NL2017998B1

NL2017998B1 - Apparatuses and methods for laser processing transparent workpieces using non-axisymmetric beam spots

Info

Publication number: NL2017998B1
Application number: NL2017998A
Authority: NL
Inventors: Andrew Piech Garrett; Tsuda Sergio; Andrew West James; Kumar AKARAPU Ravindra
Original assignee: Corning Inc
Priority date: 2016-12-14
Filing date: 2016-12-14
Publication date: 2018-06-26

Description

APPARATUSES AND METHODS FOR LASER PROCESSING TRANSPARENT WORKPIECES USING NON-AXISYMMETRIC BEAM SPOTS

Background

Field [0001] The present specification generally relates to apparatuses and methods for laser processing transparent workpieces, and more particularly, to forming contour lines in transparent workpieces for separating transparent workpieces.

Technical Background [0002] The area of laser processing of materials encompasses a wide variety of applications that involve cutting, drilling, milling, welding, melting, etc. of different types of materials. Among these processes, one that is of particular interest is cutting or separating different types of transparent substrates in a process that may be utilized in the production of materials such as glass, sapphire, or fused silica for thin film transistors (TFT) or display materials for electronic devices.

[0003] From process development and cost perspectives there are many opportunities for improvement in cutting and separating glass substrates. It is of great interest to have a faster, cleaner, cheaper, more repeatable, and more reliable method of separating glass substrates than what is currently practiced in the market. Accordingly, a need exists for alternative improved methods for separating glass substrates.

Summary [0004] The present invention is defined in the claims.

[0005] It is to be understood that both the general description and the following detailed description describe the invention and are intended to provide an overview or framework for understanding the nature and character of the claimed subject matter. The accompanying drawings are included to provide a further understanding of the invention and are incorporated into and constitute a part of this specification. The drawings illustrate the invention described herein, and together with the description serve to explain the principles and operations of the claimed subject matter.

Brief Description of the Drawings [0006] The drawings are illustrative and exemplary in nature and not intended to limit the subject matter defined by the claims. The following detailed description of the invention can be understood when read in conjunction with the following drawings, where like structure is indicated with like reference numerals and in which: [0007] FIG. 1A schematically depicts the formation of a contour line of defects, according to the present invention; [0008] FIG. IB schematically depicts an example pulsed laser beam focal line during processing of a transparent workpiece according to the present invention; [0009] FIG. 2 schematically depicts a non-axisymmetric beam spot traversing a line of desired separation to form a contour line in a transparent workpiece according to the present invention; [0010] FIG. 3 schematically depicts a conventional embodiment of an optical assembly for pulsed laser processing; [0011] FIG. 4 schematically depicts an optical assembly for pulsed laser processing comprising an offset aspheric optical element, according to the present invention; [0012] FIG. 5A schematically depicts an optical assembly for pulsed laser processing comprising an optical blocking element, according to the present invention; [0013] FIG. 5B schematically depicts an optical assembly for pulsed laser processing comprising two optical blocking elements, according to the present invention; [0014] FIG. 6 schematically depicts an optical assembly for pulsed laser processing comprising an optical delay plate, according to the present invention; [0015] FIG. 7A schematically depicts an optical assembly for pulsed laser processing comprising a split quarter waveplate, according to the present invention; [0016] FIG. 7B schematically depicts the split quarter waveplate of FIG. 7A, according to the present invention; [0017] FIG. 7C graphically depicts the relative intensity of laser pulses within an exemplary pulse burst vs. time, according to the present invention; [0018] FIG. 7D graphically depicts relative intensity of laser pulses vs. time within another exemplary pulse burst, according to the present invention; [0019] FIG. 8A depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0020] FIG. 8B depicts a logarithmic intensity plot of a Fourier transform plane of an example pulsed laser beam, according to the present invention; [0021] FIG. 8C depicts a near-field micrograph of an example pulsed laser beam, according; to the present invention [0022] FIG. 9 depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0023] FIG. 10 depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0024] FIG. 11A depicts a two-dimensional cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0025] FIG. 11B depicts a set of one-dimensional horizontal and vertical line cross sections of the two-dimensional cross-sectional intensity plot of FIG. 11 A, according to the present invention; [0026] FIG. 11C depicts another set of one-dimensional horizontal and vertical line cross sections of the two-dimensional cross-sectional intensity plot of FIG. 11 A, according to the present invention; [0027] FIG. 11D depicts a logarithmic intensity plot of a Fourier transform plane of an example pulsed laser beam, according to the present invention; [0028] FIG. 11E depicts a near-field micrograph of an example pulsed laser beam, according to the present invention; [0029] FIG. 12A depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0030] FIG. 12B depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0031] FIG. 12C depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0032] FIG. 12D graphically depicts one-dimensional cross sections of the intensity plots of FIGS. 12A-12C, according to the present invention; [0033] FIG. 12E graphically depicts the Fourier transform of an example Sgn step function, according to the present invention [0034] FIG 12F depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0035] FIG. 12G graphically depicts one-dimensional X and Y cross-sections of the two dimensional cross-sectional intensity plot of FIG. 12F, according to the present invention; [0036] FIG 12H depicts a cross-sectional intensity plot of an example pulsed laser beam, according to according to the present invention; [0037] FIG. 121 graphically depicts one-dimensional X and Y cross-sections of the two dimensional cross-sectional intensity plot of FIG. 12H, according to the present invention; [0038] FIG. 13A depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0039] FIG. 13B depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0040] FIG. 13C depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0041] FIG. 13D depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0042] FIG. 13E depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0043] FIG. 13F depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0044] FIG. 13G depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0045] FIG. 13H depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0046] FIG. 131 depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0047] FIG. 13J depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0048] FIG. 13K depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0049] FIG. 14 depicts a near-field micrograph of an example pulsed laser beam, according to the present invention; [0050] FIG. 15 depicts a near-field micrograph of an example pulsed laser beam, according to the present invention; [0051] FIG. 16 depicts example resultant non-axisymmetric beam spots formed by an optical blocking element positioned in an example optical assembly, according to the present invention; [0052] FIG. 17A depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0053] FIG. 17B depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0054] FIG. 17C depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0055] FIG. 17D depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0056] FIG. 17E depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0057] FIG. 17F depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0058] FIG. 18 depicts example resultant non-axisymmetric beam spots formed by two optical blocking elements positioned in an example optical assembly, according to the present invention; [0059] FIG. 19A depicts a cross sectional image of an example pulsed laser beam, according to the present invention; [0060] FIG. 19B depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0061] FIG. 20A depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0062] FIG. 20B graphically depicts one-dimensional X and Y cross sections of the two dimensional cross-sectional intensity plot of FIG. 20A, according to the present invention; [0063] FIG. 21A depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0064] FIG. 2IB graphically depicts one-dimensional X and Y cross sections of the two dimensional cross-sectional intensity plot of FIG. 21 A, according to the present invention; [0065] FIG. 22A depicts a cross-sectional intensity plot of an example pulsed laser beam, according to the present invention; [0066] FIG. 22B graphically depicts one-dimensional X and Y cross sections of the two dimensional cross-sectional intensity plot of FIG. 22A, according to the present invention; and [0067] FIG. 23 depicts example resultant non-axisymmetric beam spots formed by a split quarter waveplate positioned in an example optical assembly, according to the present invention.

Detailed Description [0068] Reference will now be made in detail to processes for laser processing transparent workpieces, such as glass workpieces, examples of which are illustrated in the accompanying drawings, according to the present invention. Whenever possible, the same reference numerals will be used throughout the drawings to refer to the same or like parts. According to the present invention, a transparent workpiece may be laser processed to form a contour line in the transparent workpiece comprising one or more defects that define a line of intended separation of the transparent workpiece into two or more portions. A pulsed laser beam that projects a non-axisymmetric extended focal line having a beam cross section with a long axis and a short axis onto the transparent workpiece may be utilized to preferably create a series of defects in the transparent workpiece thereby defining the contour line. These defects may be referred to as line defects, perforations, or nano-perforations in the workpiece. Further, these defects may include a central defect region and radial arms that primarily form along the long axis of the non-axisymmetric beam spot. The process may further include separating the transparent workpiece along the contour line, for example, using an infrared laser or other laser configured to heat the area of the transparent workpiece adjacent to the contour line or to bend, scribe, or otherwise mechanically stress the transparent workpiece. The transparent workpiece may be mechanically stressed to cause separation, or separation may occur spontaneously. While not intended to be limited by theory, stressing the transparent workpiece at the contour line may propagate a crack along the contour line. By controlling the direction of the radial arms of each defect along the contour line, the crack propagation may be better controlled. The present invention for processing a transparent workpiece will be described herein with specific reference to the appended drawings.

[0069] The phrase “transparent workpiece,” as used herein, means a workpiece formed from glass or glass-ceramic which is transparent, where the term “transparent,” as used herein, means that the material has an optical absorption of less than about 20% per mm of material depth, such as less than about 10% per mm of material depth for the specified pulsed laser wavelength, or such as less than about 1% per mm of material depth for the specified pulsed laser wavelength. According to the present invention the transparent workpiece may have a thickness of from about 50 microns to about 10 mm (such as from about 100 microns to about 5 mm, or from about 0.5 mm to about 3 mm).

[0070] The present invention provides a method for processing workpieces. As used herein, “laser processing” may include forming contour lines in workpieces, separating workpieces, or combinations thereof. Transparent workpieces may comprise glass workpieces formed from glass compositions, such as borosilicate glass, soda-lime glass, aluminosilicate glass, alkali aluminosilicate, alkaline earth aluminosilicate glass, alkaline earth boro-aluminosilicate glass, fused silica, or crystalline materials such as sapphire, silicon, gallium arsenide, or combinations thereof. The glass may be ion-exchangeable, such that the glass composition can undergo ion-exchange for mechanical strengthening before or after laser processing the transparent workpiece. For example, the transparent workpiece may comprise ion exchanged and ion exchangeable glass, such as Coming Gorilla® Glass available from Corning Incorporated of Corning, NY (e.g., code 2318, code 2319, and code 2320). Further, these ion exchanged glasses may have coefficients of thermal expansion (CTE) of from about 6 ppm/°C to about 10 ppm/°C. The glass composition of the transparent workpiece may include greater than about 1.0 mol.% boron and/or compounds containing boron, including, without limitation, B2O3. The glass compositions from which the transparent workpieces are formed can include less than or equal to about 1.0 mol.% of oxides of boron and/or compounds containing boron. Moreover, the transparent workpiece may comprise other components which are transparent to the wavelength of the laser, for example, crystals such as sapphire or zinc selenide.

[0071] Some transparent workpieces may be utilized as display and/or TFT (thin film transistor) substrates. Some examples of such glasses or glass compositions suitable for display or TFT use are EAGLE XG®, CONTEGO, and CORNING LOTUS™ available from Corning Incorporated of Coming, NY. The alkaline earth boro-aluminosilicate glass compositions may be formulated to be suitable for use as substrates for electronic applications including, without limitation, substrates for TFTs. The glass compositions used in conjunction with TFTs typically have CTEs similar to that of silicon (such as less than 5 x 10'6/K, or even less than 4 x 10’6/K, for example, approximately 3 x 1CT6/K, or about 2.5 x 10' 6/K to about 3.5 x 10"6/K), and have low levels of alkali within the glass. Low levels of alkali (e.g., trace amounts of about 0 wt.% to 2 wt.%, such as less than 1 wt.%, for example, less than 0.5 wt.%) may be used in TFT applications because alkali dopants, under some conditions, leach out of glass and contaminate or “poison” the TFTs, possibly rendering the TFTs inoperable. The laser cutting process of the present invention may be used to separate transparent workpieces in a controlled fashion with negligible debris, minimum defects, and low subsurface damage to the edges, preserving workpiece integrity and strength.

[0072] The phrase “contour line,” as used herein, denotes a line (e.g., a line, a curve, etc.) formed along a desired line of separation on the surface of a transparent workpiece along which a transparent workpiece will be separated into multiple portions upon exposure to the appropriate processing conditions. The contour line generally consists of one or more defects introduced into the transparent workpiece using various techniques. As used herein, a “defect” may include an area of modified material (relative to the bulk material), void space, scratch, flaw, hole, or other deformities in the transparent workpiece which enables separation by additional processing, such as by infrared laser processing, mechanical stress, or other separation processes. Moreover, each defect may comprise a central defect region and one or more radial arms extending outward from the central defect region along an imaging surface of the transparent workpiece. As used herein the “imaging surface” of the transparent workpiece is the surface of the transparent workpiece at which the pulsed laser beam initially contacts the transparent workpiece. As described in more detail below, the radial length of the one or more radial arms may be controlled by the shape of a beam spot projected onto the transparent workpiece by a pulsed laser beam. As one example, a pulsed laser beam comprising a non-axisymmetric beam spot generally comprising a long axis and a short axis may irradiate the imaging plane of the transparent workpiece to generate defects that comprise a central defect region formed at the intersection of the long axis and the short axis of the non-axisymmetric beam spot and one or more radial arms formed in the direction of the long axis of the non-axisymmetric beam spot.

[0073] A transparent workpiece, such as a glass substrate or the like, may be separated into multiple portions by first forming a contour line on the surface of the workpiece and, thereafter, heating, for example, using an infrared laser, the surface of the workpiece on the contour line to create stresses in the workpiece, such as thermal stresses. The stresses ultimately lead to the spontaneous separation of the workpiece along the contour line. Further, when each defect is formed using a pulsed laser beam having a non-axisymmetric beam spot oriented such that the long axis of the beam axis extends along the desired line of separation, crack propagation caused by stressing defects in the transparent workpiece along the contour line may extend in the desired line of separation. Forming defects having radial arms that extend in the direction of the desired line of separation may allow the defects to be spaced apart at larger spacing distances than defects having randomly extending radial arms or no radial arms, without damage to the edges of the separated transparent workpieces where the contour line existed prior to separation. Moreover, forming defects having radial arms that extend in the direction of the desired line of separation allows crack propagation to be generated by less stress, e.g., less energy, such as thermal energy, applied to the workpiece, limiting damage to the edges of the separated transparent workpieces where the contour line existed prior to separation. In contrast, when defects include randomly extending radial arms or no radial arms, cracks may propagate from the separated edge in a direction generally perpendicular to the edge of the separated transparent workpiece (i.e., generally perpendicular to the intended line of separation denoted by the contour line) which weaken the edges of separated transparent workpiece.

[0074] Referring now to FIGS. 1A and IB, a transparent workpiece 160, such as a glass workpiece or a glass-ceramic workpiece, is schematically depicted undergoing processing according to the present invention. FIGS. 1A and IB depict the formation of a contour line 170 in the transparent workpiece 160, which may be formed by translating a pulsed laser beam 112 relative to the transparent workpiece in a translation direction 101.

[0075] FIGS. 1A and IB depict the pulsed laser beam 112 along a beam pathway 111 and oriented such that the pulsed laser beam 112 may be focused into a pulsed laser beam focal line 113 within the transparent workpiece 160 by a lens (e.g., a second lens 132 as described below). Further, the pulsed laser beam focal line 113 is a portion of a quasi non-diffracting beam, as defined in more detail below. FIGS. 1A and IB depict that the pulsed laser beam 112 forms a non-axisymmetric beam spot 114 projected onto an imaging surface 162 of the transparent workpiece 160. Further, the pulsed laser beam focal line 113 is non-axisymmetric at cross sections of the pulsed laser beam focal line 113 normal to the propagation axis of the pulsed laser beam 112 (e.g., normal to the beam pathway 111). As used herein, axisymmetric refers to a shape that is symmetric, or appears the same, for any arbitrary rotation angle made about a central axis, and “non-axisymmetric” refers to a shape that is not symmetric for any arbitrary rotation angle made about a central axis. The rotation axis (e.g., the central axis) is most often taken as being the propagation axis of the laser beam. As also used herein “beam spot” refers to a cross section of a laser beam (e.g., the pulsed laser beam 112) at a point of first contact with a workpiece (e.g., the transparent workpiece 160).

[0076] Referring also to FIG. 2, the contour line 170 extends along the desired line of separation 165 and delineates a line of intended separation about which the transparent workpiece 160 may be separated into two or more portions. The contour line 170 comprises a plurality of defects 172 that extend into the surface of the transparent workpiece 160 and establish a path for crack propagation for separation of the transparent workpiece 160 into separate portions along the contour line 170. While the contour line 170 is depicted in FIG. 1A and FIG. 2 as being substantially linear, it should be understood that other configurations are contemplated and possible including, without limitation, curves, patterns, regular geometric shapes, irregular shapes, and the like.

[0077] As depicted in FIG. 2, each defect 172 includes a central defect region 174 and one or more radial arms 176 extending outward in a direction substantially perpendicular to the beam pathway 111 (e.g., in the X and/or Y directions as shown in FIGS. IA, IB, and 2). In operation, after the defects 172 of the contour line 170 are formed, for example, using the methods and systems described herein, the defects 172 may be further acted upon in a subsequent separating step to induce spontaneous separation of the transparent workpiece 160 along the contour line 170. The subsequent separating step may include using mechanical force, thermal stress induced force, or a spontaneous break occurring due to stress present in the transparent workpiece, depending on the type, thickness, and structure of the transparent workpiece 160. For example, stress may be present in the transparent workpiece 160 which may cause spontaneous separation without further heating or mechanical separation steps.

[0078] Referring to FIGS. IA, IB, and 2, a pulsed laser beam 112 (with a non-axisymmetric beam spot 114 projected onto the transparent workpiece 160) may be directed onto the transparent workpiece 160 (e.g., condensed into a high aspect ratio line focus that penetrates through at least a portion of the thickness of the transparent workpiece 160). This forms the pulsed laser beam focal line 113 having non-axisymmetric cross sections correlated with the non-axisymmetric beam spot 114. In particular, the non-axisymmetric beam spot 114 is an example cross section of the pulsed laser beam focal line 113 and the pulsed laser beam focal line 113 remains non-axisymmetric as the pulsed laser beam focal line 113 penetrates at least a portion of the transparent workpiece 160. Further, the pulsed laser beam 112 may be translated relative to the transparent workpiece 160 (e.g., in the translation direction 101) to form the plurality of defects 172 of the contour line 170. Directing the pulsed laser beam 112 into the transparent workpiece 160 causes portions of the transparent workpiece 160 to fracture, for example, depositing enough energy to break chemical bonds in the transparent workpiece 160 at spaced locations along the desired line of separation 165 to form the defects 172. The pulsed laser beam may be translated across the transparent workpiece 160 by motion of the transparent workpiece 160 (e.g., motion of a translation stage 190 coupled to the transparent workpiece 160), motion of the pulsed laser beam (e.g., motion of the pulsed laser beam focal line 113), or motion of both the transparent workpiece 160 and the pulsed laser beam focal line 113. By translating the pulsed laser beam focal line 113 relative to the transparent workpiece 160, the plurality of defects 172 may be formed in the transparent workpiece 160.

[0079] As depicted in FIG. 2, the non-axisymmetric beam spot 114 comprises a long axis 116, a short axis 115, an axis intersection 118, which may be positioned at the center of the non-axisymmetric beam spot 114, and a beam spot perimeter 119. The long axis 116 may be defined as the axis of the non-axisymmetric beam spot 114 having the longest distance from center within the non-axisymmetric beam spot 114 and the short axis 115 may be defined as the axis of the non-axisymmetric beam spot 114 having the shortest distance from center within the non-axisymmetric beam spot 114. While the non-axisymmetric beam spot 114 is depicted in FIG. 2 as an ellipse, it should be understood that any non-axisymmetric shape is contemplated, such as a non-elliptical shape. Further, the non-axisymmetric beam spot 114 may comprise a collection of multiple beam spots. Moreover, it should be understood that while the non-axisymmetric beam spot 114 is substantially discussed herein, other cross sections of the pulsed laser beam focal line 113 within the transparent workpiece 160 are also non-axisymmetric and also comprise a short axis and a long axis, as described above with respect to the non-axisymmetric beam spot 114.

[0080] As examples, the distance from center of the non-axisymmetric beam spot 114 along the long axis may comprise from about 0.25 pm to about 20 pm, such as from about 1 pm to about 10 pm, from about 2 pm to about 8 pm, or from about 3 pm to about 6 pm. Further, the distance from center of the non-axisymmetric beam spot 114 along the short axis may comprises from about 0.01 pm to about 10 pm, from about 0.1 pm to about 10 pm, or from about 0.7 pm to about 3 pm. For example, the distance from center of the non-axisymmetric beam spot 114 along the short axis may be from about 5% to about 95% of the distance from center of the non-axisymmetric beam spot 114 along the long axis, such as from about 10% to about 50%, from about 20% to about 45%, or from about 30% to about 40% of the distance from center of the non-axisymmetric beam spot 114 along the long axis. Methods for determining beam spot size are disclosed hereinbelow.

[0081] The optical assemblies shown in FIG. IB and FIG. 3, when operated using a Gaussian beam laser having axial symmetry (e.g., when a beam source 110 outputs a Gaussian beam), form an optical beam at the transparent workpiece 160 known in the art as a Gauss-Bessel beam. Such a beam is one form of a quasi-non-diffracting beam (defined in greater detail below). When the axial symmetry of the Gaussian beam is broken, even slightly broken, the beam may then be termed an non-axisymmetric Gauss-Bessel beam. However, the principles and effects described herein extend beyond beams having a Gauss-Bessel intensity profile and extend to non-axisymmetric quasi-non-diffracting laser beams in general. However, it should be noted that measuring the asymmetry in a quasi-non-diffracting beam cannot be done as simply as measuring the asymmetry of a more traditional Gaussian beam. For instance, quasi non-diffracting beams typically have transverse profiles that are oscillatory, as compared to Gaussian beams, which decay monotonically. The diameter of a Gaussian beam is typically defined by a 1/e2 drop in intensity. In contrast, the intensity of a quasi-non-diffracting beam can fluctuate above and below a 1/e2 intensity threshold multiple times as a function of radial distance. Thus, defining the size of even a radially symmetric quasi-non-diffracting beam is challenging.

[0082] Moreover, while asymmetric Gaussian beams are known in the art, they are most often discussed as being single spots, where the Gaussian beam may have a larger diameter in the x-direction than in the y-direction, for example. However, for both higher-orders Gaussian beams and quasi-non-diffracting beams, the cross section of the beam may not have a single monotonically decaying core or spot. In such a situation, the “long” or “short” cross sectional axes of the beam are not readily apparent, which makes defining how to measure the asymmetry of a beam even more difficult.

[0083] While not intending to be limited by theory, it is with the above motivation that the following discussion is made to define both a quasi-non-diffracting beam and methods of measuring the asymmetry of a quasi-non-diffracting beam. This discussion is broadly applicable to all forms of laser beams, whether they are simple low-order Gaussian beams with monotonie intensity profiles or more complex quasi non-diffracting beams that project multiple spots or behave in an oscillatory manner. In the case of Gaussian beams, the results will reduce to more simple forms that are familiar from the Gaussian beam literature for defining spots size and Rayleigh range.

[0084] Referring again to FIGS. 1A- 2, the pulsed laser beam 112 used to form the defects 172 further has an intensity distribution I(X,Y,Z), where Z is the direction of propagation of the pulsed laser beam 112, and X and Y are directions orthogonal to the direction of propagation, as depicted in the figures. The X-direction and Y-direction may also be referred to as cross-sectional directions and the X-Y plane may be referred to as a cross-sectional plane. The intensity distribution of the pulsed laser beam 112 in a cross-sectional plane may be referred to as a cross-sectional intensity distribution.

[0085] Referring still to FIG. 2, the non-axisymmetric beam spot 114 comprises a cross-sectional intensity distribution that is non-axisymmetric. For example, the non-axisymmetric beam spot 114 may have a greater intensity and thereby a greater distribution of cumulated energy from the pulsed laser beam 112 in areas along the long axis 116 of the non-axisymmetric beam spot 114 than along the short axis 115 of the non-axisymmetric beam spot 114. That is, when the long axis 116 of the non-axisymmetric beam spot 114 is aligned with the desired line of separation 165, the pulsed laser beam 112 may transfer more energy along the desired line of separation 165 than onto areas adjacent the desired line of separation 165, forming defects 172 comprising longer radial arms 176 extending along the desired line of separation 165 than radial arms 176 extending in directions not along the desired line of separation 165. As used herein, “cumulated energy” refers to all energy transferred onto a particular area of the transparent workpiece 160 by the pulsed laser beam 112 as the pulsed laser beam 112 irradiates the transparent workpiece 160.

[0086] Further, the pulsed laser beam 112 at the non-axisymmetric beam spot 114 may comprise a quasi-non-diffracting beam, for example, a beam having low beam divergence as mathematically defined below, by propagating the pulsed laser beam 112 through a aspheric optical element 120, as described in more detail below with respect to the optical assemblies 100 depicted in FIGS. 3-7A. Beam divergence refers to the rate of enlargement of the beam cross section in the direction of beam propagation (i.e., the Z direction). As used herein, the phrase “beam cross section” refers to the cross section of the pulsed laser beam 112 along a plane perpendicular to the direction of propagation of the pulsed laser beam 112, for example, along the X-Y plane. One example beam cross section discussed herein is the beam spot (e.g., the non-axisymmetric beam spot 114) of the pulsed laser beam 112 projected onto the transparent workpiece 160.

[0087] Diffraction is one factor that leads to divergence of pulsed laser beams 112. Other factors include focusing or defocusing caused by the optical systems forming the pulsed laser beams 112 or refraction and scattering at interfaces. Pulsed laser beams 112 for forming the defects 172 of the contour line 170 may have small, non-axisymmetric beam spots 114, with low divergence and weak diffraction. The divergence of the pulsed laser beam 112 is characterized by the Rayleigh range ZR, which is related to the variance σ2 of the intensity distribution and beam propagation factor M2 of the pulsed laser beam 112. In the discussion that follows, formulas will be presented using a Cartesian coordinate system. Corresponding expressions for other coordinate systems are obtainable using mathematical techniques known to those of skill in the art. Additional information on beam divergence can be found in the articles entitled “New Developments in Laser Resonators” by A.E. Siegman in SPIE

Symposium Series Vol. 1224, p. 2 (1990) and “M2 factor of Bessel-Gauss beams” by R. Borghi and M. Santarsiero in Optics Letters, Vol. 22(5), 262 (1997), the disclosures of which are incorporated herein by reference in their entirety. Additional information can also be found in the international standards ISO 11146-1:2005(E) entitled “Lasers and laser-related equipment—Test methods for laser beam widths, divergence angles and beam propagation ratios—Part 1: Stigmatic and simple astigmatic beams”, ISO 11146-2:2005(E) entitled “Lasers and laser-related equipment—Test methods for laser beam widths, divergence angles and beam propagation ratios—Part 2: General astigmatic beams”, and ISO 11146-3:2004(E) entitled “Lasers and laser-related equipment—Test methods for laser beam widths, divergence angles and beam propagation ratios—Part 3: Intrinsic and geometrical laser beam classification, propagation and details of test methods”, the disclosures of which are incorporated herein by reference in their entirety.

[0088] The spatial coordinates of the centroid of the intensity profile of the pulsed laser beam 112 having a time-averaged intensity profile I(x,y,z) are given by the following expressions:

(1)

(2) [0089] These are also known as the first moments of the Wigner distribution and are described in Section 3.5 of ISO 11146-2:2005(E). Their measurement is described in Section 7 of ISO 11146-2:2005(E).

[0090] Variance is a measure of the width, in the cross-sectional (X-Y) plane, of the intensity distribution of the pulsed laser beam 112 as a function of position z in the direction of beam propagation. For an arbitrary laser beam, variance in the X-direction may differ from variance in the Y-direction. We let σ2(ζ) and Oy{z) represent the variances in the X-direction and Y-direction, respectively. Of particular interest are the variances in the near field and far field limits. We let Oqx{z) and σ£γ(z) represent variances in the X-direction and Y-direction, respectively, in the near field limit, and we let σ^χ (z) and a£,y (z) represent variances in the X-direction and Y-direction, respectively, in the far field limit. For a laser beam having a time-averaged intensity profile I(x,y,z) with Fourier transform I{vx,vy) (where vx and vy are spatial frequencies in the X-direction and Y-direction, respectively), the near field and far field variances in the x-direction and y-direction are given by the following expressions:

(3)

(4)

(5)

(6) [0091] The variance quantities Oqx (z) , σ£y(z), σ£>χ, and o£jy are also known as the diagonal elements of the Wigner distribution (see ISO 11146-2:2005(E)). These variances can be quantified for an experimental laser beam using the measurement techniques described in Section 7 of ISO 11146-2:2005(E). In brief, the measurement uses a linear unsaturated pixelated detector to measure I(x,y) over a finite spatial region that approximates the infinite integration area of the integral equations which define the variances and the centroid coordinates. The appropriate extent of the measurement area, background subtraction and the detector pixel resolution are determined by the convergence of an iterative measurement procedure described in Section 7 of ISO 11146-2:2005(E). The numerical values of the expressions given by equations 1-6 are calculated numerically from the array of intensity values as measured by the pixelated detector.

[0092] Through the Fourier transform relationship between the transverse amplitude profile ü(x,y,z) for an arbitrary optical beam (where I(x,y,z) = \u(x,y,z)\l) and the spatial-frequency distribution P(vx,vy, z) for an arbitrary optical beam (where /(vx, vy) = IP (vx> Vy, z) I ), it can be shown that:

Oy 00 = C702y (z„y ) + Ί2 σ2 y (ζ - z0y) (8) σ* 00 = σοχ (ζοχ) + Ί2 σ£* (ζ - ζ0χ)2 (7)

[0093] In equations (7) and (8), <7oxizox) and Oqy(z0y) are minimum values of Oqx(z) and °oy(z)> which occur at waist positions z0x and z0y in the x-direction and y-direction, respectively, and λ is the wavelength of the beam. Equations (7) and (8) indicate that σχ (z) and Oy{z) increase quadratically with z in either direction from the minimum values associated with the waist position of the beam.

[0094] Equations (7) and (8) can be rewritten in terms of a beam propagation factor M2, where separate beam propagations factors M2 and My for the x-direction and the y-direction are defined as: M2 = Ana0xomx (9)

My = 47ra0yaooy (10)

, 2( \ χ2Μν r Λ2 Oy (z) = <Joy{Z0y) + --~2 lZ - z0y) (12) (4Tra0y)

[0095] Rearrangement of Equations (9) and (10) and substitution into Equations (7) and (8) yields: ^2 σ2(z) = agx(z0x) + —-^ (z - z0x)2 (11) (Απσ0χ)

which can be rewritten as:

σ|00 = σ£χ(ζ0χ) 1 + ^ 0X>) (13) ZRx

Oy(Z) = Oly(z0y) 1 + - 0y^ (Η) ZRy where the Rayleigh ranges ZRx and ZRy in the x-direction and y-direction, respectively, are given by:

(15)

(16) [0096] The Rayleigh range corresponds to the distance (relative to the position of the beam waist as defined in Section 3.12 of ISO 11146-1:2005(E)) over which the variance of the laser beam doubles (relative to the variance at the position of the beam waist) and is a measure of the divergence of the cross sectional area of the laser beam. The Rayleigh range can also be observed as the distance along the beam axis at which the optical intensity decays to one half of its value observed at the beam waist location (location of maximum intensity). Laser beams with large Rayleigh ranges have low divergence and expand more slowly with distance in the direction of propagation than laser beams with small Rayleigh ranges.

[0097] The formulas above can be applied to any laser beam (not just Gaussian beams) by using the intensity profile I (x, y, z) that describes the laser beam. In the case of the TEM0o mode of a Gaussian beam, the intensity profile is given by:

(17) where w0 is the radius (defined as the radius at which beam intensity decreases to 1/e2 of the peak beam intensity of the beam at a beam waist position z0. From Equation (17) and the above formulas, we obtain the following results for a TEM0o Gaussian beam:

(18)

(19)

(20)

(21)

(22)

(23)

(24) where ZR = ZRx = ZRy. For Gaussian beams, it is further noted that M2 = Mx = My = 1.

[0098] Beam cross section is characterized by shape and dimensions. As stated previously, it may be desired to project a beam spot onto the transparent workpiece 160 that is a non-axisymmetric beam spot 114. Example non-axisymmetric cross sections include elliptical cross sections. The dimensions of the beam cross section are characterized by a spot size of the beam. For a Gaussian beam, spot size is frequently defined as the radial extent at which the intensity of the beam decreases to 1/e2 of its maximum value, denoted in Equation (17) as wQ. The maximum intensity of a Gaussian beam occurs at the center (x = 0 and y = 0 (Cartesian) or r = 0 (cylindrical)) of the intensity distribution and radial extent used to determine spot size is measured relative to the center.

[0099] Beams with axisymmetric (i.e. rotationally symmetric around the beam propagation axis Z) cross sections can be characterized by a single dimension or spot size that is measured at the beam waist location as specified in Section 3.12 of ISO 11146-1:2005(E). For a Gaussian beam, Equation (17) shows that spot size is equal to w0, which from Equation (18) corresponds to 2σ0χ or 2a0y. Spot size can be similarly defined for non-axisymmetric beam cross sections where, unlike an axisymmetric beam, σ0χ Ψ a0y. As a result, it is necessary to characterize the cross-sectional dimensions of a non-axisymmetric beam with two spot size parameters: wox and woy in the x-direction and y-direction, respectively, where

(25)

(26) [00100] The lack of axial (i.e. arbitrary rotation angle) symmetry for a non-axisymmetric beam means that the results of a calculation of values of σ0χ and a0y will depend on the choice of orientation of the x-axis and y-axis. For example the x-axis may be the long axis 116 of the non-axisymmetric beam spot 114 and the y-axis may be the short axis 115. The x-axis may be the short axis 115 and the y-axis may be the long axis 116. ISO 11146-1:2005(E) refers to these reference axes as the principal axes of the power density distribution (Section 3.3-3.5) and in the following discussion we will assume that the x and y axes are aligned with these principal axes. Further, an angle φ about which the x-axis and y-axis may be rotated in the cross-sectional plane (e.g., an angle of the x-axis and y-axis relative to reference positions for the x-axis and y-axis, respectively) may be used to define minimum (wo,min) ar|d maximum values (womax) of the spot size parameters for a non-axisymmetric beam:

(27)

(28) where 2<Jq min ~ 2 Ooχ{.Φτηίη,χ) ~ 2ö"oy (jPminy) and 2(7,o,max ~ 2 Obx(0max,x) — 2σ0y(0max,y) The magnitude of the axial asymmetry of the beam cross section can be quantified by the aspect ratio, where the aspect ratio is defined as the ratio of wo max to w0,min· An axisymmetric beam cross section has an aspect ratio of 1.0, while elliptical and other non-axisymmetric beam cross sections have aspect ratios greater than 1.0, for example, greater than 1.1, greater than 1.2, greater than 1.3, greater than 1.4, greater than 1.5, greater than 1.6, greater than 1.7, greater than 1.8, greater than 1.9, greater than 2.0, or the like [00101] The beam cross section influences the cross sectional shape of the defects 172 formed by the pulsed laser beam 112 in the transparent workpiece 160. Cross-sectional shape of the defects 172 refers to shape of the defects in the direction perpendicular to the direction of propagation of the pulsed laser beam 112. If, for example, a laser beam is normally incident to the imaging surface 162 of the transparent workpiece 160, the cross-sectional shape of the defect 172 corresponds to the shape of the defects 172 in the plane of the imaging surface 162, or in any plane parallel to the plane of the imaging surface 162 of the workpiece. As an example, a laser beam with a circular beam cross section forms a defect 172 with a circular shape and a laser beam with a non-circular beam cross section forms a defect 172 with a non-circular shape.

[00102] Control of the beam cross section leads to more effective cutting, fewer defects, and higher edge strength in separated parts. Control of the beam cross section includes control of the spot size, cross-sectional shape, and orientation of the beam cross section. Without wishing to be bound by theory, it is believed that non-axisymmetric beam cross sections having a maximum spot size parameter wo max oriented along (or approximately along) the desired line of separation 165 improves cutting by directing crack orientation along the trajectory of cutting. In the case of an axisymmetric beam cross section, it is believed that stresses associated with the formation of damage regions are concentrated near the damage region, but with random orientations. The random stress orientations are believed to lead to fracture in directions away from the intended trajectory of cutting, manifested as micro cracks and other defects in separated parts. It is believed that such micro cracks and defects reduce the mechanical strength of the bulk and/or edges of separated parts. By employing non-axisymmetric beam cross sections and beam spots and orienting the direction of the maximum spot size wo max (e.g., the long axis 116) along the desired line of separation 165, it is believed that defects or cracks associated with forming damage regions can be directed along the cut with the formation of fewer cracks or defects in directions away from the desired line of separation 165. Defects of cracks aligned with the desired line of separation 165 are preferred to defects or cracks directed away from the desired line of separation 165.

[00103] Aspect ratios

of the beam cross section of the pulsed laser beam 112 (e.g., aspect ratios of the non-axisymmetric beam spot 114) used to form defects 172 may be greater than 1.1, greater than 1.3, greater than 1.5, greater than 2.0, greater than 2.5, greater than 3.0, greater than 3.5, greater than 4.0, greater than 5.0, greater than 7.5, greater than 10.0, in the range from 1.1 to 20.0, in the range from 1.2 to 15.0, in the range from 1.3 to 10.0, in the range from 1.3 to 7.5, in the range from 1.3 to 5.0, in the range from 1.5 to 7.5, in the range from 1.5 to 5.0, in the range from 1.5 to 3.0, in the range from 1.75 to 5.0, in the range from 2.0 to 4.0, or the like.

[00104] To promote uniformity of defects 172 in the direction of laser propagation (e.g. depth dimension of the transparent workpiece 160), a pulsed laser beam 112 having low divergence may be used. Non-axisymmetric laser beams having low divergence may be utilized for forming defects 172. As noted above, divergence can be characterized by the Rayleigh range. For non-axisymmetric beams, Rayleigh ranges for the principal axes X and Y are defined by Equations (15) and (16) for the x-direction and y-direction, respectively, where it can be shown that for any real beam, Mx > 1 and My > 1 and where Gqx and a^y are determined by the intensity distribution of the laser beam. For symmetric beams, Rayleigh range is the same in the X-direction and Y-direction and is expressed, for a beam with a Gaussian intensity distribution, by Equation (22) or Equation (23). Low divergence correlates with large values of the Rayleigh range and weak diffraction of the laser beam.

[00105] Beams with Gaussian intensity profiles may be less preferred for laser processing to form defects because, when focused to small enough spot sizes (such as spot sizes in the range of microns, such as about 1-5 microns or about 1-10 microns) to enable available laser pulse energies to modify materials such as glass, they are highly diffracting and diverge significantly over short propagation distances. To achieve low divergence, it is desirable to control or optimize the intensity distribution of the pulsed laser beam to reduce diffraction. Pulsed laser beams may be non-diffracting or weakly diffracting. Weakly diffracting laser beams include quasi-non-diffracting laser beams. Representative weakly diffracting laser beams include Bessel beams, Gauss-Bessel beams, Airy beams, Weber beams, and Mathieu beams.

[00106] For non-axisymmetric beams, the Rayleigh ranges ZRx and ZRy are unequal. Equations (15) and (16) indicate that ZRx and ZRy depend on σ0χ and a0y, respectively, and above we noted that the values of σ0χ and a0y depend on the orientation of the X-axis and Y-axis. The values of ZRx and ZRy will accordingly vary, and each will have a minimum value and a maximum value that correspond to the principal axes, with the minimum value of ZRx being denoted as ZRx rnin and the minimum value of ofZRy being denoted ZRymin . In a similar manner to the formulas that characterize the Rayleigh ranges of an axially symmetric Gaussian beam (Equation (22) or Equation (23)), for an arbitrary beam profile ZRxrnin and ZRy min can be shown to be given by

(29)

and (30) [00107] Since divergence of the laser beam occurs over a shorter distance in the direction having the smallest Rayleigh range, the intensity distribution of the pulsed laser beam used for cutting may be controlled so that the minimum values of ZRx and ZRy are as large as possible. Since the minimum value ZRxmin of ZRx and the minimum value ZRymin of ZRy differ for a non-axisymmetric beam, a laser beam with an intensity distribution may be used that makes the smaller of ZRxmin and ZRymin as large as possible when forming damage regions.

[00108] The smaller of ZRx min and ZRymin can be greater than or equal to 50 μιη, greater than or equal to 100 μιη, greater than or equal to 200 μιη, greater than or equal to 300 μιη, greater than or equal to 500 μιη, greater than or equal to 1 mm, greater than or equal to 2 mm, greater than or equal to 3 mm, greater than or equal to 5 mm, in the range from 50 μιη to 10 mm, in the range from 100 μιη to 5 mm, in the range from 200 μιη to 4 mm, in the range from 300 μιη to 2 mm, or the like.

[00109] The values and ranges for the smaller of ZRx min and ZRy min specified herein are achievable for different wavelengths to which the workpiece is transparent through adjustment of the spot size parameter wo jnin defined in Equation (27). The spot size parameter w0itnin may be greater than or equal to 0.25 μιη, greater than or equal to 0.50 μιη, greater than or equal to 0.75 μιη, greater than or equal to 1.0 μιη, greater than or equal to 2.0 μιη, greater than or equal to 3.0 μιη, greater than or equal to 5.0 μιη, in the range from 0.25 μιη to 10 μιη, in the range from 0.25 μιη to 5.0 μιη, in the range from 0.25 μιη to 2.5 μιη, in the range from 0.50 μιη to 10 μιη, in the range from 0.50 μιη to 5.0 μιη, in the range from 0.50 μιη to 2.5 μιη, in the range from 0.75 μιη to 10 μιη, in the range from 0.75 μιη to 5.0 μιη, in the range from 0.75 μιη to 2.5 μιη, or the like.

[00110] The Rayleigh range of the laser beam used to form damage regions may be greater than the Rayleigh range of a Gaussian beam having the same wavelength. Accordingly, the ratio of the smaller of ΖΚχτηίη and ZRy min to the Rayleigh range ZR of a Gaussian beam (as specified in either of Equations (22) or (23)), at a common wavelength λ, may be greater than or equal to 2, greater than or equal to 5, greater than or equal to 10, greater than or equal to 25, greater than or equal to 50, greater than or equal to 100, greater than or equal to 250, greater than or equal to 500, greater than or equal to 1000, in the range from 2 to 1500, in the range from 5 to 1250, in the range from 10 to 1000, in the range from 25 to 1000, in the range from 100 to 1000, or the like.

[00111] Non-diffracting or quasi non-diffracting beams generally have complicated intensity profiles, such as those that decrease non-monotonically vs. radius. By analogy to a Gaussian beam, an effective spot size wo eff can be defined for non-axisymmetric beams as the shortest radial distance, in any direction, from the radial position of the maximum intensity (r = 0) at which the intensity decreases to 1/e2 of the maximum intensity. A criterion for Rayleigh range based on the effective spot size wo eff can be specified non-diffracting or quasi non-diffracting beams for forming damage regions, as follows:

(31) where FD is a dimensionless divergence factor having a value of at least 10, at least 50, at least 100, at least 250, at least 500, at least 1000, in the range from 10 to 2000, in the range from 50 to 1500, in the range from 100 to 1000. By comparing Equation (31) to Equation (22) or (23), one can see that for a non-diffracting or quasi non-diffracting beam the distance, Smaller of ZRxmin,ZRyrnin in Equation (31), over which the effective beam size doubles, is Fd times the distance expected if a typical Gaussian beam profile were used.

[00112] The dimensionless divergence factor FD provides a criterion for determining whether or not a laser beam is quasi-non-diffracting. As used herein, a laser beam is considered quasi-non-diffracting if the characteristics of the laser beam satisfy Equation (31) with a value of FD > 10. As the value of FD increases, the laser beam approaches a more nearly perfectly non-diffracting state.

[00113] Referring now to FIGS. 3-7A, optical assemblies 100 for producing a pulsed laser beam 112 that is quasi non-diffracting (FIGS. 3-7A) and can produce a non-axisymmetric beam spot 114 at the transparent workpiece 160 (FIGS. 4-7A). For example, FIG. 3 depicts a conventional optical assembly 100 for pulsed laser processing, for example, for producing a pulsed laser beam 112 that is quasi-non-diffracting. Further, FIGS. 4-7A each depict optical assemblies 100 that comprise additional components and arrangements not present in FIG. 3, for forming the non-axisymmetric beam spot 114 at the transparent workpiece 160. For example, the optical assembly 100 of FIG. 4 comprises an aspheric optical element 120 that is offset relative to the beam pathway 111, the optical assemblies 100 of FIGS. 5A and 5B include one or more optical blocking elements 140 positioned in the beam pathway 111. Further, the optical assemblies 100 of FIGS. 6 and 7A each comprise one or more decohering optical elements configured to decohere a first beam portion of the pulsed laser beam 112 from a second beam portion of the pulsed laser beam 112. In particular, decohering optical element of the optical assembly 100 of FIG. 6 comprises an optical delay plate 142 positioned in the beam pathway 111, and the decohering optical element of the optical assembly 100 of FIG. 7A comprises a split quarter waveplate 150 (also depicted in FIG. 7B) positioned in the beam pathway 111. As used herein, to “decohere” means to make a first portion of the pulsed laser beam incoherent with a second portion of the pulsed laser beam.

[00114] Each of FIGS. 3-7A comprise a beam source 110, the aspheric optical element 120 (e.g., an axicon lens), a first lens 130, and a second lens 132. Further, the transparent workpiece 160 may be positioned such that the pulsed laser beam 112 output by the beam source 110 irradiates the transparent workpiece 160, for example, after traversing the aspheric optical element 120 and thereafter, both the first and second lens 130, 132. An optical axis 102 extends between the beam source 110 and the transparent workpiece 160 along the Z-axis. Moreover, the optical assemblies 100 of FIGS. 3-7A may optionally comprise a dove prism 180 positioned between the aspheric optical element 120 and the transparent workpiece 160 in the beam pathway 111. While the dove prism 180 is depicted in FIGS. 5A, 5B, and 6, it should be understood that any of the optical assemblies 100 described herein may comprise the dove prism 180. Further, rotation of the dove prism 180 about the optical axis 102 may rotate the beam cross section of the pulsed laser beam 112 (e.g., the non-axisymmetric beam spot 114). Rotation of the non-axisymmetric beam spot 114 facilitates orienting the long axis 116 of the non-axisymmetric beam spot 114 along the desired line of separation 165 of the transparent workpiece 160. As described below, other methods of rotating the non-axisymmetric beam spot 114 are contemplated.

[00115] Referring still to FIGS. 3-7A, the beam source 110 may comprise any known or yet to be developed beam source 110 configured to output pulsed laser beams 112. In operation, the defects 172 of the contour line 170 are produced by interaction of the transparent workpiece 160 with the pulsed laser beam 112 output by the beam source llO.The beam source 110 may output a pulsed laser beam 112 comprising a wavelength of for example, 1064 nm, 1030 nm, 532 nm, 530 nm, 355 nm, 343 nm, or 266 nm, or 215 nm. Further, the pulsed laser beam 112 used to form defects 172 in the transparent workpiece 160 may be well suited for materials that are transparent to the selected pulsed laser wavelength.

[00116] Suitable laser wavelengths for forming defects 172 are wavelengths at which the combined losses of absorption and scattering by the transparent workpiece 160 are sufficiently low. The combined losses due to absorption and scattering by the transparent workpiece 160 at the wavelength may be less than 20%/mm, or less than 15%/mm, or less than 10%/mm, or less than 5%/mm, or less than 1%/mm, where the dimension “/mm” means per millimeter of distance within the transparent workpiece 160 in the direction of propagation of the pulsed laser beam 112 (e.g., the Z direction). Representative wavelengths for many glass workpieces include fundamental and harmonic wavelengths of Nd3+ (e.g. Nd3+:YAG or Nd3+:YV04 having fundamental wavelength near 1064 nm and higher order harmonic wavelengths near 532 nm, 355 nm, and 266 nm). Other wavelengths in the ultraviolet, visible, and infrared portions of the spectrum that satisfy the combined absorption and scattering loss requirement for a given substrate material can also be used.

[00117] In operation, the pulsed laser beam 112 output by the beam source 110 may create multi-photon absorption (MPA) in the transparent workpiece 160. MPA is the simultaneous absorption of two or more photons of identical or different frequencies that excites a molecule from one state (usually the ground state) to a higher energy electronic state (i.e., ionization). The energy difference between the involved lower and upper states of the molecule is equal to the sum of the energies of the involved photons. MPA, also called induced absorption, can be a second-order or third-order process (or higher order), for example, that is several orders of magnitude weaker than linear absorption. It differs from linear absorption in that the strength of second-order induced absorption may be proportional to the square of the light intensity, for example, and thus it is a nonlinear optical process.

[00118] The perforation step that creates the contour line 170 may utilize the beam source 110 (e.g., an ultra-short pulse laser) in combination with the optics depicted and described below with respect to FIGS. 3A-7A, to project the non-axisymmetric beam spot 114 on the transparent workpiece 160 and generate the pulsed laser beam focal line 113 of FIG. IB. The pulsed laser beam focal line 113 comprises a quasi non-diffracting beam, such as a non-axisymmetric Gauss-Bessel beam, as defined above, to fully perforate the transparent workpiece 160 to form the series of defects 172 in the transparent workpiece 160. The pulse duration of the individual pulses can be in a range of from about 1 picosecond to about 100 picoseconds, such as from about 5 picoseconds to about 20 picoseconds, and the repetition rate of the individual pulses may be in a range from about 1 kHz to 4 MHz, such as in a range from about 10 kHz to about 3 MHz, or from about 10 kHz to about 650 kHz.

[00119] Referring also to FIGS. 7C and 7D, in addition to a single pulse operation at the aforementioned individual pulse repetition rates, the pulses may be produced in pulse bursts 500 of two pulses 500A (e.g., sub-pulses) or more (such as, for example, 3 pulses, 4 pulses, 5 pulses, 10 pulses, 15 pulses, 20 pulses, or more per pulse burst, such as from 1 to 30 pulses per pulse burst 500, or from 5 to 20 pulses per pulse burst 500). The pulses 500A within the pulse burst 500 may be separated by a duration that is in a range from about 1 nsec to about 50 nsec, for example, from about 10 nsec to about 30 nsec, such as about 20 nsec. The pulses 500A within the pulse burst 500 may be separated by a duration of up to 100 psec (for example, 0.1 psec, 5 psec, 10 psec, 15 psec, 18 psec, 20 psec, 22 psec, 25 psec, 30 psec, 50 psec, 75 psec, or any range therebetween). For a given laser, the time separation Tp (FIG. 7D) between adjacent pulses 500A within a pulse burst 500 may be relatively uniform (e.g., within about 10% of one another). For example, each pulse 500A within a pulse burst 500 can be separated in time from the subsequent pulse by approximately 20 nsec (50 MHz). For example, the time between each pulse burst 500 may be from about 0.25 microseconds to about 1000 microseconds, e.g., from about 1 microsecond to about 10 microseconds, or from about 3 microseconds to about 8 microseconds.

[00120] The time separation Tb (FIG. 7D) can be about 5 microseconds for the beam source 110 outputting a pulsed laser beam 112 comprising a burst repetition rate of about 200 kHz. The laser burst repetition rate is related to the time Tb between the first pulse in a burst to the first pulse in the subsequent burst (laser burst repetition rate = l/Tb).The laser burst repetition rate may be in a range of from about 1 kHz to about 4 MHz. The laser burst repetition rates may be, for example, in a range of from about 10 kHz to 650 kHz. The time Tb between the first pulse in each burst to the first pulse in the subsequent burst may be from about 0.25 microsecond (4 MHz burst repetition rate) to about 1000 microseconds (1 kHz burst repetition rate), for example from about 0.5 microseconds (2 MHz burst repetition rate) to about 40 microseconds (25 kHz burst repetition rate), or from about 2 microseconds (500 kHz burst repetition rate) to about 20 microseconds (50k Hz burst repetition rate). The exact timing, pulse duration, and burst repetition rate may vary depending on the laser design, but short pulses (Td <20 psec and, in can be Td- 15 psec) of high intensity have been shown to work particularly well.

[00121] The burst repetition rate may be in a range of from about 1 kHz to about 2 MHz, such as from about 1 kHz to about 200 kHz. Bursting or producing pulse bursts 500 is a type of laser operation where the emission of pulses 500A is not in a uniform and steady stream but rather in tight clusters of pulse bursts 500. The pulse burst laser beam may have a wavelength selected based on the material of the transparent workpiece 160 being operated on such that the material of the transparent workpiece 160 is substantially transparent at the wavelength. The average laser power per burst measured at the material may be at least about 40 pJ per mm of thickness of material. For example the average laser power per burst may be from about 40 pJ/mm to about 2500 pJ/mm, or from about 500 pJ/mm to about 2250 pj/mm. In a specific example, for 0.5 mm to 0.7 mm thick Coming EAGLE XG® transparent workpiece, pulse bursts of from about 300 pJ to about 600 pJ may cut and/or separate the workpiece, which corresponds to an exemplary range of about 428 pj/mm to about 1200 pj/mm (i.e., 300 pJ/0.7 mm for 0.7 mm EAGLE XG® glass and 600 pJ/0.5 mm for a 0.5 mm EAGLE XG® glass).

[00122] The energy required to modify the transparent workpiece 160 may be described in terms of the burst energy (i.e., the energy contained within a pulse burst 500 where each pulse burst 500 contains a series of pulses 500A), or in terms of the energy contained within a single laser pulse (many of which may comprise a burst). The energy per pulse burst may be from about 25 pJ to about 750 pJ, e.g., from about 50 pJ to about 500 pJ, or from about 50 pJ to about 250 pJ. For some glass compositions, the energy per pulse burst may be from about 100 pJ to about 250 pJ. However, for display or TFT glass compositions, the energy per pulse burst may be higher (e.g., from about 300 pJ to about 500 pJ, or from about 400 pJ to about 600 pJ, depending on the specific glass composition of the transparent workpiece 160). The use of a pulsed laser beam 112 capable of generating such bursts is advantageous for cutting or modifying transparent materials, for example glass. In contrast with the use of single pulses spaced apart in time by the repetition rate of the single-pulsed laser, the use of a burst sequence that spreads the laser energy over a rapid sequence of pulses within the burst allows access to larger timescales of high intensity interaction with the material than is possible with single-pulse lasers.

[00123] Referring again to FIGS. 3-7A, the aspheric optical element 120 is positioned within the beam pathway 111 between the beam source 110 and the transparent workpiece 160. In operation, propagating the pulsed laser beam 112, e.g., an incoming Gaussian beam, through the aspheric optical element 120 may alter pulsed laser beam 112 such that the portion of the pulsed laser beam 112 propagating beyond the aspheric optical element 120 is quasi-non-diffracting, as described above. The aspheric optical element 120 may comprise any optical element comprising an aspherical shape. The aspheric optical element 120 may comprise a conical wavefront producing optical element, such as an axicon lens, for example, a negative refractive axicon lens, a positive refractive axicon lens, a reflective axicon lens, a diffractive axicon lens, a programmable spatial light modulator axicon lens (e.g., a phase axicon), or the like.

[00124] The aspheric optical element 120 can comprise at least one aspheric surface whose shape is mathematically described as:

where z' is the surface sag of the aspheric surface, r is the distance between the

aspheric surface and the optical axis 102 in a radial direction (e.g., in an x-direction or a y-direction), c is the surface curvature of the aspheric surface (i.e. c^UR^ where R is the surface radius of the aspheric surface), k is the conic constant, and coefficients at are the first through the twelfth order aspheric coefficients or higher order aspheric coefficients (polynomial aspheres) describing the aspheric surface. At least one aspheric surface of the aspheric optical element 120 can include the following coefficients aq-aq, respectively: -0.085274788; 0.065748845; 0.077574995; -0.054148636; 0.022077021; -0.0054987472; 0.0006682955; and the aspheric coefficients α8-α12 are 0. The at least one aspheric surface can have the conic constant k = 0. However, because the a1 coefficient has a nonzero value, this is equivalent to having a conic constant k with a non-zero value. Accordingly, an equivalent surface may be described by specifying a conic constant k that is non zero, a coefficient a1 that is non-zero, or a combination of a nonzero k and a non-zero coefficient aq. Further, the at least one aspheric surface can be described or defined by at least one higher order aspheric coefficients α2-α12 with non-zero value (i.e., at least one of a2 a3 ... , ai2^0)-The agphgrïc optical element 120 can comprise a third-order aspheric optical element such as a cubically shaped optical element, which comprises a coefficient a3 that is non-zero.

[00125] When the aspheric optical element comprises an axicon, the axicon may have a laser output surface 126 (e.g., conical surface) having an angle of about 1.2°, such as from about 0.5° to about 5°, or from about 1° to about 1.5°, or even from about 0.5° to about 20°, the angle measured relative to the laser input surface 124 (e.g., flat surface) upon which the pulsed laser beam 112 enters the axicon lens. Further, the laser output surface 126 terminates at a conical tip. Moreover, the aspheric optical element 120 includes a centerline axis 122 extending from the laser input surface 124 to the laser output surface 126 and terminating at the conical tip. The aspheric optical element 120 may comprise a waxicon, a spatial phase modulator such as a spatial light modulator, or a diffractive optical grating. In operation, the aspheric optical element 120 shapes the incoming pulsed laser beam 112 (e.g., an incoming Gaussian beam) into a quasi-non-diffracting beam, which, in turn, is directed through the first lens 130 and the second lens 132.

[00126] Referring still to FIGS. 3-7A, the first lens 130 and the second lens 132 may collimate the pulsed laser beam 112 within a collimation space 134 between the first and second lens 130, 132. Further, the second lens 132 may focus the pulsed laser beam 112 into the transparent workpiece 160, which may be positioned at an imaging plane 104. The first lens 130 and the second lens 132 can each comprise plano-convex lenses. When the first lens 130 and the second lens 132 each comprise plano-convex lenses, the curvature of the first lens 130 and the second lens 132 may each be oriented toward the collimation space 134. The first lens 130 may comprise other collimating lenses and the second lens 132 may comprise a meniscus lens, an asphere, or another higher-order corrected focusing lens.

[00127] Further, the first lens 130 comprises a first focal length Fi and the second lens 132 comprises a second focal length F2. As used herein “focal length” is defined as the distance between the lens and the focal point of the lens. The first focal length Fi and second focal length F2 may be equal. The first focal length Fi and the second focal length F2 may be different, for example, the second focal length F2 may be less than the first focal length Fi or alternatively may be greater than the second focal length F2. The first and second lens 130, 132 may have focal lengths Fi, F2. respectively, of from about 10 mm to about 200 mm (such as from about 25 mm to about 200 mm, or from about 50 mm to 150 mm or from about 75 mm to about 100 mm, or from about from about 25 mm to about 50 mm, or the like).

[00128] The first lens 130 may be spaced from the second lens 132 by the sum of the first focal length Fi and the second focal length F2 such that a common focal plane 105 is positioned in the collimation space 134 between the first lens 130 and the second lens 132. However, it should be understood that other spacing arrangements are contemplated. The common focal plane 105 is a location along the beam pathway 111 between the first lens 130 and the second lens 132 spaced a first focal length Fi downstream from the first lens 130 and spaced a second focal length F2 upstream from the second lens 132. As used herein “upstream” and “downstream” refer to the relative position of two locations or components along the beam pathway 111 with respect to the beam source 110. For example, a first component is upstream from a second component if the pulsed laser beam 112 traverses the first component before traversing the second component. Further, a first component is downstream from a second component if the pulsed laser beam 112 traverses the second component before traversing the first component.

[00129] Referring now to FIG. 4, the optical assembly 100 is depicted comprising the aspheric optical element 120 positioned offset relative to the beam pathway 111 of the pulsed laser beam 112 in a radial direction (e.g., a direction along a radius of the pulsed laser beam 112, orthogonal to the beam propagation direction). By offsetting the aspheric optical element 120 relative to the beam pathway 111, the resultant beam spot projected onto the transparent workpiece 160 may comprise the non-axisymmetric beam spot 114 depicted in FIG. 2. The aspheric optical element 120 may be positioned offset from the beam pathway 111 (e.g., offset in the X-Y plane) by an offset distance a. In particular, the offset distance a is the distance in the X-Y plane between the centerline axis 122 of the aspheric optical element 120 and the cross-sectional center of the pulsed laser beam as the pulsed laser beam irradiates the laser input surface 124 of the aspheric optical element 120. The relative offset between the aspheric optical element 120 and the beam pathway may be achieved by shifting the aspheric optical element 120 along the X-Y plane, shifting the beam source 110 along the X-Y plane, or both. The magnitude of the offset required to sufficiently break the symmetry of the resulting beam spot is a function of the diameter of the pulsed laser beam 112, with smaller input laser beam diameters requiring less offset to sufficiently break the symmetry. The offset distance a may comprise from about 10 microns to about 500 microns, for example, 20 microns, 50 microns, 100 microns, 250 microns, or the like. The offset distance a may be from about 20 microns to about 100 microns, or from about 50 microns to about 100 microns, or the like.The offset distance may comprise a distance from about 10% to about 75% of a cross sectional diameter of the pulsed laser beam 112 at a contact location between the pulsed laser beam 112 and the aspheric optical element 120 (e.g., at the laser input surface 124 of the aspheric optical element 120).

[00130] By offsetting the aspheric optical element 120 relative to the beam pathway 111, the resultant pulsed laser beam 112 may comprise a decreased overall intensity, for example, by a factor of about 4. Further the cross section of the pulsed laser beam 112 may broaden in the X-direction, the Y-direction, or a combination thereof in the X-Y plane by a factor of from about 1.2 to about 2, for example, 1.4, 1.6, 1.8, or the like. Broadening the cross section of the pulsed laser beam 112 forms the non-axisymmetric beam spot 114 having the long axis 116 in the direction of broadening. The resultant pulsed laser beam 112 may comprise a non-axisymmetric cone of rays, which form a non-axisymmetric ring in the collimation space 134 after traversing the first lens 130. Further, the cross section of the pulsed laser beam 112 (e.g., the non-axisymmetric beam spot 114) may be rotated by rotating the aspheric optical element 120 about the optical axis 102.

[00131] Referring now to FIGS. 5A and 5B, the optical assembly 100 are depicted comprising one or more optical blocking elements 140 (e.g., opaque optical elements) that are positioned at one or more blocking locations 141 along the beam pathway 111, blocking a portion of the pulsed laser beam 112 propagating between the beam source 110 and the transparent workpiece 160. The optical blocking elements 140 may comprise an opaque plate which may further comprise an aperture. For example, the optical blocking elements 140 may comprise a metal plate, or other substance that can withstand the energy of the pulsed laser beam 112 without breaking or being damaged. The optical blocking element 140 may be positioned in the beam pathway 111 such that the optical blocking element 140 blocks from about 5% to about 95% of the beam intensity of the pulsed laser beam 112, for example, at least about 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 85%, 90%, or the like. As one example, the optical blocking element 140 blocks from about 25% to about 80% of the beam intensity of the pulsed laser beam 112. Blocking a larger percentage of the beam intensity of the pulsed laser beam 112 increases the length of the long axis 116 of the non-axisymmetric beam spot 114 relative to the length of the short axis 115 of the non-axisymmetric beam spot 114. However, blocking a larger percentage of the beam intensity of the pulsed laser beam 112 increases the amount of power in the pulsed laser beam 112 lost at the optical blocking element 140.

[00132] The optical blocking element 140 may block a cross sectional sector of the pulsed laser beam 112 (i.e., a sector defined by an azimuthal angle range or “pie slice” of the pulsed laser beam 112 that extends from a central location of the pulsed laser beam 112 to the outermost diameter of the pulsed laser beam 112). An optical blocking element 140 in the form of a sector has the advantage that equal percentages of the rays at all radii in the pulsed laser beam 112 are blocked. In such an optical assembly, the optics map rays of specific radii to corresponding specific locations along the pulsed laser beam focal line 113. In FIGS. 5A and 5B, the lower radius rays in the vicinity of the aspheric optical element 120 will be mapped to locations at the upstream end of the pulsed laser beam focal line 113, and the higher radius rays in the vicinity of the aspheric optical element 120 will be mapped to locations near the downstream end of the pulsed laser beam focal line 113. If the optical blocking element 140 cuts out a larger fraction of rays at small radii than at large radii, then the magnitude or aspect ratio of the ellipticity of the cross sections of pulsed laser beam focal line 113 (the non-axisymmetric beam spot 114, as one example) will change throughout its length. As such, shaping the optical blocking element 140 in the form of a pie slice ensures that the resulting cross sections of the pulsed laser beam focal line 113 will maintain a constant ellipticity through the full length of the pulsed laser beam focal line 113.

[00133] The optical blocking element 140 may block a cross sectional chord portion of the pulsed laser beam 112, wherein the cross-sectional chord portion of the pulsed laser beam 112 is bounded by a portion of the cross sectional circumference of the pulsed laser beam 112 and an arbitrary cross-sectional chord of the pulsed laser beam 112. Further, a portion of the optical blocking element 140 that is positioned in the beam pathway 111 may be coterminous with the arbitrary cross-sectional chord. Moreover, it should be understood that the optical blocking element 140 may block any arbitrary cross sectional portion of the pulsed laser beam 112.

[00134] Further, the optical blocking element 140 may be positioned between the beam source 110 and the transparent workpiece 160. Because the optical blocking element 140 is positioned between the beam source 110 and the transparent workpiece 160, in operation, the pulsed laser beam 112 will travel through the aspheric optical element 120 and beyond the optical blocking element 140 (e.g., an unblocked portion of the pulsed laser beam 112 will travel beyond the optical blocking element 140 but the blocked portion of the pulsed laser beam 112 not travel beyond the optical blocking element 140). Further, the pulsed laser beam 112 will travel through the aspheric optical element 120 and beyond the optical blocking element 140 regardless of the relative order of positioning of the aspheric optical element 120 and the optical blocking element 140 along the direction of beam propagation (e.g., the Z-direction). For example, the optical blocking element 140 may be positioned upstream from the aspheric optical element 120, such that the optical blocking element 140 is positioned between the beam source 110 and the aspheric optical element 120. Further, the optical blocking element 140 may be positioned downstream from the aspheric optical element 120, such that the optical blocking element 140 is positioned between the aspheric optical element 120 and the transparent workpiece 160.

[00135] The optical blocking element 140 may be positioned in the collimation space 134 between the first and second lens 130, 132, for example, at the common focal plane 105. Further, the cross-section of the pulsed laser beam focal line 113 (e.g., the non-axisymmetric beam spot 114) may be rotated by rotating the optical blocking element 140 about the optical axis 102. The non-axisymmetric beam spot 114 may be formed by both offsetting the aspheric optical element 120 relative to the beam pathway 111 and blocking a portion of the pulsed laser beam 112 with the optical blocking element 140. If the offset of the aspheric optical element 120 is used to direct more of the laser beam energy past the optical blocking element 140, then this combination of offsetting and blocking may lower the amount of power loss caused by the optical blocking element 140 while still ensuring that the elliptical or otherwise non-axisymmetric beam spot 114 is generated and projected onto the transparent workpiece 160.

[00136] Further, as depicted in FIG. 5B, the optical assembly 100 may comprise a first optical blocking element 140a and a second optical blocking element 140b. The first optical blocking element 140a is positioned in the beam pathway 111 at a first blocking location 141a and the second optical blocking element is positioned in the beam pathway 111 at a second blocking location 141b. The first optical blocking element 140a and the second optical blocking element 140b may be positioned such that they each block a portion of the beam pathway 111, for example, different portions of the beam pathway 111. The first optical blocking element 140a and the second optical blocking element 140b may each block different cross section segments of the pulsed laser beam 112. For example, the optical blocking element 140a, 140b may define cross sectional chord portions of each blocked cross sectional segment that are positioned in parallel such that they block opposite sides of the cross section of the pulsed laser beam 112. Or, in another example, the optical blocking element 140a, 140b may define different sectors of a circle, such that they block opposite sides of the cross section of the pulsed laser beam 112.

[00137] The first and second blocking locations 141a, 141b can be positioned at the same Z-axis location along the optical axis 102, as depicted in FIG. 5B. The first and second blocking locations 141a 141b may be different locations along optical axis 102. Further, the first and second optical blocking elements 140a, 140b may collectively block from about 5% to about 75% of the intensity of the pulsed laser beam 112. Further, the first and second first and second optical blocking elements 140a, 140b may block equivalent percentages of the intensity of the pulsed laser beam 112 or different percentages of the intensity of the pulsed laser beam 112.

[00138] Moreover, while the blocking locations 141, 141a, 141b in FIGS. 5A and 5B are each depicted between the beam source 110 and the aspheric optical element 120, it should be understood that the blocking locations 141, 141a, 141b may be any location between the beam source 110 and the and the transparent workpiece 160, for example, between the first lens 130 and the second lens 132, for example, at the common focal plane 105. While not intending to be limited by theory, blocking the pulsed laser beam 112 with multiple (e.g., two) optical blocking elements 140 may project multiple beam spots onto the imaging surface 162 of the transparent workpiece shaped such that the multiple beam spots collectively defining the non-axisymmetric beam spot 114 at the transparent workpiece 160, as depicted in FIG. 2.

[00139] Referring now to FIG. 6, the optical assembly 100 is depicted comprising one or more optical delay plates 142 positioned between the beam source 110 and the transparent workpiece 160. In operation, positioning the optical delay plate 142 in the beam pathway 111 may form the non-axisymmetric beam spot 114 depicted in FIG. 2 by inducing an optical delay within a portion of the pulsed laser beam 112 to decohere a first beam portion of the pulsed laser beam 112 from a second beam portion by directing the first portion of the pulsed laser beam 112 through the optical delay plate to induce optical retardation of the first beam portion. The optical delay plate 142 may be positioned within the beam pathway 111 such that about 50% of the pulsed laser beam 112 (e.g., about 50% of the intensity of the pulsed laser beam 112) traverses the optical delay plate 142. While not intending to be limited by theory, the optical delay over half the pulsed laser beam 112 may form two beams collectively defining a non-axisymmetric beam spot 114 at the transparent workpiece 160. Further, the cross section of the pulsed laser beam 112 (e.g., the non-axisymmetric beam spot 114) may be rotated by rotating the optical delay plate 142 about the optical axis 102. Further, the optical delay plate 142 may be positioned upstream or downstream the aspheric optical element 120. For example, the optical delay plate 142 can be positioned between the aspheric optical element 120 and the transparent workpiece 160 or the optical delay plate 142 can be positioned between the beam source 110 and the aspheric optical element 120.

[00140] Optically delaying a portion (for example, one half) of the pulsed laser beam 112 may form a single non-axisymmetric beam spot 114 if the portion of the beam that traverses the optical delay plate 142 and the portion of the beam that does not traverse the optical delay plate 142 combine incoherently. To achieve incoherence, the coherence length of the pulsed laser beam 112 may be shorter than the optical thickness of the optical delay plate 142. In such a case, the optical delay of the two beams need not be set to any exact amount or controlled precisely; the optical delay may only be greater than the coherence time of the laser pulse. This is substantially equivalent to randomizing the optical phase difference between the two portions of the laser beam. The coherence time Tc of an individual laser pulse may be calculated using methods known in the art, and is mathematically described as

where λ is the wavelength of the radiation, c is the speed of light, and Δλ is the spectral bandwidth of the laser pulse. The thickness difference supplied by the optical delay plate 142 may be greater than the coherence time of the laser pulse, or equivalently, thicker than the coherence length of the laser pulse in the plate, which is mathematically described as

, where n is the refractive index of the material of the optical delay plate 142. For example, for a 1030 nm laser of 12.2 nm spectral pulse width, the coherence time Tc will be about 290 psec, and the required thickness of a n=1.5 glass plate to decohere the beam will be greater than 38 microns. In another example, for a 1064 nm laser of 0.38 nm spectral pulse width, the coherence time will be about 290 psec, the required thickness of an index n=1.5 glass plate to decohere the beam will be greater than 1.3 mm.

[00141] While not intending to be limited by theory, the exact coherence time and coherence length are functions of the exact temporal and spectral shapes of the laser pulses, and as such, the formulas above are approximations. Thus, it is possible for sufficient decohering functionality of the delay plate to be achieved with thickness that may be slightly less than the values calculated by the above formulas (e.g. about 10% less , about 25% less , about 50% less, or the like).

[00142] Rather than decohere the two portions of the beam and/or in addition thereto the optical delay plate 142 may be configured to induce a specific optical delay, for example, the optical delay plate 142 may induce an optical retardation of π over half the pulsed laser beam 112 (where one optical period of the laser wavelength is considered to cover 2π radians of optical phase, so an optical retardation of π is a delay of one-half the optical period), an optical retardation of 0.875π over half the pulsed laser beam 112, and can have an optical retardation of 0.5π over half the laser beam. The exact profile of the intensity cross section of the beam can be altered from that of two equal high intensity spots near the center of the beam, to having one spot with more intensity and the other with less intensity near the center of the beam, to other more complex interference patterns, simply by adjusting the precise optical phase delay between the two portions of the beam. The specific optical retardation induced by the optical delay plate 142 is correlated with the optical thickness of the optical delay plate 142. However, while such a system generates a non-axisymmetric beam spot 114, the resultant beam spot is sensitive to exact optical path lengths of the two beam portions, which can be altered by environmental changes such as temperature and humidity. Such a multi-spot pattern has a complex multi-axis stress concentration, which may not be as useful a stress concentration for controlling crack formation as would a beam with an elliptical core.

[00143] Referring now to FIGS. 7A and 7B, the optical assembly 100 is depicted comprising the split quarter waveplate 150 positioned between the beam source 110 and the transparent workpiece 160. The split quarter waveplate 150 comprises a first plate portion 152 having a first fast axis 156a and a first slow axis 158a. The split quarter waveplate 150 also comprises and a second plate portion 154 having a second fast axis 156b and a second slow axis 158b. Further, the first fast axis 156a is orthogonal to the second fast axis 156b and the first slow axis 158a is orthogonal to the second slow axis 158b. When the pulsed laser beam 112 traverses the split quarter waveplate 150, the first plate portion 152 having the first fast axis 156a and first slow axis 158a polarizes a first beam portion of the pulsed laser beam 112 into a first polarization (e.g., a specific horizontal, vertical, or circular polarization) and the second plate portion 154 having the second fast axis 156b polarizes a second beam portion of the pulsed laser beam 112 into a second polarization (e.g., another specific horizontal, vertical, or circular polarization). Polarizing the first beam portion to a first polarization and polarizing the second beam portion to a second polarization that is orthogonal the second beam portion decoheres the first beam portion from the second beam portion.

[00144] Further, the first polarization can be orthogonal to the second polarization such that the first beam portion and the second beam portion combine incoherently downstream from the split quarter waveplate 150 to form the non-axisymmetric beam spot 114 depicted in FIG. 2. While not intending to be limited by theory, two pulsed laser beam portions having orthogonal polarizations (e.g., vertical and horizontal, right-handed circular and left-handed circular) do not interfere and, when each are projected onto the transparent workpiece 160, each beam portion combines incoherently and collectively form the non-axisymmetric beam spot 114 (e.g., an ellipse). As an illustrative example, the first polarization and the second polarization each comprise a location on a Poincaré Sphere positioned apart by about 90° such that they are orthogonal. It should be understood that incoherent combination between the first and second beam portions may occur with any two orthogonal polarizations.

[00145] As depicted in FIG. 7A, the optical assembly 100 may further comprise a polarizer 144 and a quarter waveplate 146. The polarizer 144 and the quarter waveplate 146 are each positioned in the beam pathway 111 between the beam source 110 and the split quarter waveplate 150 such that the pulsed laser beam 112 traverses the polarizer 144 and the quarter waveplate 146 prior to traversing the split quarter waveplate 150. In operation, the polarizer 144 may filter (e.g., prevent) one or more specific polarizations from traversing the polarizer 144. The quarter waveplate 146 may polarize the pulsed laser beam 112 into a single polarization such that the pulsed laser beam 112 comprises a single polarization, such as right-handed circular polarization, or left-handed circular polarization, when the pulsed laser beam 112 reaches the split quarter waveplate 150. Further, as depicted in FIG. 7A, the split quarter waveplate 150 is positioned in the beam pathway 111 between the quarter waveplate 146 and the transparent workpiece 160. The split quarter waveplate 150 may be positioned upstream or downstream the aspheric optical element 120. For example, the split quarter waveplate 150 can be positioned between the aspheric optical element 120 and the transparent workpiece 160 or the split quarter waveplate 150 can be positioned between the beam source 110 and the aspheric optical element 120.

[00146] In FIG. 7A, the split quarter waveplate 150 may be positioned in the collimation space 134 between the first lens 130 and the second lens 132, for example, positioned at the common focal plane 105, such that a minimal amount of power in the pulsed laser beam 112 is lost due to interaction at the contact location between the first plate portion 152 and the second plate portion 154 of the split quarter waveplate 150.

[00147] While the split quarter waveplate 150 is depicted as comprising two plate portions (e.g., the first and second plate portions 152, 154), the split quarter waveplate 150 may comprise any number of plate portions. As with the previously described blocking elements, these portions of the spilt quarter waveplate 150 may be made in the form of cross sectional chord portions, or more preferably sectors. A first plurality of plate portions can comprise the first fast axis 156a and the first slow axis 158a and a second plurality of plate portions comprise the second fast axis 156b and the second slow axis 158b. Further, the first plurality of plate portions may collectively comprise about 50% of the split quarter waveplate 150 and the second plurality of plate portions may collectively comprise another 50% of the split quarter waveplate 150.

[00148] Referring again to FIGS. 1A-7B, a method for forming the contour line 170 comprising defects 172 along the desired line of separation 165 includes directing (e.g., localizing) a pulsed laser beam 112 oriented along the beam pathway 111 and output by the beam source 110 into the transparent workpiece 160 such that the portion of the pulsed laser beam 112 directed into the transparent workpiece 160 generates an induced absorption within the transparent workpiece and the induced absorption produces a defect 172 within the transparent workpiece 160. For example, the pulsed laser beam 112 may comprise a pulse energy and a pulse duration sufficient to exceed a damage threshold of the transparent workpiece 160. Directing the pulsed laser beam 112 into the transparent workpiece 160 may comprise focusing the pulsed laser beam 112 from output by the beam source 110 into a pulsed laser beam focal line 113 oriented along the beam propagation direction (e.g., the Z axis). The transparent workpiece 160 is positioned in the beam pathway 111 to at least partially overlap the pulsed laser beam focal line 113 of pulsed laser beam 112. The pulsed laser beam focal line 113 is thus directed into the transparent workpiece 160. The pulsed laser beam 112, e.g., the pulsed laser beam focal line 113 generates induced absorption within the transparent workpiece 160 to create the defect 172 in the transparent workpiece 160. The first lens 130 and/or the second lens 132 may focus the pulsed laser beam 112. If the first lens 130 and the second lens 132 are not included, the aspheric optical element 120 (e.g., an axicon lens) may focus the pulsed laser beam 112. Individual defects 172 may be created at rates of several hundred kilohertz (i.e., several hundred thousand defects per second).

[00149] In operation, the position of pulsed laser beam focal line 113 may be controlled by suitably positioning and/or aligning the pulsed laser beam 112 relative to the transparent workpiece 160 as well as by suitably selecting the parameters of the optical assembly 100. Further, the pulsed laser beam focal line 113 may have a length in a range of from about 0.1 mm to about 100 mm or in a range of from about 0.1 mm to about 10 mm. A pulsed laser beam focal line 113 with a length 1 of about 0.1 mm, about 0.2 mm, about 0.3 mm, about 0.4 mm, about 0.5 mm, about 0.7 mm, about 1 mm, about 2 mm, about 3 mm, about 4 mm, or about 5 mm e.g., from about 0.5 mm to about 5 mm can be configured.

[00150] Referring still to FIGS. 1A-7A, the method for forming the contour line 170 comprising defects 172 along the desired line of separation 165 may include translating the transparent workpiece 160 relative to the pulsed laser beam 112 (or the pulsed laser beam 112 may be translated relative to the transparent workpiece 160, for example, in a translation direction 101 depicted in FIGS. 1A and 2) to form contour lines 170 that trace out the shape of a desired part with defects 172. The defects 172 that may penetrate the full depth of the glass. It should be understood that while sometimes described as “holes” or “hole-like,” the defects 172 disclosed herein may generally not be void spaces, but are rather portions of the workpiece which has been modified by laser processing as described herein. The defects 172 may generally be spaced apart from one another by a distance of from about 5 microns to about 20 microns. For example, suitable spacing between the defects 172 may be from about 0.1 microns to about 30 microns, such as from about 5 microns to about 15 microns, from about 5 microns to about 12 microns, from about 7 microns to about 15 microns, or from about 7 microns to about 12 microns for the TFT/display glass compositions. Further, the translation of the transparent workpiece 160 relative to the pulsed laser beam 112 may be performed by moving the transparent workpiece 160 and/or the beam source 110 using one or more translation stages 190.

[00151] Beyond the perforation of a single transparent workpiece 160, the process may also be used to perforate stacks of transparent workpieces 160, such as stacks of sheets of glass, and may fully perforate glass stacks of up to a few mm total height with a single laser pass. A single glass stack can comprise of various glass types within the stack, for example one or more layers of soda-lime glass layered with one or more layers of Corning code 2318 glass. The glass stacks additionally may have air gaps in various locations. Ductile layers such as adhesives may be disposed between the glass stacks. However, the pulsed laser process described herein will still, in a single pass, fully perforate both the upper and lower glass layers of such a stack.

[00152] Further, following the formation of the contour line 170 in the transparent workpiece 160, a stress inducing source, such as a mechanical or thermal source may be utilized to separate the transparent workpiece 160 along the contour line 170. The thermal source, such as an infrared laser beam, may be used to create thermal stress and thereby separate the transparent workpiece 160 at the contour line 170. An infrared laser may be used to initiate spontaneous separation and then the separation may be finished mechanically. Suitable infrared lasers to create thermal stress in glass would typically have wavelengths that are readily absorbed by glass, typically having wavelengths ranging from 1.2 microns to 13 microns, for example, a range of 4 microns to 12 microns. The infrared laser beam, such as a laser beam produced by a carbon dioxide laser (a “CO2 laser”), a carbon monoxide laser (a “CO laser”), a solid state laser, a laser diode, or combinations thereof, is a controlled heat source that rapidly increases the temperature of the transparent workpiece 160 at or near the contour line 170. This rapid heating may build compressive stress in the transparent workpiece 160 on or adjacent to the contour line 170. Since the area of the heated glass surface is relatively small compared to the overall surface area of the transparent workpiece 160, the heated area cools relatively rapidly. The resultant temperature gradient induces tensile stress in the transparent workpiece 160 sufficient to propagate a crack along the contour line 170 and through the thickness of the transparent workpiece 160, resulting in full separation of the transparent workpiece 160 along the contour line 170. Without being bound by theory, it is believed that the tensile stress may be caused by expansion of the glass (i.e., changed density) in portions of the workpiece with higher local temperature.

[00153] In view of the foregoing description, it should be understood that formation of a contour line comprising defects along a desired line of separation may be enhanced by utilizing a pulsed laser beam which is shaped by an optical assembly such that the pulsed laser beam projects a non-axisymmetric beam spot onto the workpiece along the desired line of separation.

EXAMPLES

[00154] Example 1 [00155] Example 1 is a modeled result of a pulsed laser beam having a 532 nm wavelength output into an example optical assembly having an aspheric optical element that is aligned with the beam pathway (e.g., no offset). The pulsed laser beam is output as a symmetric Gaussian beam and is formed into a quasi-non-diffracting beam by the aspheric optical element. FIG. 8A depicts an example cross-sectional intensity plot of the pulsed laser beam focal line (e.g., quasi-non diffracting pulsed laser beam focal line). As shown in FIG. 8A, without an offset, the beam spot is radially symmetric. The full-width half maximum (FWHM) of the cross-sectional intensity plot of FIG. 8A is 3.8 microns. FIG. 8B depicts a logarithmic intensity plot of the Fourier transform plane of the quasi-non diffracting pulsed laser beam focal line formed without an offset. Further, FIG. 8C depicts an experimental near-field micrograph of the quasi-non diffracting pulsed laser beam focal line formed without an offset at a peak line-focus position.

[00156] Example 2 [00157] Example 2 is a modeled result of a pulsed laser beam having a 1064 nm wavelength output into an example optical assembly having an aspheric optical element that is offset relative to the beam pathway by an offset distance of 20 microns in the X-direction. The pulsed laser beam is output as an axisymmetric Gaussian beam and is formed into a quasi-non-diffracting beam by the aspheric optical element. FIG. 9 depicts an example cross-sectional intensity plot of the resultant non-axisymmetric pulsed laser beam focal line formed by the offset between the aspheric optical element and the beam pathway.

[00158] Example 3 [00159] Example 3 is a modeled result of a pulsed laser beam having a 1064 nm wavelength output into an example optical assembly having an aspheric optical element that is offset relative to the beam pathway by an offset distance of 50 microns in the X-direction. The pulsed laser beam is output as an axisymmetric Gaussian beam and is formed into a quasi-non-diffracting beam by the aspheric optical element. FIG. 10 depicts an example cross-sectional intensity plot of the resultant non-axisymmetric pulsed laser beam focal line formed by the offset between the aspheric optical element and the beam pathway.

[00160] Example 4 [00161] Example 4 includes modeled and experimental results of a pulsed laser beam having a 1064 nm wavelength that is output into an example optical assembly having an aspheric optical element that is offset relative to the beam pathway by an offset distance of 100 microns in the X-direction. The pulsed laser beam is output as an axisymmetric

Gaussian beam and is formed into a quasi-non-diffracting beam by the aspheric optical element. FIG. 11A depicts an example cross-sectional intensity plot of the modeled resultant non-axisymmetric pulsed laser beam focal line formed by the offset between the aspheric optical element and the beam pathway. FIG. 11B depicts X and Y cross-sections of the cross-sectional intensity plot of the modeled result of FIG. 11A at a best focus axial position, which a location approximately mid-way along the length of the pulsed laser beam focal line. FIG. 11C depicts a cross-section of the cross-sectional intensity plot of the modeled result of FIG. 11A at an axial position shifted by about 200 microns from the best focus axial position of FIG. 11B. The FWHM of the intensity plot of FIG. 11C is 7.0x4.5 microns, showing an asymmetry of about 1.6. Further, FIG. 11D depicts a modeled logarithmic intensity plot of the Fourier transform plane of the pulsed laser beam (e.g., quasi-non diffracting pulsed laser beam) formed with a 100 micron offset. As shown in FIG. 11D, the logarithmic intensity plot is not uniform. Further, FIG. 11E depicts an experimental near-field micrograph of the pulsed laser beam focal line of example 4 at the peak line-focus position.

[00162] Example 5 [00163] Example 5 is a modeled result of an example optical assembly includes an axicon as the aspheric optical element and an optical blocking element positioned between the first and second lens such that the optical blocking element blocks 50% of the intensity of a pulsed Gauss-Bessel beam. Blocking 50% of the intensity of the pulsed Gauss-Bessel beam produces the same mathematical outcome as multiplying a Fourier transform of the pulsed Gauss-Bessel beam by a one-dimensional Heaviside step function. In a 2D image space this generates a 2D Gauss-Bessel beam convolved with the Fourier transform of a ID Heaviside step function H(x). The Heaviside step function is related to the Sgn step function by H(x)= HlSgnlx) + 1). Tables of Fourier transforms show that in two dimensions:

(32)

Such that: (33) [00164] A Gauss-Bessel beam convolved with a delta function mathematically describes a Gauss-Bessel at an origin point. For illustration, FIG. 12A depicts a cross sectional intensity plot (along the X-Y plane) of a Bessel-Gauss beam convolved with a delta function. Further, FIG. 12B depicts a cross sectional intensity plot (along the X-Y plane) of a Gauss-Bessel beam convolved with 1 Ιίκχ' Moreover, equation 33 mathematically describes a convolution of the Gauss-Bessel beam with the Fourier transform of a Sgn function which is mathematically equivalent to blocking 50% of the intensity of the Gauss-Bessel beam. FIG. 12C depicts a cross sectional intensity plot (along the X-Y plane) of a Gauss-Bessel beam convolved with the Fourier transform of a Heaviside step function as mathematically described in Eq. 33. The cross-sectional intensity plot (along the X-Y plane) of FIG. 12C is also the resultant cross sectional intensity of the pulsed laser beam focal line formed by blocking 50% of the beam pathway. Accordingly, spacing of the spots or peaks of intensity in the resultant non-axisymmetric pulsed laser beam focal line is governed by the axicon angle and the telescope magnification (e.g., the magnification generated by the ratio of the focal length of the lens 132 to the focal length of the lens 130) but not the tilt, offset, or aberrations in the optics. Further, FIG. 12D graphically depicts X-axis cross sections of the intensity plots of FIGS. 12A-12C and FIG. 12E graphically depicts the Fourier transform of an example Sgn step function.

[00165] FIG. 12F depicts a cross-sectional intensity plot of a resultant non-axisymmetric pulsed laser beam focal line formed when the pulsed laser beam traverses the axicon and 50% of the beam intensity of the pulsed laser beam is blocked by an optical blocking element positioned along the beam pathway halfway between the first lens and the second lens. FIG. 12G graphically depicts X and Y cross-sections of the intensity plot of FIG. 12F. FIG. 12H depicts a cross-sectional intensity of a resultant non-axisymmetric pulsed laser beam focal line when 50% of the beam intensity is blocked by an optical blocking element positioned at the beam source (e.g., positioned at a Z=0 location). FIG. 121 graphically depicts X and Y cross-sections of the intensity plot of FIG. 12H. As shown in FIGS 12F-12I, the Z-axis position of the optical blocking element along the beam pathway has minimal effect on the resultant pulsed laser beam focal line. This shows that the optical blocking element can be effective whether it is placed in the space before the axicon, or after the axicon, such as in the collimation space 134 between the two lens 130 and 132. Thus, it may be preferred to generate non-axisymmetric pulsed laser beam focal line using the optical blocking element.

[00166] Example 6 [00167] Example 6 is a modeled result of incrementally blocking cross sectional segments of a pulsed laser beam having a 600 micron 1/e2 diameter. In particular, example 6 includes blocking different cross section segments of the pulsed laser beam each having an increased maximum blocked width, where the term “maximum blocked width” is defined as the width of the blocked portion of the pulsed laser beam (e.g., the blocked portion of the beam pathway) measured perpendicular from a center point of the cross sectional chord portion of the blocked cross sectional segment. FIG. 13A depicts an example intensity plot in the X-Y plane of the resultant pulsed laser beam focal line without blocking the pulsed laser beam. As shown in FIG. 13A, with no blocking, the cross-sectional pulsed laser beam focal line is axisymmetric. FIGS. 13B-13K depict example intensity plots in the X-Y plane having blocked cross sectional segments with increasing maximum blocked widths. For example, the maximum blocked width in FIG. 13B is 50 microns, the maximum blocked width in FIG. 13C is 100 microns, the maximum blocked width in FIG. 13D is 150 microns, the maximum blocked width in FIG. 13E is 200 microns, the maximum blocked width in FIG. 13F is 250 microns, the maximum blocked width in FIG. 13G is 300 microns (e.g., blocking half of the pulsed laser beam), the maximum blocked width in FIG. 13H is 350 microns, the maximum blocked width in FIG. 131 is 400 microns, the maximum blocked width in FIG. 13J is 450 microns, and the maximum blocked width in FIG. 13K is 500 microns.

[00168] Example 7 [00169] In example 7, a quasi-non-diffracting pulsed laser beam having a wavelength of 532 nm is output into an example optical assembly having an optical blocking element positioned such that the optical blocking element blocks 50% of the pulsed laser beam. FIG. 14 depicts a near field micrograph of a cross-section of a non-axisymmetric pulsed laser beam focal line formed by blocking 50% of the pulsed laser beam in example 7.

[00170] Example 8 [00171] In example 8, a quasi-non-diffracting pulsed laser beam having a wavelength of 532 nm is output into an example optical assembly having an optical blocking element positioned such that the optical blocking element blocks 75% of the pulsed laser beam. FIG. 15 depicts a near field micrograph of a cross-section of a non-axisymmetric pulsed laser beam focal line formed by blocking 75% of the pulsed laser beam in example 8. Note that the non-axisymmetric pulsed laser beam focal line of example 8 comprises a larger aspect ratio than the non-axisymmetric pulsed laser beam focal line of example 7.

[00172] Example 9 [00173] In example 9, an optical blocking element is positioned in an example optical assembly such that the optical blocking element blocks a quarter sector of the cross sectional pulsed laser beam (and thus blocks 25% of the intensity of the pulsed laser beam). FIG. 16 depicts example resultant cross-section of non-axisymmetric pulsed laser beam focal lines formed by the optical blocking element at incremental 45° rotations of the optical blocking element about the optical axis (e.g., about the propagation direction of the pulsed laser beam).

[00174] Example 10 [00175] Example 10 models blocking two cross sectional segments of a pulsed laser beam having a 600 micron 1/e2 diameter at the common focal plane between the first lens and the second lens using two optical blocking elements oriented such that they block cross sectional chord portion of the pulsed laser beam each terminating at parallel chords and each having equal maximum blocked widths (as defined above with respect to example 6). FIG. 17A depicts an example intensity plot in the X-Y plane of the resultant pulsed laser beam focal line without blocking the pulsed laser beam. As shown in FIG. 17A, with no blocking, the cross-section of the pulsed laser beam focal line is axisymmetric. FIGS. 17B-17F depict example intensity plots in the X-Y plane having two parallel blocked cross sectional segments with increasing and equal maximum blocked widths. For example, each maximum blocked width in FIG. 17B is 50 microns, each maximum blocked width in FIG. 17C is 100 microns, each maximum blocked width in FIG. 17D is 150 microns, each maximum blocked width in FIG. 17E is 200 microns, and each maximum blocked width in FIG. 17F is 250 microns. Note that the pulsed laser beam focal line cross sections in FIGs. 17A-17F show multiple fringes and much of the laser energy is thrown outside of the central core spot of the pulsed laser beam focal line, even for Figure 17B. This means the central spot has lower intensity and more laser power may be needed at the input of the optical system to facilitate cutting the transparent workpiece. The large amount of energy present in the non-central fringes of Figure 17B-17F will also create different stress profiles at the transparent workpiece that do not concentrate the stress as well as when the optical energy is mostly contained in the central ellipse.

[00176] Example 11 [00177] Example 11 is an experimental confirmation of the modeled results of example 10 and is done with an example optical assembly that includes a 632 nm HeNe laser. In example 11, two optical blocking elements are positioned in the example optical assembly such that each optical blocking element blocks a cross sectional segment of the pulsed laser beam within the collimation space 134 between the two lenses 130 and 132, where the diameter of the collimated beam ring is about 22mm and the cross sectional chord portions formed by each optical blocking element terminate at chords that are positioned parallel and are spaced apart by about 9 mm. FIG. 18 depicts the example resultant cross sections of non-axisymmetric pulsed laser beam focal lines (each comprising multiple beam spots) formed by each of the example optical blocking elements at incremental 45° rotations of the example optical blocking elements about the optical axis (e.g., about the propagation direction of the pulsed laser beam).

[00178] Example 12 [00179] In example 12, an optical blocking element is positioned in an example optical assembly that also includes an aspheric optical element which is offset relative to the optical pathway of the pulsed laser beam. For example, FIG. 19A depicts a cross sectional image of a pulsed laser beam after the pulsed laser beam traversed an axicon offset from the beam pathway by 50 microns and a half aperture optical blocking element positioned to block 50% of a pulsed laser beam in a non-offset system. FIG. 19B depicts an example cross-sectional intensity plot of the resultant non-axisymmetric pulsed laser beam focal line formed by the block and shift arrangement depicted in FIG. 19A.

[00180] Example 13 [00181] In example 13, an optical delay plate that induces an optical delay of π is positioned within a beam pathway such that 50% of the pulsed laser beam traverses the optical delay plate and undergoes an optical delay of π. FIG. 20A depicts a cross-sectional intensity plot of the resultant non-axisymmetric pulsed laser beam focal line formed by the optical delay of π of 50% of the pulsed laser beam. FIG. 20B depicts cross-sections of the cross-sectional intensity plot of FIG. 20A.

[00182] Example 14 [00183] In example 14, an optical delay plate that induces an optical delay of 0.875π is positioned within a beam pathway such that 50% of the pulsed laser beam traverses the optical delay plate and undergoes an optical delay of π. FIG. 21A depicts a cross-sectional intensity plot of the resultant non-axisymmetric pulsed laser beam focal line formed by the optical delay of 0.875π of 50% of the pulsed laser beam. FIG. 21B depicts a cross-sections of the cross-sectional intensity plot of FIG. 21A.

[00184] Example 15 [00185] In example 15, an optical delay plate that induces an optical delay of 0.5π is positioned within a beam pathway such that 50% of the pulsed laser beam traverses the optical delay plate and undergoes an optical delay of π. FIG. 22A depicts a cross-sectional intensity plot of the resultant non-axisymmetric pulsed laser beam focal line formed by the optical delay of 0.5π of 50% of the pulsed laser beam. FIG. 22B depicts cross-sections of the cross-sectional intensity plot of FIG. 22A.

[00186] Example 16 [00187] In example 16, a split quarter waveplate as described above may be positioned in a beam pathway of a laser beam output by a HeNe laser such that a first beam portion of the HeNe laser beam is polarized into a first polarization and a second beam portion of the HeNe laser beam is polarized into a second polarization that is orthogonal the first polarization. FIG. 23 depicts example resultant non-axisymmetric pulsed laser beam focal lines formed by the split quarter waveplate at incremental 45° rotations of the example split quarter waveplate about the optical axis (e.g., about the propagation direction of the pulsed laser beam).

[00188] Ranges can be expressed herein as from “about” one particular value, and/or to “about” another particular value. When such a range is expressed, another example includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another example. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[00189] Directional terms as used herein - for example up, down, right, left, front, back, top, bottom - are made only with reference to the figures as drawn and are not intended to imply absolute orientation.

[00190] Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order, nor that with any apparatus specific orientations be required. Accordingly, where a method claim does not actually recite an order to be followed by its steps, or that any apparatus claim does not actually recite an order or orientation to individual components, or it is not otherwise specifically stated in the claims or description that the steps are to be limited to a specific order, or that a specific order or orientation to components of an apparatus is not recited, it is in no way intended that an order or orientation be inferred, in any respect. This holds for any possible non-express basis for interpretation, including: matters of logic with respect to arrangement of steps, operational flow, order of components, or orientation of components; plain meaning derived from grammatical organization or punctuation.

[00191] As used herein, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a” component includes aspects having two or more such components, unless the context clearly indicates otherwise.

[00192] It will be apparent to those skilled in the art that various modifications and variations can be made to the invention described herein without departing from the spirit and scope of the claimed subject matter. Thus it is intended that the specification cover the modifications and variations of the invention described herein provided such modification and variations come within the scope of the appended claims and their equivalents.

Claims

A method of laser processing a transparent workpiece, such as a glass substrate, the method comprising: providing a transparent workpiece, directing a laser beam onto the workpiece to thereby form a contour line in the transparent workpiece, along which contour line the transparent workpiece can be separated.

The method of claim 1, wherein the laser beam is a pulsed laser beam that is emitted from a laser beam source, wherein the pulsed laser beam is located in the transparent workpiece, the pulsed laser beam propagating along a beam path in a z direction, which comprises pulsed laser beam : a wavelength λ; an effective spot size w0; a pulse energy and a pulse duration sufficient to exceed a damage threshold of the transparent workpiece so as to form the contour line in the transparent workpiece, which contour line comprises a defect in the transparent workpiece;

a non-axisymmetrical beam cross-section with a minimum Rayleigh range ZRx> rnin in an x direction and a minimum Rayleigh range ZRy> min in a y direction; wherein the smaller of ZRx min and ZRy rnin is greater than, wherein FD has a dimensionless divergence factor with a value of 10 or greater.

The method of claim 1 or 2, wherein the laser beam has pulse energy and a pulse duration that is sufficient to exceed a damage threshold of the transparent workpiece to form sufficient contour line which contour line includes a defect in the transparent work piece.

Processing method according to one of the preceding claims, wherein the smaller of ZRx min and ZRy min is one or more of the following: greater than or equal to 200 μπι, greater than or equal to 1 mm, located in the range of 50 μιη up to 10 mm, is in the range of 300 μιη to 2 mm.

Processing method according to any of the preceding claims, wherein the non-axisymmetric cross-section has a maximum spot size parameter wo min, a minimum spot size parameter has wo min and an aspect ratio

where the aspect ratio is greater than 1.1.

The editing method of claim 4, wherein the aspect ratio is one or more of the following: greater than 2.0, is in the range of 1.2 to 15.0, is in the range of 1.5 to 3, 0.

The processing method according to claim 5 or 6, wherein wo min is one or more of the following: greater than or equal to 0.25 µm, greater than or equal to 1.0 µm, in the range of 0.25 µm to 10 µm, in the range of 0.5 µm to 2.5 µm.

Processing method according to any of the preceding claims 2-7, wherein the non-axisymmetrical beam cross-section has a non-elliptical shape.

Processing method according to any of the preceding claims 2-8, wherein the smaller of ZRXimin and ZRy min is greater than

, or greater than

Processing method according to any of claims 2-9, wherein the pulsed laser beam has a wavelength λ where the transparent workpiece has combined losses due to absorption and scattering of less than 20% / mm in the z direction.

The processing method according to any of the preceding claims 2-10, further comprising forming the pulsed laser beam with the non-axisymmetric beam cross-section from a Gaussian laser beam, wherein the Gaussian laser beam has a Rayleigh range ZR.

Processing method according to any of the preceding claims 2-11, wherein the ratio of the smallest of ZRxrnin and ZRymin to ZR is greater or equal to 5, or wherein the ratio of the smallest of ZRxrnin and ZRymin to ZR is greater or equal to 50.

The method of any one of the preceding claims, wherein the laser beam comprises a first portion and a second portion, wherein the first portion is inconsistent with respect to the second portion.

A method according to any one of the preceding claims, wherein the laser beam is directed through an aspherical optical element so that the laser beam generates an indicated absorption within the transparent workpiece.

The method of claim 14, wherein the aspherical optical element is shifted to a radial direction of the beam path.

Method according to any of the preceding claims 2-15, further comprising translating the transparent workpiece and the pulsed laser beam relative to each other along the peripheral line, so as to form a number of defects along the contour line within the transparent workpiece with laser.

The method of any preceding claim, further comprising directing an infrared laser beam at the transparent workpiece along or near the contour line to separate the transparent workpiece along the contour line.

The method of any one of claims 16 or 17, wherein the distance between the neighboring defects is from 1 micron to about 30 microns.

A method according to any of claims 14-18, wherein the aspherical optical element comprises a refractive axicon, reflective axicon, waxicon, negative axicon and spatial light modulator, a difractic opical element or a cubically shaped optical element.

The method of any one of claims 14-19, wherein: the aspherical optical element is offset from the beam path in the radial direction by a shift distance; and the offset distance is a distance of about 10% to about 75% of a cross-sectional diameter of the pulsed laser beam at a contact location between the pulsed laser beam and the aspheric optical element.

A method according to any of the preceding claims 2-20, wherein the dimensionless divergence factor FD comprises a value from about 10 to about 2000, preferably wherein the dimensionless divergence factor FD comprises from about 50 to about 1500, more preferably wherein the dimensionless divergence factor FD includes a value of about 100 to about 1000.

A method according to any of the preceding claims 2-21, wherein the non-axisymmetric beam cross-section of the pulsed laser beam arranged in the transparent workpiece comprises a long axis with womax beam size parameter and a short axis with spot size parameter w0> min where wo rnax longer is then wo rnin and an aspect ratio of wo rnax to w0> min is greater than 1.3.

A method according to any of the preceding claims 3-22, wherein the defect comprises a central defect region and at least one radial arm extending outward from the central defect region along the long axis of the non-axisymmetric beam cross-section of the pulsed laser beam that is focused in the transparent workpiece.

The method of any one of the preceding claims 14-23, further comprising: rotating a deaf prism around the road, the deaf prism being positioned along the road between the aspherical optical element and the transparent workpiece such that the pulsed laser beam deaf prism; and translating the transparent workpiece and the pulsed laser beam relative to each other along the contour line whereby a number of defects along the contour line within the transparent workpiece are formed by the laser such that a portion of the contour line curves along an image surface of the transparent workpiece includes.

The method of any one of the preceding claims 14-24, further comprising: rotating the aspherical optical element about the beam path, and translating the transparent workpiece and the pulsed laser beam relative to each other along the contour line, causing a number of defects are formed by the laser along the contour line within the transparent workpiece such that a portion of the contour line comprises a curvature along an imaging surface of the transparent workpiece.

The method of any one of the preceding claims, wherein the transparent workpiece comprises glass, sapphire, fused silica or combinations thereof.

The method of any one of claims 2-26, wherein the beam source produces pulse bursts having from about 1 pulse per pulse burst to about 30 pulses per pulse burst and a pulse burst energy of from about 100 µJ to about 600 pJ per pulse burst.

The method of any one of claims 14 to 27, wherein the pulsed laser beam is directed through the aspherical optical element and beyond an optical blocking element.

The method of claim 28, wherein the aspherical optical element and the optical blocking element are each positioned between the beam source and the transparent workpiece.

The method of claim 28 or 29, wherein the optical blocking element is positioned between the aspherical optical element and the transparent workpiece, wherein the optical blocking element is positioned between the beam source and the aspheric optical element.

The method of any one of claims 28-30, wherein: a first lens and a second lens are each positioned between the beam source and the transparent method within the beam path; and the optical blocking element is positioned between the first lens and the second lens.

The method of claim 31, wherein: the first lens comprises a first focal length and the second lens comprises a second focal length; and the first lens and the second lens are spaced apart along the beam path that forms the sum of the first focal length and the second focal length.

A method according to any of claims 28-32, wherein the optical blocking element is positioned within the beam path such that the optical blocking element is blocked from about 25% to about 80% of the intensity of the pulsed laser beam, preferably such that the optical blocking element blocks approximately 50% of the intensity of the pulsed laser beam.

The method of any one of claims 28 to 33, wherein the optical blocking element is positioned within the beam path so that the optical blocking element blocks a cross-sectional chord portion and / or a cross-sectional sector of the pulsed laser beam.

The method of any of claims 28-34 further comprising rotating a deaf prism about the beam path with deaf prism positioned along the beam path between the optical blocking element and the transparent workpiece so that the pulsed laser beam traverses the deaf prism; and translating the transparent workpiece and the pulsed laser beam relative to each other along the contour line, whereby a number of defects along the contour line within the transparent workpiece are formed by the laser such that a portion of the contour line curves along an imaging surface of the transparent workpiece.

The method of any of claims 28-35, further comprising: rotating the optical blocking element about the beam path; and translating the transparent workpiece and the pulsed laser beam relative to each other along the contour line wherein a number of defects along the contour line within the transparent workpiece are formed by the laser such that a portion of the contour line curves along an imaging surface of the transparent workpiece.

The method of any one of the preceding claims, further comprising decoding a first beam portion of the laser beam from a second beam portion of the laser beam using a decohering optical element which is preferably positioned between the beam source and the transparent workpiece.

The method of claim 37, wherein the decohering optical element is positioned between the aspherical optical element and the transparent workpiece, or between the beam source and the aspherical optical element.

The method of claim 37 or 38, wherein the decohering optical element comprises an optical delay plate and decooning the first beam portion with respect to the second beam portion comprising directing the first beam portion of the pulsed laser beam through the optical delay plate to perform optical retardation of induce the first beam portion with respect to the second beam portion.

The method of claim 39, wherein the optical delay plate is positioned between the beam source and the aspherical optical element.

A method according to any of claims 37-40 wherein decoding the first beam portion from the second beam portion comprises: polarizing the first beam portion of the pulsed laser beam such that the first beam portion of the pulsed laser beam has a first polarization at the transparent workpiece includes; and polarizing the second beam portion of the pulsed laser beam such that the second beam portion of the pulsed laser beam comprises a second polarization at the transparent workpiece, the first polarization being orthogonal to the second polarization.

The method of any one of claims 37 to 41, wherein the decohering optical element comprises a split quarter wavelength plate.

The method of claim 42, wherein: the split wavelength plate is positioned between the aspherical optical element and the transparent workpiece; the split quarter wavelength plate comprises a first plate portion and a second plate portion; the first plate portion comprises a first fast axis and a first slow axis and the second plate portion comprises a second fast axis and a second slow axis; the first fast axis is orthogonal to the second fast axis and the second fast axis is orthogonal to the second slow axis; and the first beam portion of the pulsed laser beam is polarized into the first polarization by traversing the first plate portion and a second beam of the pulsed laser beam is polarized in the second polarization by traversing the second plate portion.

The method of any one of claims 42 to 43 wherein a polarizer and a quarter wavelength plate are each positioned between the beam source and the decohering optical element within the beam path.

The method of any one of claims 37 to 44, wherein: a first lens and a second lens are each positioned between the aspherical optical element and the transparent workpiece between the beam path; and the decohering optical element is positioned between the first lens and the second lens.

The method of claim 45, wherein the first lens comprises a first focal length and the second lens comprises a second focal length; the first lens and the second lens are spaced apart along the beam path which is a sum of the first focal length and the second focal length; and the decohering optical element is positioned between the first lens and the second lens such that the split quarter wavelength plate is at the first focal length of the first lens and the second focal length of the second lens.

A method according to any one of the preceding claims for perforating one or more transparent workpieces in a stack of transparent workpieces.

A laser processing system for the transparent workpiece preferably according to the method according to any of the preceding claims, wherein the system comprises: a laser beam source, preferably a pulsed laser beam source, which provides a beam path and an aspherical optical element which is preferably shifted with respect to the beam path, which aspherical optical element is preferably formed by an axicon lens for directing the laser beam on the transparent workpiece.

The system of claim 48, further comprising one or more additional lenses for focusing the laser beam on the transparent workpiece.

The system of claim 48 or 49 further comprising an optical blocking element that is blocked in the beam path for blocking a portion of the beam path which blocking element is preferably an opaque element.

The system of any of claims 48-50 further comprising a decohering optical element configured to decoose a first bundle portion from a second bundle portion.

The system of claim 51, comprising a first decohering optical element that includes an optical retardation plate positioned in the beam path and a second decohering optical element that includes a split quarter wavelength plate 150 positioned in the beam path.

A transparent workpiece obtainable according to the method according to any of the preceding claims 1-46.