array of lasers with an output having annular geometry, the ratio between the dimension in the azimuthal (in other words tangential) direction of the apertures and the periodicity of the apertures being less than 1. The periodicity of the apertures may lie in the range from 0.7 to 0.95.

The method advantageously provides for the use of an annular laser with a periodic cavity filter having a parameter (filling factor) Δ - 0.7÷0.95 and a re-phasing surface at a distance δF of the order of, for example, a few tens of cm, for a periodicity of a few mm and a wavelength of approximately 10 microns, in which the amplitude variations of the emitted field are minimal and the phase variations are maximal, where δF is to be determined as a function of Δ, and the optimal distance for the location of the re-phasing changes with the variation of Δ (the filling factor).

Another object of the invention is a laser source for obtaining concentrated laser energy beams, this source comprising a laser emission of annular section divided into lobes with dark regions whose thickness - in the tangential direction - amounts to a total ranging from 5% to 30% of the annular extension, and a modulated optical means for re-phasing the lobes by an alternation from one lobe to another of the optical path in the overall path which causes the concentration of the beams.

The laser source in question may comprise a Talbot filter for the division into lobes. - 7 - In one embodiment, it is possible to provide an optical plate with a refractive index different from that of the normal means of propagation (usually air), this optical plate having on at least one of its surfaces a modulation of thickness which corresponds to the energy lobes to be re-phased by variation of the optical path.

In another embodiment it is possible to provide a beam compression system with two conical or toroidal reflecting surfaces, this system having at least one or both of said reflecting surfaces modulated in steps, to obtain a variation of the path of the rays of the various lobes and consequently their re- phasing.

The re-phasing means can be located at a distance (δF) from the periodic filter such that a substantially uniform annular illumination is obtained as a result of the diffraction of said lobes.

When a beam compression system with two conical or toroidal reflecting surfaces is used, one or both of said reflecting surfaces have their thicknesses modulated in steps or otherwise, to flatten the phase modulation due to the phase difference between the lobes and to their propagation.

The desired emission to the correctly separated and phase-shifted lobes is obtained with a cavity length according to the formula

I - (2n + l) n = 0,1 ....

The invention will be more clearly understood from the description and the attached drawing, which shows a nonrestrictive practical example of the invention. In the drawing,

Figs. 1A, 1 B and 1 C show a diagram of an annular laser of a known type in longitudinal section, in a view through IB-IB in Fig. 1A and in an enlarged detail in Fig. 1 B;

Fig. 2 shows graphs of the phase re-adjustment on different field distributions, with the transverse (azimuthal) direction shown on the horizontal axis and the field amplitude on the vertical axis; Figs. 3A, 3B, 3C show a first embodiment of the invention, using an active plate to obtain differences in the refractive index; - 8 -

Figs. 4A, 4B, 4C, 4D show an embodiment of the invention with modulation obtained by variation of the optical path by reflection;

Figs. 5A, 5B, 5C show a further embodiment similar to that shown in Figs. 4A to 4D; Fig. 6 shows another embodiment similar to the preceding ones;

Fig. 7 shows for comparison the improvements of the field obtainable with a periodic annular source in the different cases; and

Fig. 8 shows for comparison graphs for different cases.

Figs. 1A and 1B illustrate the prior art. They show schematically an annular laser with a Talbot cavity filter, as disclosed by S. Anikitchev et al. in

DE Pat. Appl. No. 4,325,063, 1993, and an optical beam compression system based on axicons. The number 1 indicates a totally reflecting mirror, 2 indicates a zone of optical gain of annular section, 3 indicates a Talbot cavity filter, 4 indicates a half-reflecting output mirror, 5 indicates a first external conical (or toroidal) surface for compressing the beam and 6 indicates a second conical (or toroidal) surface for recollimating the beam which emerges as the beam FR. In Fig. 1B, which is a front view of the Talbot filter 3, the apertures 3A will be noted; these are as large as possible, as disclosed in DE

Pat. 4,325,063. The letter d indicates the azimuthal, in other words tangential, interval of the apertures 3A, a indicates the tangential dimension of the apertures 3A, and b indicates their radial dimension, while r indicates the maximum radius of the apertures 3A.

Fig. 2 is a schematic demonstration of the effect of the phase readjustment on different field distributions, in an illustration with reference to a single direction which is transverse (azimuthal) with respect to the direction of propagation. A is a harmonic (sinusoidal) field distribution (in other words, a pure mode) and B is the distribution which is obtained by re-phasing the even- numbered lobes with respect to the odd-numbered ones; C is a nonharmonic field distribution (as obtained with small apertures of the Talbot cavity filter); D is that which is obtained by re-phasing this field. E is a representation of the distribution C propagated over a distance of the order of a quarter of the Talbot distance, and F is the distribution obtained by re-phasing the - 9 - distribution E; the result is that the distribution F has a higher content of the fundamental mode (where the field is uniform with respect to the coordinate, considered) than the distribution B.

Figs. 3A, 3B, 3C are schematic illustrations of a first embodiment of the invention. The number 11 indicates the totally reflecting mirror, 12 indicates the zone of optical gain having an annular section, 13 indicates the Talbot cavity filter, and 14 indicates the half-reflecting output mirror. The number 15 indicates the first conical (or toroidal) surface for compressing the beam and 16 indicates the second conical (or toroidal) surface for recollimating the beam FR. The number 17 indicates a transparent plate or window with its surface profile modulated, in other words with a modulated refractive index, to differentiate, in any case, the optical paths of the lobes which form the laser beam, in such a way as to re-phase them. The components 15, 16, 17 are at a distance δF from the output mirror 14 of the resonator of the laser. In Fig. 3B, which is the front view through IIIB-IIIB in Fig. 3A of the Talbot filter 13, the apertures 13A will be noted; these have a tangential dimension a and an interval d, which optimize the phase filtering. Fig. 3C is the front view of the window 17, which is placed before the axicon. One of the two surfaces of the window has a thickness modulated periodically, to differentiate the optical paths of the different lobes of the electromagnetic field. The two areas of different thickness are identified in the drawing by hatched areas and white areas.

Figs. 4A to 4D illustrate schematically a second embodiment of the invention. The number 21 indicates the totally reflecting mirror, 22 indicates the zone of optical gain having an annular section, 23 indicates the Talbot cavity filter, 24 indicates the half-reflecting output mirror, 25 indicates the first conical (or toroidal) surface for compressing the beam and 26 indicates the second conical (or toroidal) surface for recollimating the beam. The components 25 and 26 are at a distance δF from the output mirror 24 of the resonator of the laser. Fig. 4B is the front view of the Talbot filter 23 with the apertures 23A having dimensions a and the interval d which optimize the phase filtering. Fig. 4C is a front view of the axicon; the first reflecting surface - 10 - has a thickness modulated periodically, as seen at 25M, especially in the enlarged detail (with exaggerated thickness for clarity of illustration) in Fig. 4D._ This provides a variation of the optical path.

An arrangement similar to that of Fig. 4A may have the modulated reflecting surface on the component 26 instead of on the component 25.

Figs. 5A and 5E schematically illustrate a third embodiment of the invention. The number 31 indicates the totally reflecting mirror, 32 indicates the zone of optical gain having an annular section, 33 indicates the Talbot cavity filter, and 34 indicates the half-reflecting output mirror; 35 indicates the first conical (or toroidal) surface for compressing the beam, and 36 indicates the second conical (or toroidal) surface for recollimating the beam FR. The components 35 and 36 are at a distance δF from the output mirror 34 of the laser resonator. Fig. 5B (front view of the Talbot filter 33) shows the apertures 33A with dimensions a and the interval d which optimize the phase filtering. In Fig. 5C, the front view of the axicon shows the second reflecting surface 36A which has its thickness 36M modulated periodically, in a similar way to the surface 25M of the preceding embodiment.

Clearly, a further possible embodiment, not shown in the drawing, may have the axicon before the filtering window. Additionally, those who are skilled in the art will know that it is possible to use different systems for compressing the beam in the radial direction. For example, conical or toroidal components may be used for transmission instead of reflection, or the optical path may be bent by using what is known as a W-axicon. Clearly, these variations do not depart from the principal concept of the invention. Fig. 6 schematically represents a further embodiment of the invention.

To show the various stages of transformation of the optical beam more distinctly, the figure relates to axicons with an aperture angle (α in the figure) of 45°; however, it is evident that a larger aperture angle is generally advantageous even if it does not make the operating mechanism of this system so clear.

In the diagram in Fig. 6, the beam rebounds twice from each of the conical (or toroidal, as shown here in the case of the first reflecting surface) - 11 - surfaces 52a, 51a, 52b, 51 b formed by the two components 51 and 52; this already provides an advantage in terms of the overall dimensions of the _ optical system for compressing and re-phasing the lobes. At the same time, following the first reflection, the beam is propagated along the path C3 whose dimensions are smaller and therefore provide the optimal condition for the re- phasing at a distance δF" which is smaller than δF. The re-phasing may then be advantageously carried out on the portion 52b of the axicon 52 and/or on the portion 51 b of the axicon 51. The component 52 (and also the component 51) may have one or both of the portions 52a and 52b (or 51a, 51 b) of the reflecting surfaces toroidal instead of conical, as shown in the case of the portion 52a. With this arrangement, both the dimensions and the radial divergence of the beam can be controlled. In Fig. 6, a concave (toroidal) curvature of the portion of reflecting surface 52a of the component 52 is used to radially recollimate the annular beam. Fig. 7 shows examples of improvement of the field which can be obtained from a periodic annular source. In Fig. 7, A indicates the close field in the case of Talbot filtering with a maximum aperture as disclosed in DE Pat. 4,326,063 and E is the corresponding distant (or focusing) field. B indicates the close field in the case of Talbot filtering with Δ = 0.8, and F indicates the corresponding distant field. These two fields clearly have very poor characteristics of focusability. C indicates the field A re-phased by a binary phase plate and G is its corresponding distant field. D is the field B propagated to a distance δF and re-phased there, and H is its corresponding distant field. The excellent focusing property of this field can be appreciated. Fig. 8 shows a graph in which the horizontal axis shows the half diffraction angle in mrad and the vertical axis shows the energy contained in the solid angle defined by the horizontal axis, to show the percentage of energy concentrated within a cone having a given angle, shown on the graph as a function of said angle, for the field propagated to long distances, in other words focused.

Curve 1 → case E in Fig. 7 Curve 2 → case F in Fig. 7 - 12 - Curve 3 → case G in Fig. 7

Curves 4, 5, 6 → case H in Fig. 7 for different distances δF around the optimaL distance.

From these last curves it may be seen that different values of δF give rise to different distributions and therefore to different concentrations of energy on the focusing plane.

A typical embodiment of the invention will be described below. Possible systems for the embodiment of the invention will now be described with reference to the information in the different Figures 3, 4, 5, by means of which the optical path can be varied either by variation of the overall optical path (Figs. 4, 5) by variation of the refractive index along the optical path (Fig. 3). Clearly, however, many other configurations of the laser cavity different from that shown - such as those disclosed in the patents U.S.

5,373,525, EP 457 061 , EP 610.170 and U.S. 5,648,980 - can produce an output beam with the characteristics indicated above, to which the phase filtering method according to the present invention can therefore also be advantageously applied.

The laser considered here has an annular section and a cavity length selected as disclosed in Formula (3) shown above. The cavity is assumed to contain a filter (indicated as component 13 or 23 or 33 in Figs. 3, 4 and 5), formed for example from a metal plate, and consisting of a series of apertures such that these apertures cover a portion equal to 70-95% of the annular section in the azimuthal direction, in other words one in which there are obstructions which are of the order of 5-30% of the ring. The loss of power of the source related to the obstructions can be kept low by the way in which the cavity length is selected, in accordance with equation (3).

In fact, it has been demonstrated at the theoretical level (A.A.

Golunbentsev, V.V. Likhanskii, A.P. Napartovich, 'Theory of phase locking of an array of lasers", SPIE Proc. Vol. 2109, pp. 205-218, 1993) that for an

"array" (as it is called in the technical terminology) having infinite apertures, the percentage field loss in the cavity (γ) can be estimated, in the first - 13 - approximation, by the following formula:

where Δ is the ratio a/d where a is the azimuthal dimension of the apertures in the tangential (azimuthal) direction with respect to the ring and d is their periodicity. δL is the difference between the cavity length and a Talbot length selected according to equation (2) or (3), and D_τ is the Talbot distance, γc (for L=D_τ) is the field loss in the Talbot cavity - as defined by equations (2) or (3) - and does not depend on the ratio Δ.

This means that reducing the dimension of the apertures of the filter (in other words the "filling factor" as Δ is called in the literature of this field) causes a greater sensitivity to the cavity length, but does not affect the losses at the Talbot distance. The statements made up to this point are theoretically valid for an array which can be considered to have an infinite transverse dimension. The annular laser approximates closely to the infinite array in that it has boundary conditions (in other words the conditions of connection of the e.m. field) which are periodic in the azimuthal direction (because of the closing of the ring). The problem of diffraction can then be approximated by a one- dimensional treatment, in other words one which considers only one direction transverse to the propagation, if the ring is large and thin. This is because, in this case, the behavior of the field in the radial direction does not change the properties of the azimuthal distribution of the field within the propagation distances in question. In formulae, this condition is expressed as follows:

^■k AL » i : - r « 1 (5) where r is the mean radius of the ring, b is its thickness, L is the cavity length and λ is the wavelength.

The beam emitted by this cavity is propagated over a distance δF permitting the diffraction of the field emitted by each aperture, in such a way as to fill the dark regions of the ring as far as possible (in other words to make the illumination of the ring uniform); at this point, the lobes are re-phased by means of an optical component which produces a difference in optical path - 14 - between adjacent lobes.

An optical component which performs this function may be formed as part of the transmission system by modulating the thickness of a window or plate (as indicated in the case of the component 17 in Fig. 3A) having a refractive index n_ή which is different from the refractive index n₀ of the normal propagation medium (generally air); this also provides a variation of the optical path.

For high-power lasers, it may be more convenient to form the component in the reflection system, again by modulating the profile of the reflecting surface, and thus changing the optical path of the different lobes forming the extracted beam. This modulation may be produced (Figs. 4, 5, 6) by engraving the substrate of the mirror, or by successive deposition of thin layers on the substrate, by positioning a mask in the process of deposition of one or more of the thin layers, in such a way as to form steps of thickness equal to half (because of the double passage in reflection) of the difference of the optical path to be produced.

Since the radial dimension of the beam emitted from a source is also an extremely important parameter for achieving good focusability of the beam, the focusing is improved in the case of annular beams, and particularly in the case of good azimuthal uniformity, by using optical means which increase the ratio b/r (where b and r are the radial dimension and the mean radius of the ring, as shown in the drawing, particularly in Fig. 1). Alternatively, it is possible to use optical means which distribute the field more uniformly over the aperture which comprises the ring illuminated by the source. For this purpose, solutions based on optical components known as axicons have generally been adopted in practically all the proposed versions of annular lasers (for example in DE Pat. 4,325,063, U.S. Pat. 5,373,525 and U.S. Pat. 5,099,492). These are optical components with conical or toroidal optical surfaces capable of compressing the beam. In this case, the present invention may advantageously be integrated into these optical systems, by designing them in such a way that they have a surface of the component at the optimal position for the phase filtering referred to above, to make the phases of the lobes

Claims

- 15 - uniform (for this, see Figs. 3, 4 and 5) and by introducing the profile modulation on this surface.

This can be done - as shown in Fig. 4 and as mentioned above - by positioning an axicon 25, 26 at a distance δF and modulating the first reflection surface 25M of the component 25, or by changing the angles of the axicon and modulating the second surface 36M of the component 36 in Fig. 5.

In this case, the length of the optical system outside the cavity will be markedly more compact, being equal to the distance at which the component

35 in Fig. 5 is positioned. This distance is generally less than half of the previously cited distance δF, since the path followed by the beam before the re-phasing component (the component 36 in the case in question, as described in Fig. 5) is folded in two. The distance δF' has to be calculated in a numerical way, with allowance for the action of convergence of the beam caused by the first surface (of the component 35 in Fig. 5) of the beam compression system.

It should be borne in mind that, in the conditions indicated by the equations (5), which as stated are satisfied well in the case of annular gas lasers with electrodes having a large surface area, the Talbot effect on the ring can easily be estimated by means of calculations based on a one- dimensional theory as shown in Fig. 2, which allows for the field distribution in a single direction transverse to the propagation. In this way the optimal pair of parameters Δ (the filling factor of the filter inside the optical cavity) and δF (the distance at which the delays in the path which correct the phase of the extracted beam are to be introduced by means of the optical component with the modulated profile) can be selected in a first approximation.

The result of these choices is that the greater uniformity (of both amplitude and phase) in the ring of the field to be focused is manifested in a higher energy content of the fundamental mode of the ring. This greater azimuthal uniformity is also manifested in a greater efficiency of the radial compression of the beam provided by the system based on an axicon optical element, to the extent that up to 90% of the energy of the beam can be conveyed to the central lobe of the focused field. - 16 -

It should be understood that the drawing shows only an example provided solely as a practical demonstration of the invention, and that this invention may be varied in its forms and arrangements without departure from the scope of the guiding concept of the invention.