Low numerical aperture optics for enabling laser cutting of textured substrates

Abstract

A method of processing a transparent workpiece includes directing a defect-forming laser beam to an impingement surface of the transparent workpiece, the defect-forming laser beam having a numerical aperture of 0.10 to 0.25, the transparent workpiece having a textured surface having an Ra value greater than or equal to 0.5 [mu] m.

Description

[0001] This application claims priority to U.S. Provisional Application Serial No. 63 / 501,865, filed May 12, 2023, and U.S. Provisional Application Serial No. 63 / 412,826, filed Oct. 3, 2022, under 35 U.S.C. § 120. This application is based on the content of the provisional applications and the content of the provisional applications is incorporated herein by reference in its entirety. Technical Background Technical Field

[0002] This specification generally relates to apparatuses and methods for laser machining transparent workpieces. Background Art

[0003] Advances in precision micromachining and related process improvements to reduce size, weight, and material costs have facilitated the rapid growth of products such as, but not limited to, flat panel displays for touchscreens, tablet computers, smartphones, and televisions. Due to these advances, ultrafast pulsed industrial lasers have become an important tool for applications requiring high-precision micromachining. Laser cutting processes that utilize such lasers are expected to separate substrates in a controlled manner, forming negligible debris and subsurface damage to the substrates. The surface texture of the substrate may reduce the effectiveness of the laser cutting process. For example, the surface texture may scatter or distort the laser beam, preventing the laser beam from having sufficient energy density to traverse the entire thickness of the substrate and modify the substrate. Additionally, the separation of a textured substrate may form an unacceptable amount of debris and may also result in subsurface damage to the separated portion of the substrate. Summary of the Invention

[0004] A first aspect of the present disclosure includes a method of machining a transparent workpiece, the method including directing a defect-forming laser beam to an impact surface of the transparent workpiece, the defect-forming laser beam having a numerical aperture of 0.10 to 0.25, the transparent workpiece having a textured surface, the textured surface having an Ra value greater than or equal to 0.5 μm.

[0005] Additional features and advantages of the processes and systems described herein will be set forth in the detailed description below, and in part will be apparent to those of ordinary skill in the art from the description, or may be learned by practice of the embodiments described herein, including the detailed description, the claims, and the drawings.

[0006] It should be understood that both the foregoing general description and the following detailed description describe various embodiments and are intended to provide an overview or framework for understanding the nature and characteristics of the claimed subject matter. The accompanying drawings are included to provide a further understanding of the various embodiments, and the drawings are incorporated into and constitute a part of this specification. The drawings illustrate the various embodiments described herein and, together with the specification, are used to explain the principles and operations of the claimed subject matter. Description of the Drawings

[0007] The embodiments set forth in the drawings are illustrative and exemplary in nature and are not intended to limit the subject matter defined by the claims. The following detailed description of the illustrative embodiments can be understood when read in conjunction with the following drawings, in which like reference numerals indicate like structures, and in which:

[0008] Figure 1 Conventional mechanical scribing and fracture laser cutting are schematically depicted;

[0009] Figure 2 A comparison between laser cutting using Gaussian beam focusing and laser cutting using Bessel-like beam focusing is schematically depicted;

[0010] Figure 3 The formation of the profile of a defect in a transparent workpiece having a textured surface according to one or more embodiments described herein is schematically depicted;

[0011] Figure 4 An example pulse laser beam focal line during the machining of a transparent workpiece according to one or more embodiments described herein is schematically depicted;

[0012] Figure 5 An optical assembly for laser machining using a pulse laser beam focal line according to one or more embodiments described herein is schematically depicted;

[0013] Figure 6 The relationship between the relative intensity of laser pulses within an example pulse train and time is graphically depicted according to one or more embodiments described herein;

[0014] Figure 7 A beam focused by an axicon is schematically depicted according to one or more embodiments described herein;

[0015] Figure 8 The cross-sectional profile of a Bessel-like beam formed by an axicon is depicted according to one or more embodiments described herein;

[0016] Figure 9Graphically depicts the on-axis intensity of a Gaussian-Bessel beam as a function of distance along the optical axis according to one or more embodiments described herein;

[0017] Figure 10 Schematically depicts an optical setup for creating a line focus by relaying and magnifying an image of a line focus first formed by an axicon using a telescope according to one or more embodiments described herein;

[0018] Figure 11 Schematically depicts an optical setup according to one or more embodiments described herein having an additional magnifying telescope with a magnification of N placed before the axicon;

[0019] Figure 12 Schematically depicts an optical assembly for laser processing using an infrared laser beam according to one or more embodiments described herein;

[0020] Figure 13 Schematically depicts an infrared laser beam incident on a textured surface of a transparent workpiece according to one or more embodiments described herein Figure 4 depicted in A;

[0021] Figure 14 Schematically depicts a transparent workpiece according to one or more embodiments described herein having a plurality of defects extending along discrete contours and lines;

[0022] Figure 15 Schematically depicts a separated portion of a transparent workpiece at a cutting edge according to one or more embodiments described herein;

[0023] Figure 16 Depicts a view of a transparent workpiece having a textured surface separated along a curved contour according to one or more embodiments described herein;

[0024] Figure 17 Depicts a view of nanopores according to one or more embodiments described herein for effecting the separation of a glass sheet into discrete pieces and subsequent separation of the glass pieces after the application of stress (e.g., mechanical stress or thermal stress);

[0025] Figure 18 Depicts a view of the separation edge of a 700 μm thick glass sheet cut with a nanopore process according to one or more embodiments described herein, where each vertical stripe is an individual nanopore;

[0026] Figure 19 Depicts an example of nanoporing a circular part corner using an asymmetric quasi-non-diffracting beam according to one or more embodiments described herein;

[0027] Figure 20 Depicts a comparison of the nano-perforations and separated edges of a glass sheet according to one or more embodiments described herein, where the nano-perforations penetrate the entire thickness of the sheet strongly (top image), and where the nano-perforations are weak or incomplete near the bottom of the glass sheet (bottom image);

[0028] Figure 21 Depicts nano-perforations and separated glass edges in the region of a rounded corner of a part;

[0029] Figure 22 Is a microscopic image of a textured glass article according to one or more embodiments described herein;

[0030] Figure 23 Is a microscopic image of a textured glass article according to one or more embodiments described herein;

[0031] Figure 24 Is a microscopic image of a textured glass article according to one or more embodiments described herein;

[0032] Figure 25 Is an interferometric roughness characterization image of the surface of a textured glass article according to one or more embodiments described herein;

[0033] Figure 26 Depicts an example of nano-perforations of a textured glass sheet according to one or more embodiments shown and described herein;

[0034] Figure 27 Depicts an example of nano-perforations of a textured glass sheet according to one or more embodiments shown and described herein;

[0035] Figure 28 Depicts an example of "cantilever curling";

[0036] Figure 29 Depicts a textured glass sheet with nano-perforations using a second pass and at different focus heights;

[0037] Figure 30 Depicts an edge view of a nano-perforated and separated glass sheet, where the surface of the glass was mechanically polished before laser exposure;

[0038] Figure 31 Depicts a description of the conditions used when modeling a NA = 0.37 Gaussian-Bessel beam incident on a textured glass piece;

[0039] Figure 32Depicts a distortion model of a NA = 0.37 Gaussian - Bessel beam incident on a glass surface having a periodic height deformation with an amplitude of 0.125 μm;

[0040] Figure 33 Depicts a distortion model of a NA = 0.37 Gaussian - Bessel beam incident on a glass surface having a periodic height deformation with an amplitude of 5 μm;

[0041] Figure 34 Graphically depicts a distortion model of a NA = 0.37 Gaussian - Bessel beam incident on a glass surface with surface deformations having varying amplitudes and a constant pitch;

[0042] Figure 35 Graphically depicts a distortion model of a NA = 0.37 Gaussian - Bessel beam incident on a glass surface having surface deformations with varying amplitudes and a constant pitch;

[0043] Figure 36 Graphically depicts a distortion model of a NA = 0.37 Gaussian - Bessel beam incident on a glass surface having surface deformations with varying amplitudes and a constant pitch;

[0044] Figure 37 Graphically depicts a distortion model of a NA = 0.37 Gaussian - Bessel beam incident on a glass surface having surface deformations with varying amplitudes and a constant pitch;

[0045] Figure 38 Graphically depicts a distortion model of a NA = 0.37 Gaussian - Bessel beam incident on a glass surface having surface deformations with varying amplitudes and a constant pitch;

[0046] Figure 39A Depicts a model of the relationship between the cross - sectional intensity and the propagation distance along the optical axis of a NA = 0.15 Gaussian - Bessel beam propagating only in air;

[0047] Figure 39B Depicts a model of the relationship between the cross - sectional intensity and the propagation distance along the optical axis of a NA = 0.16 Gaussian - Bessel beam propagating only in air;

[0048] Figure 39C Depicts a model of the relationship between the cross - sectional intensity and the propagation distance along the optical axis of a NA = 0.18 Gaussian - Bessel beam propagating only in air;

[0049] Figure 39D Depicts a model of the relationship between the cross - sectional intensity and the propagation distance along the optical axis of a NA = 0.21 Gaussian - Bessel beam propagating only in air;

[0050] Figure 39E A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.26 propagating only in air and the propagation distance along the optical axis;

[0051] Figure 40A Shows Figure 39A the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam of

[0052] Figure 40B Shows Figure 39B the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam of

[0053] Figure 40C Shows Figure 39C the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam of

[0054] Figure 40D Shows Figure 39D the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam of

[0055] Figure 40E Shows Figure 39E the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam of

[0056] Figure 41A is a model of the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.15 interacting with a flat glass substrate and the propagation distance along the optical axis;

[0057] Figure 41B is a model of the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.16 interacting with a flat glass substrate and the propagation distance along the optical axis;

[0058] Figure 41C is a model of the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.18 interacting with a flat glass substrate and the propagation distance along the optical axis;

[0059] Figure 41D is a model of the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.21 interacting with a flat glass substrate and the propagation distance along the optical axis;

[0060] Figure 41E is a model of the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.26 interacting with a flat glass substrate and the propagation distance along the optical axis;

[0061] Figure 42A ShowsFigure 41A The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0062] Figure 42B Shows Figure 41B The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0063] Figure 42C Shows Figure 41C The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0064] Figure 42D Shows Figure 41D The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0065] Figure 42E Shows Figure 41E The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0066] Figure 43A Is a model of the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.15 interacting with a textured glass substrate and the propagation distance along the optical axis;

[0067] Figure 43B Is a model of the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.16 interacting with a textured glass substrate and the propagation distance along the optical axis;

[0068] Figure 43C Is a model of the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.18 interacting with a textured glass substrate and the propagation distance along the optical axis;

[0069] Figure 43D Is a model of the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.21 interacting with a textured glass substrate and the propagation distance along the optical axis;

[0070] Figure 43E Is a model of the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.26 interacting with a textured glass substrate and the propagation distance along the optical axis;

[0071] Figure 44A Shows Figure 43A The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0072] Figure 44B Shows Figure 43B The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0073] Figure 44C shows the Figure 43C relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0074] Figure 44D shows the Figure 43D relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0075] Figure 44E shows the Figure 43E relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0076] Figure 45 graphically depicts the Figures 44A to 44E length of the Gaussian - Bessel beam shown in

[0077] Figure 46A as a function of the numerical aperture, where the length of the Gaussian - Bessel beam is characterized by the full width at half - maximum of the on - axis beam intensity; 6 model depicting the relationship between the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.15 and the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.15 interacts with a textured glass surface having an amplitude of 5μm*(Sin(2x)+Sin(2y))

[0078] Figure 46B model depicting the relationship between the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.16 and the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.16 interacts with a textured glass surface having an amplitude of 5μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset of 0.0 mm (i.e., y - offset);

[0079] Figure 46C model depicting the relationship between the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.18 and the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.18 interacts with a textured glass surface having an amplitude of 5μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset of 0.0 mm (i.e., y - offset);

[0080] Figure 46DA model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.21 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.21 interacts with a textured glass surface having an amplitude of 5μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y-offset) of 0.0 mm;

[0081] Figure 46E A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.26 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.26 interacts with a textured glass surface having an amplitude of 5μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y-offset) of 0.0 mm;

[0082] Figure 47A Shows Figure 46A the relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0083] Figure 47B Shows Figure 46B the relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0084] Figure 47C Shows Figure 46C the relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0085] Figure 47D Shows Figure 46D the relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0086] Figure 47E Shows Figure 46E the relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0087] Figure 48 Graphically depicts the length of the Gaussian-Bessel beam shown in Figures 47A to 47E as a function of the numerical aperture, where the length of the Gaussian-Bessel beam is characterized by the full width at half maximum of the on-axis beam intensity;

[0088] Figure 49A A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.15 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.15 interacts with a textured glass surface having an amplitude of 5μm*(Sin(2x)+Sin(2y)) 6interacts with a textured glass surface having an amplitude of

[0089] Figure 49B A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.16 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.16 interacts with a textured glass surface having 5 μm * (Sin(2x) + Sin(2y)) 6 interacts with a textured glass surface having an amplitude of

[0090] Figure 49C A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.18 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.18 interacts with a textured glass surface having 5 μm * (Sin(2x) + Sin(2y)) 6 interacts with a textured glass surface having an amplitude of

[0091] Figure 49D A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.21 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.21 interacts with a textured glass surface having 5 μm * (Sin(2x) + Sin(2y)) 6 interacts with a textured glass surface having an amplitude of

[0092] Figure 49E A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.26 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.26 interacts with a textured glass surface having 5 μm * (Sin(2x) + Sin(2y)) 6 interacts with a textured glass surface having an amplitude of

[0093] Figure 50A Shows Figure 49A the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam and the propagation distance along the optical axis;

[0094] Figure 50B Shows Figure 49B the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam and the propagation distance along the optical axis;

[0095] Figure 50C Shows Figure 49A the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam and the propagation distance along the optical axis;

[0096] Figure 50Dshows Figure 49D the relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0097] Figure 50E shows Figure 49E the relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0098] Figure 51 graphically depicts the Figures 50A to 50E length of the Gaussian - Bessel beam shown in

[0099] Figure 52A as a function of the numerical aperture, where the length of the Gaussian - Bessel beam is characterized by the full width at half maximum of the on - axis beam intensity; 6 and the Gaussian - Bessel beam with NA = 0.15 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y))

[0100] Figure 52B depicts a model of the relationship between the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.16 and the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.16 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset of 0.0 mm (i.e., y - offset);

[0101] Figure 52C depicts a model of the relationship between the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.18 and the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.18 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset of 0.0 mm (i.e., y - offset);

[0102] Figure 52D depicts a model of the relationship between the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.21 and the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.21 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset of 0.0 mm (i.e., y - offset);

[0103] Figure 52EA model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.26 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.26 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y-offset) of 0.0 mm;

[0104] Figure 53A Shows Figure 52A the on-axis intensity of the modeled Gaussian Bessel beam as a function of the propagation distance along the optical axis;

[0105] Figure 53B Shows Figure 52B the on-axis intensity of the modeled Gaussian Bessel beam as a function of the propagation distance along the optical axis;

[0106] Figure 53C Shows Figure 52C the on-axis intensity of the modeled Gaussian Bessel beam as a function of the propagation distance along the optical axis;

[0107] Figure 53D Shows Figure 52D the on-axis intensity of the modeled Gaussian Bessel beam as a function of the propagation distance along the optical axis;

[0108] Figure 53E Shows Figure 52E the on-axis intensity of the modeled Gaussian Bessel beam as a function of the propagation distance along the optical axis;

[0109] Figure 54 Graphically depicts the length of the Gaussian-Bessel beam shown in Figures 53A to 53E as a function of the numerical aperture, where the length of the Gaussian-Bessel beam is characterized by the full width at half maximum of the on-axis beam intensity;

[0110] Figure 55A A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.15 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.15 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y-offset) of 0.35 mm;

[0111] Figure 55B A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.16 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.16 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6interacts with the textured glass surface with an amplitude of

[0112] Figure 55C A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.18 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.18 interacts with a textured glass surface having an amplitude of 10 μm*(Sin(2x)+Sin(2y)) 6 interacts with the textured glass surface with an amplitude of

[0113] Figure 55D A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.21 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.21 interacts with a textured glass surface having an amplitude of 10 μm*(Sin(2x)+Sin(2y)) 6 interacts with the textured glass surface with an amplitude of

[0114] Figure 55E A model depicting the relationship between the cross-sectional intensity of a Gaussian-Bessel beam with NA = 0.26 and the propagation distance along the optical axis, where the Gaussian-Bessel beam with NA = 0.26 interacts with a textured glass surface having an amplitude of 10 μm*(Sin(2x)+Sin(2y)) 6 interacts with the textured glass surface with an amplitude of

[0115] Figure 56A Shows Figure 55A the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam and the propagation distance along the optical axis;

[0116] Figure 56B Shows Figure 55B the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam and the propagation distance along the optical axis;

[0117] Figure 56C Shows Figure 55C the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam and the propagation distance along the optical axis;

[0118] Figure 56D Shows Figure 55D the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam and the propagation distance along the optical axis;

[0119] Figure 56E Shows Figure 55E the relationship between the on-axis intensity of the modeled Gaussian-Bessel beam and the propagation distance along the optical axis;

[0120] Figure 57 graphically depicts the length of a Gaussian - Bessel beam as a function of numerical aperture Figures 56A to 56E shown in, where the length of the Gaussian - Bessel beam is characterized by the full width at half maximum of the on - axis beam intensity;

[0121] Figure 58A a model depicting the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.15 as a function of the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.15 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y - offset) of 1.0 mm;

[0122] Figure 58B a model depicting the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.16 as a function of the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.16 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y - offset) of 1.0 mm;

[0123] Figure 58C a model depicting the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.18 as a function of the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.18 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y - offset) of 1.0 mm;

[0124] Figure 58D a model depicting the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.21 as a function of the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.21 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y - offset) of 1.0 mm;

[0125] Figure 58E a model depicting the cross - sectional intensity of a Gaussian - Bessel beam with NA = 0.26 as a function of the propagation distance along the optical axis, where the Gaussian - Bessel beam with NA = 0.26 interacts with a textured glass surface having an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y - offset) of 1.0 mm;

[0126] Figure 59A shows Figure 58AThe relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0127] Figure 59B Shows Figure 58B The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0128] Figure 59C Shows Figure 58C The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0129] Figure 59D Shows Figure 58D The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0130] Figure 59E Shows Figure 58E The relationship between the on-axis intensity of the modeled Gaussian Bessel beam and the propagation distance along the optical axis;

[0131] Figure 60 Graphically depicts the Figures 59A to 59E Length of the Gaussian - Bessel beam shown in, where the length of the Gaussian - Bessel beam is characterized by the full width at half maximum of the on-axis beam intensity;

[0132] Figure 61 Depicts the cross-section of the separation edge of a glass sheet after nanopatterning;

[0133] Figure 62 Depicts a cross-section of the separation edge of a glass sheet after nanopatterning;

[0134] Figure 63 Depicts a cross-section of a separation edge of a glass sheet after nanopatterning;

[0135] Figure 64 Depicts a cross-section of a separation edge of a glass sheet after nanopatterning;

[0136] Figure 65 Depicts a cross-section of a separation edge of a glass sheet after nanopatterning;

[0137] Figure 66 Depicts a further magnified Figure 66 Cross-section;

[0138] Figure 67 Depicts the nanopatterning depth as a function of the angle of incidence on an inclined glass surface;

[0139] Figure 68Graphically depicts a comparison of the tolerances of the penetration depths of Bessel beams with two different numerical apertures for glass tilt;

[0140] Figure 69 Depicts a ray - tracing model comparing the intensity cross - sectional distributions and propagation distances of Bessel beams with different numerical apertures for the tolerance of a curved glass surface;

[0141] Figure 70 Depicts the focal line measurement of a Gaussian - Bessel beam with NA = 0.201 for nanopiercing of a glass tube;

[0142] Figure 71 Depicts the focal line measurement of a Gaussian - Bessel beam with NA = 0.312 for nanopiercing of a glass tube; and

[0143] Figure 72 Depicts a comparison of the penetration depths of nanopiercing on a curved surface with a radius of 5 mm of a glass tube using Gaussian - Bessel beams with NA = 0.201 and NA = 0.312. DETAILED DESCRIPTION

[0144] Now, embodiments for separating a transparent workpiece including a textured surface will be described in detail. It is desired to separate the transparent workpiece along a separation line that does not deviate significantly from the desired separation line to reduce the need for post - processing steps (e.g., grinding, polishing, etc.) to be performed on the separated transparent workpiece to make the separated transparent workpiece have the desired shape. The textured surface of the transparent workpiece can scatter and distort the laser beam used for laser - processing the transparent workpiece, resulting in a separation line that deviates from the desired separation line and / or damage to the underlying layer along the separation line, thus requiring a post - processing step of removing a large portion of the transparent workpiece to produce a workpiece that conforms to the desired shape, thereby reducing material utilization and increasing manufacturing costs. The methods described herein utilize a laser beam with a low numerical aperture (e.g., less than or equal to 0.25) to fully pierce the transparent workpiece and guide a crack to propagate along the desired separation line to reduce the extent of post - processing required to produce a workpiece with the desired shape.

[0145] As used herein, the term "textured surface" refers to the surface of a transparent workpiece having a Ra value greater than or equal to 0.5 μm. It should be understood that the methods described herein can be used for textured surfaces having a wide range of Ra values. For example, in embodiments, the textured surfaces described herein can have a Ra value greater than or equal to 0.5 μm and less than or equal to 5 μm, or greater than or equal to 0.5 μm and less than or equal to 10 μm, or greater than or equal to 1.0 μm, or greater than or equal to 2.0 μm, or greater than or equal to 3.0 μm, or greater than or equal to 4.0 μm, or less than or equal to 10 μm, or less than or equal to 8.0 μm, or less than or equal to 6.0 μm. Such textured surfaces can be produced by the formation of the transparent workpiece. For example, embodiments can relate to the laser machining of a transparent workpiece that is a rolled glass or glass-ceramic precursor formed by applying a roller to a glass or glass-ceramic precursor. The contact of the roller with the precursor can impart a textured surface to the transparent workpiece. Embodiments can also relate to the laser machining of a glass-ceramic transparent workpiece, where the ceramization process imparts surface texture to the transparent workpiece. Additionally, the rolling or ceramization process can include the use of boron nitride as a lubricant, which can leave residual boron nitride embedded in the glass surface after rolling or ceramization is complete and produce a textured surface.

[0146] As used herein, the term "Ra value" refers to the surface roughness measurement of the arithmetic mean of the filtered roughness profile determined based on the deviation of the center line of the filtered roughness. For the purposes of this disclosure, Ra is determined by the following relationship: where the summation is over n measurement points on the surface, the summation index i identifies each measurement point, and H i is the surface height measurement of the surface at measurement point i, and H CLSurface height measurements corresponding to the centerline between filtered profile data points (e.g., the center between the maximum and minimum surface height values). Alternatively, the Sa value can be used to characterize surface roughness, which is determined by the area extrapolation method of Equation (1) herein. The filter values (e.g., cut-off wavelength) used to determine the Ra value described herein can be found in ISO 25718. Surface height can be measured with various tools, such as optical interferometers, stylus-based profilometers, or laser confocal microscopes. Unless otherwise specified herein, the Ra value is measured via a laser confocal microscope. To evaluate the roughness of a textured surface, a measurement area that is as large as practically possible should be used in order to evaluate the variability that may occur on a large spatial scale. For example, a transparent workpiece made of rolled glass may have inclusions caused by boron nitride particles with a lateral scale of approximately 100 μm. Thus, for the textured surfaces described herein, a measurement area of 3 × 3 mm is typically used to evaluate Ra. In particular, measurements are made using a Keyence VK-X200 laser confocal with a 5X objective, which gives a measurement field of view of approximately 2.2 mm × 2.9 mm corresponding to a resolution of 2.84 μm per pixel. The mode used is the "surface profile" mode, the quality is set to "high precision", the sampling pitch for calculation and analysis is 8 μm. AI noise cancellation has been "turned on". The tilt surface noise filter is "auto (on)". However, to evaluate the cut edge surface, the thickness of the transparent workpiece limits the actual size of the measurement area, making an area with dimensions of at least 100 μm × 100 μm more suitable.

[0147] As used herein, the term "about" refers to a quantity, dimension, formulation, parameter, and other quantities and properties that are not and need not be exact, but can be approximate and / or larger or smaller as desired, reflecting tolerances, conversion factors, rounding, measurement errors, and other factors known to those of ordinary skill in the art. When the term "about" is used in connection with the endpoint of a value or range, the specific value or endpoint being referred to is included. Whether or not the numerical or range endpoint in the specification is preceded by "about", two embodiments are described: one modified by "about" and one not modified by "about". It will be further understood that each endpoint of a range is significant relative to the other endpoint and independent of the other endpoint.

[0148] As used herein, directional terms (e.g., up, down, right, left, front, back, top, bottom) are made only with reference to the drawings as depicted and are not intended to imply an absolute orientation.

[0149] As used herein, the singular forms "a / an" and "the" include plural referents unless the context clearly dictates otherwise. Thus, for example, a reference to "a" component includes aspects having two or more such components unless the context clearly indicates otherwise.

[0150] As used herein, "as-cut pristine state" refers to the state of a portion of a transparent workpiece immediately after the transparent workpiece has been separated along a plurality of defects formed in the transparent workpiece, without any post-processing steps (e.g., grinding, polishing, etching, roughening, etc.) being applied to that portion of the transparent workpiece. This separation can occur in response to stress (e.g., thermal stress, mechanical stress, etc.) applied to the transparent workpiece at the plurality of defects or other separation means (e.g., chemical etchant). The separated portion of the transparent workpiece can include a cut edge where the separation occurs. When the separated portion is in the as-cut pristine state, portions (or all) of the plurality of defects can remain in the separated portion at or near the cut edge.

[0151] As used herein, "laser machining" includes directing a laser beam onto and / or into a transparent workpiece. In some embodiments, laser machining further includes translating the laser beam relative to the transparent workpiece, e.g., along a contour line or other path. Examples of laser machining include using a laser beam to form a contour including a series of defects extending into the transparent workpiece, and using an infrared laser beam to heat the transparent workpiece. Other examples of laser machining include using a laser beam to form a contour including a series of defects extending into the transparent workpiece, and using alternative means to separate the transparent workpiece along the series of defects (e.g., mechanical stress, application of chemical etchant, etc.). Laser machining can separate the transparent workpiece along one or more separation lines.

[0152] As used herein, "beam spot" refers to the cross-section (e.g., beam cross-section) of a laser beam at the impact location of the laser beam on the impact surface of the transparent workpiece. The impact surface is the surface of the transparent workpiece onto which the laser beam first impinges. The beam spot is the cross-section at the impact location. In the embodiments described herein, the beam spot is sometimes referred to as being "axisymmetric" or "non-axisymmetric". As used herein, axisymmetric refers to a shape that is symmetric or appears the same for any arbitrary angle of rotation about a central axis (e.g., circular), and "non-axisymmetric" refers to a shape that is not symmetric for any arbitrary angle of rotation about a central axis (e.g., oval, elliptical). The axis of rotation (e.g., central axis) is most often taken as the optical axis (propagation axis) of the laser beam, which is the axis extending in the beam propagation direction, which is referred to herein as the Z-direction.

[0153] As used herein, "upstream" and "downstream" refer to the relative positioning of two locations or components along a beam path relative to a beam source. For example, if a first component is closer to the laser source than a second component along a path traversed by a laser beam, the first component is upstream of the second component. If, along the path traversed by the laser beam, the first component is farther from the beam source than the second component (that is, if the laser beam impinges on the second component before impinging on the first component), then the first component is downstream of the second component.

[0154] As used herein, "laser beam focal line" or "pulsed laser beam focal line" refers to a pattern of rays at the interaction (e.g., crossing) of a laser beam, which form an elongated focal region in the beam propagation direction. In conventional laser machining, a pulsed laser beam is tightly focused to a focal point. The focal point is the point of minimum cross-section of the pulsed laser beam, commonly referred to as the beam "waist", and is located in a focal plane in a substrate (such as a transparent workpiece). In contrast, in the elongated focal region of a pulsed laser beam focal line, the region of minimum cross-section of the pulsed laser beam is no longer a single point, but forms a linear or approximately linear extended region aligned with the beam propagation direction. As discussed below, the focal line has a length in the beam propagation direction and a cross-section of finite size in a direction perpendicular to the beam propagation direction. A pulsed laser beam focal line is formed by causing the intersecting (e.g., crossing) rays of a pulsed laser beam to converge to form a continuous series of focal points aligned with the beam propagation direction. The pulsed laser beam focal lines described herein are formed using quasi-non-diffracting beams, which are defined mathematically in detail below.

[0155] As used herein, a "contour line" corresponds to a set of intersection points of a laser beam with a transparent workpiece due to relative motion between the laser beam and the transparent workpiece. The shape of the contour line can be linear, angled, polygonal, or curved. The contour line can be closed (i.e., defining a closed region on the surface of the transparent workpiece) or open (i.e., not defining a closed region on the surface of the transparent workpiece). The contour line represents a boundary along which separation of the transparent workpiece into two or more parts is facilitated. In an embodiment, the contour line represents a boundary between a discarded portion of the transparent workpiece and a primary or utilized region of the transparent workpiece.

[0156] As used herein, a "contour" refers to a set of defects formed in a transparent workpiece by a laser beam through relative motion of the laser beam and the transparent workpiece along a contour line. The defects are spaced along the contour line and are all contained within the interior of the transparent workpiece or extend into the interior of the transparent workpiece through one or more surfaces. The defects can also extend through the entire thickness of the transparent workpiece. Separation of the transparent workpiece preferably occurs along a boundary defined by the contour line by connecting the defects (such as by propagation of cracks).

[0157] As used herein, "defect" refers to an area of a transparent workpiece that has been modified by a laser beam. Modification means that the substrate has been mechanically weakened (and thus "damaged") by the laser beam. Typical modifications include compression and breakage of chemical bonds. A defect includes an area of the transparent workpiece that has a modified refractive index relative to the unmodified area surrounding the transparent workpiece. Common defects include structurally modified areas in the transparent workpiece created by the focal line of a pulsed laser beam, such as void spaces, cracks, scratches, flaws, holes, perforations, densification, or other deformations. In various embodiments herein, a defect may also be referred to as a defect line or damage track. The defects described herein include material modifications (e.g., refractive index modification, cracks, void spaces, defects) that are completely encapsulated within the thickness of the transparent workpiece. The defects described herein may extend through the entire thickness of the transparent workpiece or a portion thereof, such as through greater than 50%, or greater than 60%, or greater than 70%, or greater than 80%, or greater than 90% of the thickness of the transparent workpiece, or in the range of 50% to 100%, or in the range of 60% to 95%, or in the range of 70% to 90%.

[0158] As used herein, the term "defect-forming laser beam" refers to a laser beam that forms a defect in a transparent workpiece.

[0159] In an embodiment, a plurality of nanopores includes a modified material diameter. As used herein, the term "modified material diameter" includes aspects of each nanopore and excludes cracks that extend into the transparent workpiece due to the formation of the plurality of nanopores. For example, the modified material diameter may measure the dimensions of a portion of the transparent workpiece within one of the nanopores of the plurality of nanopores, including refractive index modification, changes in molecular bonding, and voids that are completely encapsulated within the thickness of the transparent workpiece. In an embodiment, the aspect ratio of one of the nanopores in the plurality of nanopores may be described as the ratio of the nanopore length to the modified material diameter. In an embodiment, the aspect ratio of each of the plurality of nanopores is greater than or equal to 50:1 (e.g., greater than or equal to 100:1).

[0160] In an embodiment, a defect or damage track is formed by the interaction of the focal line of a pulsed laser beam with the transparent workpiece. As described more fully below, the focal line of the pulsed laser beam is generated by a pulsed laser. A defect at a particular location along a contour line is formed by the focal line of a pulsed laser beam generated by a single laser pulse at that particular location, a train of sub-pulses at that particular location, or a plurality of laser pulses at that particular location. The relative movement of the laser beam and the transparent workpiece along the contour line results in the formation of a plurality of defects that form the contour.

[0161] As used herein, the phrase "transparent workpiece" refers to a workpiece formed of glass, glass-ceramic, or other transparent material, where the term "transparent" as used herein means that the material has a linear optical absorption of less than 20% per millimeter of material depth, such as less than 10% per millimeter of material depth for a specified pulsed laser wavelength, or such as less than 1% per millimeter of material depth for a specified pulsed laser wavelength. Unless otherwise specified, a material is transparent if it has a linear optical absorption of less than about 20% per millimeter of material depth. In an embodiment, the linear optical absorption of the transparent workpiece described herein is measured by transmitting a non-focused (e.g., collimated) laser beam (e.g., not having a high enough intensity to induce non-linear absorption) through the transparent workpiece. The power of the non-focused laser beam transmitted through the transparent workpiece is then compared to the initial power of the non-focused laser beam to determine the percentage of light absorbed by the transparent workpiece. The measured absorption value can be normalized for the transparent workpiece thickness. In an embodiment, the transparent workpiece described herein can have a depth (e.g., thickness) greater than or equal to 50 micrometers (μm), or greater than or equal to 100 μm, or greater than or equal to 250 μm, or greater than or equal to 500 μm, or greater than or equal to 1.0 millimeter (mm), or greater than or equal to 2.0 mm, or greater than or equal to 3.0 mm, or greater than or equal to 4.0 mm, or greater than or equal to 5.0 mm, or greater than or equal to 6.0 mm, or greater than or equal to 8.0 mm, or greater than or equal to 50 μm and less than or equal to 10.0 mm, or greater than or equal to 100 μm and less than or equal to 5.0 mm, or greater than or equal to 0.5 mm and less than or equal to 3.0 mm. The transparent workpiece can include a glass workpiece formed of a glass composition such as borosilicate glass, soda-lime glass, aluminosilicate glass, alkali metal aluminosilicate, alkaline earth metal aluminosilicate glass, alkaline earth metal borosilicate glass, fused silica, or a crystalline material (such as sapphire, silicon, gallium arsenide), or a combination thereof. In some embodiments, the glass can be ion-exchangeable such that the glass composition can undergo ion exchange to achieve glass strengthening before or after laser processing the transparent workpiece.

[0162] As used herein, "glass-ceramic" is a solid prepared by the controlled crystallization of a precursor glass and has one or more crystalline phases and a residual glass phase.

[0163] As used herein, the term "quasi-non-diffracting beam" is used to describe a laser beam having low beam divergence, as mathematically described below. In particular, the laser beam is used to form the profile of a defect in the embodiments described herein. The laser beam has an intensity distribution I(X,Y,Z), where Z is the beam propagation direction of the laser beam, and X and Y are directions orthogonal to the beam propagation direction, as depicted in the accompanying drawings. The X and Y directions may also be referred to as cross-sectional directions, and the X-Y plane may be referred to as the cross-sectional plane. In this document, the coordinates and directions X, Y, and Z are also referred to as x, y, and z, respectively. The intensity distribution of the laser beam in the cross-sectional plane may be referred to as the cross-sectional intensity distribution. A quasi-non-diffracting laser beam can be formed by impinging a diffracting laser beam (such as a Gaussian beam) into, onto, or through a phase-change optical element to modify the phase of the beam, reduce the beam divergence, and increase the Rayleigh range, as defined mathematically below, the phase-change optical element being such as: an adaptive phase-change optical element (e.g., a spatial light modulator, an adaptive phase plate, a deformable mirror, etc.), a static phase-change optical element (e.g., a static phase plate, an aspherical optical element, such as an axicon, etc.). Example quasi-non-diffracting beams include Bessel beams, Airy beams, and Weber beams. As used herein, the term "Bessel beam" refers to Bessel beams, Gaussian-Bessel beams, and Bessel-like beams.

[0164] Now referring to Figure 1 , conventional mechanical scribing and fracture laser cutting have limitations in accuracy (about 100 microns) and can cause significant chipping and subsurface damage to the scribed edges (about 150 microns) of the glass. "Subsurface damage" is defined as the distance that edge defects (cracks or other defects) extend vertically inward from the cut edge of the glass sheet. To achieve high edge strength and reliability of the final part, these edge defects must be removed by mechanical grinding and polishing. With mechanical scribing and fracture laser cutting, it may also be difficult to fabricate parts with a circular edge profile, such as the rounded corners (also referred to herein as "round corners") found on many handheld electronic devices. Mechanical scribing and fracture laser cutting may also require a minimum spacing between parts to be cut (e.g., 5-10 mm). This required minimum separation requires grinding and polishing of the edges to round the corners to a specified radius of curvature and to remove subsurface damage and account for the lack of precision in the cut edge itself. Depending on the exact part shape and the incoming glass sheet size, this can result in a sheet utilization percentage ranging from as low as 50% to 90%. Some of the lost material is still macroscopic in size and can be recycled and remelted as cullet in future glass melting. However, the ground material cannot be recycled as cullet, meaning that the resulting disposal and environmental costs vary with the volume of material to be ground and polished. For mechanically scribed and fracture laser cut parts, this ground material loss can be 10% to 30% of the total material.

[0165] Now referring to Figure 2 , quasi-non-diffracting laser beams, such as Bessel beams, can be used for laser machining of glass sheets. Non-diffracting means that these laser beams maintain a tightly focused spot (e.g., a core diameter of about 1 - 10 μm) through a greater depth of focus in the beam propagation direction than is possible with conventional Gaussian profile laser beams. The cross-sectional profile of a quasi-non-diffracting laser beam typically resembles a Bessel function profile, having a high-intensity central peak and multiple annular side lobes of lesser intensity.

[0166] Referring to Figure 3 、 Figure 4 and Figure 5 , the pulsed laser beam 112 for forming the defect further has an intensity distribution I(X, Y, Z), where Z is the beam propagation direction of the pulsed laser beam 112, and X and Y are directions orthogonal to the propagation direction, as depicted in the figure. The X direction and the Y direction may also be referred to as cross-sectional directions, and the X - Y plane may be referred to as the cross-sectional plane. The intensity distribution of the pulsed laser beam 112 in the cross-sectional plane may be referred to as the cross-sectional intensity distribution.

[0167] The pulsed laser beam 112 at the beam spot 114 or other cross-section may include a quasi-non-diffracting beam, e.g., a beam having a low beam divergence as defined mathematically herein, which is achieved by propagating the pulsed laser beam 112 (e.g., outputting a pulsed laser beam 112 such as a Gaussian beam using the beam source 110) through an aspherical optical element 135, as described in more detail herein with respect to the optical assembly 100 depicted in Figure 5 . Beam divergence refers to the magnification of the beam cross-section in the beam propagation direction (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 beam propagation direction of the pulsed laser beam 112 (e.g., along the X - Y plane). One example beam cross-section discussed herein is the beam spot 114 of the pulsed laser beam 112 projected onto the textured surface 123 of the transparent workpiece 120.

[0168] The length of the pulsed laser beam focal line generated from the quasi-non-diffracting beam is determined by the Rayleigh range of the quasi-non-diffracting beam. In particular, the quasi-non-diffracting beam defines a pulsed laser beam focal line 113 having a first end point and a second end point, each end point being defined by a position where the quasi-non-diffracting beam propagates from the beam waist a distance equal to the Rayleigh range of the quasi-non-diffracting beam. The length of the laser beam focal line corresponds to twice the Rayleigh range of the quasi-non-diffracting beam. A detailed description of the formation of quasi-non-diffracting beams and the determination of their lengths, including the generalization of the description of such beams to non-symmetric (such as non-axisymmetric) beam cross-sectional profiles, is provided in U.S. Patent No. 10,730,783, which is incorporated herein by reference in its entirety.

[0169] The Rayleigh range corresponds to the distance (as defined in section 3.12 of ISO 11146-1:2005(E), relative to the position of the beam waist) at which the variance of the laser beam (relative to the variance at the beam waist) doubles, and this distance 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 peak light intensity observed in the beam cross-sectional profile decays to half of the value observed in the beam cross-sectional profile at the beam waist position (maximum intensity position). A laser beam with a large Rayleigh range has low divergence and spreads more slowly with distance in the beam propagation direction compared to a laser beam with a small Rayleigh range.

[0170] The beam cross-section is characterized by shape and size. The size of the beam cross-section is characterized by the spot size of the beam. For a Gaussian beam, the spot size is often defined as the radial range at which the beam intensity decreases to 1 / e of its maximum value. 2 The maximum intensity of a Gaussian beam occurs at the center of the intensity distribution (x = 0 and y = 0 (Cartesian) or r = 0 (cylindrical)), and the radial range used to determine the spot size is measured relative to the center.

[0171] Beams with a Gaussian intensity distribution may not be preferably used for laser processing to form the profile of a defect because when focused to a sufficiently small spot size (such as a spot size in the micron range, such as about 1 - 5 μm or about 1 - 10 μm) so that the available laser pulse energy can modify materials such as glass, they are highly diffractive and significantly diverge over a short propagation distance (low Rayleigh range). To achieve low divergence (high Rayleigh range), it is desirable to control or optimize the intensity distribution of the pulsed laser beam to reduce diffraction. The pulsed laser beam can be non-diffractive or weakly diffractive. Weakly diffractive laser beams include quasi-non-diffractive laser beams. Representative weakly diffractive laser beams include Bessel beams, Airy beams, Weber beams, and Mathieu beams.

[0172] Non-diffractive or quasi-non-diffractive beams typically have a complex intensity distribution, such as those that do not decrease monotonically with respect to the radius. By analogy with a Gaussian beam, for any beam (even a non-axisymmetric beam), an effective spot size w o,eff can be defined as the shortest radial distance from the radial position (r = 0) of the maximum intensity in any direction, at which the intensity decreases to 1 / e of the maximum intensity. 2 . Further, for an axisymmetric beam, w o,eff is the radial distance from the radial position (r = 0) of the maximum intensity, at which the intensity decreases to 1 / e of the maximum intensity. 2。In Equation (3), the effective spot size w of the non-axisymmetric beam o,eff and the Rayleigh range Z R can be specified as a non-diffracting beam or a quasi-non-diffracting beam for forming a damage region, as follows: where F D is a dimensionless divergence factor having a value of at least 10, in one embodiment at least 50, in one embodiment at least 100, in one embodiment at least 250, particularly at least 500 and in another embodiment at least 1000. In another embodiment, F D can be in the range of 10 to 2000, particularly in the range of 50 to 1500, and further particularly in the range of 100 to 1000. For a non-diffracting or quasi-non-diffracting beam, the distance (Rayleigh range) Z R in Equation (1) at which the effective spot size doubles is F D multiplied by the distance expected when using a typical Gaussian beam profile. The dimensionless divergence factor F D provides a criterion for determining whether a laser beam is quasi-non-diffracting. As used herein, if the characteristics of the pulsed laser beam 112 satisfy Equation (1) when the value of F D ≥ 10, the pulsed laser beam 112 is considered quasi-non-diffracting. As the value of F D increases, the pulsed laser beam 112 approaches a more perfect non-diffracting state. Therefore, as the value of F D increases, the length of the laser beam focal line increases, which is beneficial for forming longer defects.

[0173] Additional information regarding the Rayleigh range, beam divergence, intensity distribution, axially symmetric and non-axially symmetric beams, and spot size, as used herein, can be found in 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 these documents are incorporated herein by reference in their entirety.

[0174] Reference is now made to Figure 3 and Figure 4 in which a transparent workpiece 120, including a textured surface 123, is schematically depicted as undergoing laser machining in accordance with the method described herein. Specifically, Figure 3 and Figure 4Schematically depicts guiding a pulsed laser beam 112 output from a pulsed beam source 110 (such as a Gaussian beam source) along a beam path 111 and directing it into a transparent workpiece 120 to form a defect 172 in the transparent workpiece 120. For example, the defect extends into the transparent workpiece 120. The pulsed laser beam 112 propagates along the beam path 111 and is directed such that the pulsed laser beam 112 can be focused, for example, using an aspherical optical element 135 and one or more lenses ( Figure 5 ) into a pulsed laser beam focal line 113 within the transparent workpiece 120. The laser pulse beam focal line 113 generates induced absorption within the transparent workpiece 120 to create a defect 172 that can extend into the interior of the transparent workpiece 120. Additionally, by translating at least one of the pulsed laser beam 112 and the transparent workpiece 120 relative to each other such that the pulsed laser beam 112 is translated relative to the transparent workpiece 120 in a translation direction 101, a profile 170 of the defect 172 can be formed in the transparent workpiece 120. The pulsed laser beam 112 forms a beam spot 114 that is projected onto a textured surface 123 of the transparent workpiece 120.

[0175] Also refer to Figure 5 , the pulsed laser beam 112 can be focused into the pulsed laser beam focal line 113 using a lens 132, which is the final focusing element in the optical assembly 100. Although a single lens 132 is depicted in Figure 3 and 4 , the optical assembly 100 further includes an aspherical optical element 135 that modifies the pulsed laser beam 112 such that the pulsed laser beam 112 has quasi-non-diffracting characteristics downstream of the aspherical optical element 135. Thus, when the portion of the pulsed laser beam 112 as shown in Figure 3 and Figure 4 irradiates the lens 132, the pulsed laser beam 112 has quasi-non-diffracting characteristics. Additionally, some embodiments may include a lens assembly 130 that includes, for example, a first lens 131 and a second lens 132 and their repetitions ( Figure 5 ) to focus the pulsed laser beam 112 into the pulsed laser beam focal line 113. Other standard optical elements (such as prisms, beam splitters, etc.) may also be included in the lens assembly 130.

[0176] As Figure 3 depicts, the pulsed laser beam 112 may include an annular shape when it impinges on the lens 132. Although the lens 132 is depicted in Figure 3 as focusing the pulsed laser beam 112 into the pulsed laser beam focal line 113, other embodiments may use the aspherical optical element 135 ( Figure 2) that modifies the pulsed laser beam 112 such that the pulsed laser beam 112 has a quasi-non-diffracting characteristic downstream of the aspherical optical element 135 and also focuses the pulsed laser beam 112 into the pulsed laser beam focal line 113. In other words, in some embodiments, the lens 132 can be the final focusing element, and in other embodiments, the aspherical optical element 135 can be the final focusing element. The pulsed laser beam focal line 113 can have a length in the range of from about 0.1 mm to about 100 mm or in the range of from about 0.1 mm to about 10 mm. Various embodiments can be configured to have a pulsed laser beam focal line 113 having a length l 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 1.0 mm, about 2.0 mm, about 3.0 mm, about 4.0 mm, or about 5.0 mm, or about 10.0 mm, or a range therebetween; for example, from about 0.5 mm to about 5.0 mm, or from about 1.0 mm to about 10.0 mm, etc. In other embodiments, the length of the laser beam focal line is greater than or equal to the thickness of the transparent workpiece, or greater than or equal to 50% of the thickness of the transparent workpiece, or greater than or equal to 75% of the thickness of the transparent workpiece. The length of the pulsed laser beam focal line 113 can be selected based on a particular laser processing objective. As an example, for a thicker transparent workpiece 120, it may be advantageous to form a longer pulsed laser beam focal line 113. As another example, if it is desired that the defect 172 only extends into a discrete depth portion of the transparent workpiece 120, it may be advantageous to form a shorter pulsed laser beam focal line 113.

[0177] Now referring to Figure 5 , an optical assembly 100 for generating a pulsed laser beam 112 is schematically depicted, the laser beam 112 being quasi-non-diffracting and using an aspherical optical element 135 (e.g., an axicon 136) to form a pulsed laser beam focal line 113 at a transparent workpiece 120. The optical assembly 100 includes a pulsed beam source 110 that outputs the pulsed laser beam 112 and a lens assembly 130 that includes a first lens 131 and a second lens 132. The transparent workpiece 120 can be positioned such that the pulsed laser beam 112 output by the pulsed beam source 110 irradiates the transparent workpiece 120, for example, after passing through the aspherical optical element 135 and then through both the first lens 131 and the second lens 132.

[0178] The aspherical optical element 135 is positioned within the beam path 111 between the pulsed beam source 110 and the transparent workpiece 120. In operation, propagating the pulsed laser beam 112 (e.g., an incoming Gaussian beam) through the aspherical optical element 135 can alter (e.g., phase-alter) the pulsed laser beam 112 such that the portion of the pulsed laser beam 112 that propagates beyond the aspherical optical element 135 is quasi-non-diffracting, as described above. The aspherical optical element 135 can include any optical element that includes an aspherical shape. In some embodiments, the aspherical optical element 135 can include a conical wavefront generating optical element such as an axicon lens, e.g., a negative refractive index axicon lens (e.g., a negative axicon), a positive refractive index axicon lens, a reflective axicon lens, a diffractive axicon lens, a phase axicon, a diffractive optical device, an optical element having a cubic shape, etc.

[0179] Although the optical assembly 100 is primarily described as using the aspherical optical element 135 to alter the pulsed laser beam 112 into a quasi-non-diffracting beam, it should be understood that a quasi-non-diffracting beam can also be formed by other phase-altering optical elements such as a spatial light modulator, an adaptive phase plate, a static phase plate, a deformable mirror, a diffraction grating, etc. Each of these phase-altering optical elements, including the aspherical optical element 135, modifies the phase of the pulsed laser beam 112 to reduce beam divergence, increase the Rayleigh range, and form a quasi-non-diffracting beam as mathematically defined herein.

[0180] Still referring to Figure 5, the lens assembly 130 includes two lenses, where the first lens 131 is positioned upstream of the second lens 132. The first lens 131 can collimate the pulsed laser beam 112 within the collimation space 134 between the first lens 131 and the second lens 132. Additionally, the second lens 132, which is the most downstream lens of the lens assembly 130, can focus the pulsed laser beam 112 into the transparent workpiece 120. In some embodiments, each of the first lens 131 and the second lens 132 includes a plano-convex lens. When each of the first lens 131 and the second lens 132 includes a plano-convex lens, the curvatures of the first lens 131 and the second lens 132 can be each oriented towards the collimation space 134. In other embodiments, the first lens 131 can include a collimating lens, and the second lens 132 can include a meniscus lens, an aspherical lens, or other higher-order correction focusing lens. In operation, the lens assembly 130 can control the position of the pulsed laser beam focal line 113 along the beam path 111. In still other embodiments, the lens assembly 130 can include an 8F lens assembly, a 4F lens assembly including the first lens 131 and the second lens 132 of a single group, or any other known or yet-to-be-developed lens assembly 130 for focusing the pulsed laser beam 112 into the laser beam focal line 113. Additionally, it should be understood that some embodiments may not include the lens assembly 130, and instead, an aspherical optical element 135 can focus the pulsed laser beam 112 into the pulsed laser beam focal line 113. For example, the aspherical optical element can convert the pulsed laser beam 112 into a quasi-non-diffracting laser beam and focus the quasi-non-diffracting laser beam into the pulsed laser beam focal line 113.

[0181] Referring again to Figures 3 to 5 , the pulsed beam source 110 is configured to output a pulsed laser beam 112. In operation, a defect 172 of the profile 170 is generated by the interaction of the transparent workpiece 120 with the pulsed laser beam 112, which is output by the pulsed beam source 110 modified by the aspherical optical element 135 and / or the lens assembly 130. In operation, the pulsed laser beam 112 output by the pulsed beam source 110 can induce multi-photon absorption (MPA) in the transparent workpiece 120. MPA is the simultaneous absorption of two or more photons of the same or different frequencies, and this simultaneous absorption 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 state and higher state of the molecule is equal to the sum of the energies of the involved photons. MPA (also referred to as induced absorption) can be, for example, a second-order or third-order (or higher-order) process that is several orders of magnitude weaker than linear absorption. It differs from linear absorption in that, for example, the intensity of second-order induced absorption can be proportional to the square of the light intensity, so it is a non-linear optical process.

[0182] In some embodiments, the pulsed beam source 110 can output a pulsed laser beam 112 having a wavelength such as 1064 nm, 1030 nm, 532 nm, 530 nm, 355 nm, 343 nm, or 266 nm or 215 nm. Additionally, the pulsed laser beam 112 for forming the defect 172 in the transparent workpiece 120 can be well-suited for materials that are transparent to the selected pulsed laser wavelength. A suitable laser wavelength for forming the defect 172 is a wavelength at which the combined loss of linear absorption and scattering in the transparent workpiece 120 (e.g., after propagating through the textured surface 123) is low enough. In an embodiment, the combined loss caused by linear absorption and scattering in the transparent workpiece 120 at the laser wavelength is less than 20% / mm, or less than 15% / mm, or less than 10% / mm, or less than 5% / mm or less than 1% / mm, such as 0.5% / mm to 20% / mm, 1% / mm to 10% / mm, or 1% / mm to 5% / mm. For example, 1% / mm, 2.5% / mm, 5% / mm, 10% / mm, 15% / mm, or any range having any two of these values as endpoints, or any open range having any one of these values as the lower limit. As used herein, the dimension " / mm" means per millimeter distance within the transparent workpiece 120 in the beam propagation direction (i.e., the Z-direction) of the pulsed laser beam 112. Representative laser wavelengths for many glass workpieces include the fundamental and harmonic wavelengths of Nd 3+ (e.g., Nd 3+ :YAG or Nd 3+ :YVO 4 ) having a fundamental wavelength close to 1064 nm and higher harmonic wavelengths close to 532 nm, 355 nm, and 266 nm. Other laser wavelengths in the ultraviolet, visible, and infrared portions of the spectrum that meet the combined linear absorption and scattering loss requirements for a given substrate material can also be used.

[0183] Still referring to Figures 3 to 5 , in operation, the profile 170 can be formed in the transparent workpiece 120 by irradiating the profile line 142 with the pulsed laser beam 112 and translating at least one of the pulsed laser beam 112 and the transparent workpiece 120 relative to each other in the translation direction 101 along the profile line 142 to form the defect 172 of the profile 170. Although Figure 3The profile 170 depicted therein is linear, but it should be understood that the profile 170 can be non-linear, for example, curved. Additionally, in some embodiments, the profile 170 can be a closed profile, such as a circle, rectangle, ellipse, square, hexagon, oval, regular geometric shape, irregular shape, polygon, arbitrary shape, etc. In an embodiment, the profile line 142 represents the boundary between the used portion of the transparent workpiece 120 (e.g., incorporated into a glass article) and the discarded portion of the transparent workpiece 120.

[0184] The pulsed laser beam 112 is directed or positioned into the transparent workpiece 120 to generate induced absorption (e.g., MPA) within the transparent workpiece 120, and sufficient energy is accumulated to break chemical bonds in the transparent workpiece 120 at spaced-apart locations along the profile line 142 to form defects 172. According to one or more embodiments, the pulsed laser beam 112 can be translated across the transparent workpiece 120 by the movement of the transparent workpiece 120 (e.g., the movement of the translation stage 190 coupled to the transparent workpiece 120), the movement of the pulsed laser beam 112 (e.g., the movement of the pulsed laser beam focal line 113), or the movement of both the transparent workpiece 120 and the pulsed laser beam focal line 113. By translating at least one pulsed laser beam focal line 113 relative to the transparent workpiece 120, multiple defects 172 can be formed in the transparent workpiece 120.

[0185] In some embodiments, the defects 172 can generally be spaced from each other along the profile 170 by a distance of from 0.1 μm to 500 μm, such as from 1 μm to 200 μm, from 2 μm to 100 μm, or from 5 μm to 20 μm, from 0.1 μm to 50 μm, from 5 μm to 15 μm, from 5 μm to 12 μm, from 7 μm to 15 μm, from 8 μm to 15 μm, or from 8 μm to 12 μm, such as 50 μm or less, 45 μm or less, 40 μm or less, 35 μm or less, 30 μm or less, 25 μm or less, 20 μm or less, 15 μm or less, 10 μm or less, such as 100 μm, 75 μm, 50 μm, 40 μm, 30 μm, 25 μm, 10 μm, 5 μm, or any range with any two of these values as endpoints, or any open range with any of these values as the lower limit. While not intending to be limited by theory, increasing the spacing distance between adjacent defects 172 can increase the processing speed (i.e., reduce the processing time), and decreasing the spacing distance between adjacent defects 172 can reduce the fracture resistance of the profile 170 of the defects 172. Additionally, the translation of the transparent workpiece 120 relative to the pulsed laser beam 112 can be performed by moving the transparent workpiece 120 and / or the pulsed beam source 110 using one or more translation stages 190.

[0186] Now refer to Figures 3 to 6, in an embodiment, a defect 172 of one or more contours 170 is formed by a pulse train 50 having at least two sub-pulses 51. In such an embodiment, compared with the fracture resistance of a contour 170 of the same shape having the same spacing between adjacent defects 172 in the same transparent workpiece 120 formed by a single-pulse laser having the same energy as the combined energy of the sub-pulses of the pulse train 50, the force required to separate the transparent workpiece 120 along the contour 170 (i.e., the fracture resistance) is reduced. A pulse train (such as pulse train 50) is a short and fast group of sub-pulses (i.e., a tight cluster of sub-pulses, such as sub-pulse 51) emitted by a laser and interacting with a material (i.e., transparent workpiece 120). Using the pulse train 50 (relative to single-pulse operation) increases the size of the defect 172 (e.g., the cross-sectional size), which helps the connection of adjacent defects 172 when separating the transparent workpiece 120 along the contour 170, thereby minimizing crack formation away from the contour 170 in the separated section of the transparent workpiece 120.

[0187] Still referring to Figures 3 to 6 , in some embodiments, the pulses generated by the pulse beam source 110 are generated in a pulse train 50, and each pulse train 50 has two sub-pulses 51 or more sub-pulses, such as each pulse train 50 having 2 to 30 sub-pulses 51, or each pulse train 50 having 5 to 20 sub-pulses 51. In addition, the energy required to modify the transparent workpiece 120 is the pulse energy, which can be described according to the pulse train energy (i.e., the energy contained in the pulse train 50, where each pulse train 50 contains a series of sub-pulses 51; that is, the pulse train energy is the combined energy of all sub-pulses within the pulse train). The pulse energy (e.g., the pulse train energy) can be 25 μJ to 1000 μJ or 25 μJ to 750 μJ, such as 100 μJ to 600 μJ, 50 μJ to 500 μJ, or 50 μJ to 250 μJ, for example, 25 μJ, 50 μJ, 75 μJ, 100 μJ, 200 μJ, 250 μJ, 300 μJ, 400 μJ, 500 μJ, 600 μJ, 750 μJ, or any range with any two of these values as endpoints, or any open range with any of these values as the lower limit.

[0188] Now referring to Figure 7 , to form a Bessel beam, a conical wavefront is typically created by employing an axicon, the optical axis of which is aligned with the beam propagation direction and centered with respect to the intensity distribution of the incident laser beam. This imparts a phase delay to the incident wavefront of the incident laser beam, which is linearly proportional to the distance from the optical axis. Such an axicon can be a refractive optical device, a reflective optical device, a phase plate element, or a diffractive optical device.

[0189] Now referring to Figure 8 and Figure 9, the interference of the conical wavefront will cause any cross-sectional profile of the beam emerging from the axicon to be modulated with a Bessel function-like dependence. The intensity of the beam emerging from the axicon rolls off precisely with the radius (the direction perpendicular to the beam propagation direction) and the z-distance (the beam propagation direction), depending on the nature of the beam illuminating the axicon. The input beam illuminating the axicon typically has a Gaussian cross-sectional intensity distribution. In this case, the beam emerging from the axicon is a type of Bessel beam, which is referred to herein as a "Gaussian-Bessel beam".

[0190] The formed focus is called a "focal line" or "line focus". The important properties of the focal line are its core diameter and length.

[0191] The numerical aperture NA of the focused laser beam is given by the following equation (A): NA = n * sin(β) (A) where n is the refractive index of the medium (i.e., air), and β is the maximum ray angle measured with respect to the beam propagation axis in the focused light cone. Note that in the context of a laser beam, the "numerical aperture" is defined by the light beam that actually propagates through the optical device and is focused by the optical device, rather than by the maximum physical diameter of the optical device itself. Thus, if the physical size of the optical device increases in diameter, but the size of the laser beam propagating through the optical device does not change, the numerical aperture of the focused laser beam remains the same.

[0192] The relationship between the numerical aperture NA of the focused light and the core diameter d of the Bessel beam is governed by the following equation (B): where λ 0 is the wavelength of the light source, and n 0 is the refractive index of the medium, which is approximately 1.0 for air. The core diameter d is the diameter of the first zero in the Bessel function cross-section of the light beam. Thus, this formula indicates that the focused core is only a function of the wavelength and the numerical aperture. Conventionally, when performing Bessel beam cutting of glass, a numerical aperture of 0.25 to 0.45 is used. At common wavelengths of 1030 nm and 1064 nm, high short-pulse (ns, ps, or fs) laser pulse energies can be easily achieved. This means using a core diameter of 3.25 microns to 1.8 microns.

[0193] As can be seen from equation (B), a lower numerical aperture will create a larger core diameter. This reduces the energy density in the material, which should be considered when forming a strong laser modification (nanoporation) through the full thickness of the substrate.

[0194] The input beam irradiating the axicon can have a Gaussian cross-sectional intensity distribution. The intensity is highest at the center of the beam, i.e., along the beam propagation axis, and decays radially. In this case, the Gaussian-Bessel beam emerging from the axicon will have an on-axis intensity distribution in the beam propagation direction ( Figure 9 ). Figure 9 The distance of 0 mm corresponds to the exit surface of the axicon. As Figure 9 shown, the on-axis intensity distribution of the Gaussian-Bessel beam has a peak normalized intensity of 1 and is shown to rise rapidly to the peak and then decay slowly with distance after the peak. The distance L between points along the beam propagation direction (where the intensity has decreased to 50% of the peak intensity) can be approximated by the following equation (C): L ∼ 0.8*R z / sin(β) (C) L in Equation (3) is actually the length of the line focus (or the extent along the optical axis). It is a function of both the input Gaussian beam size (1 / e 2 radius, R z ) and the aperture angle β ( Figure 7 ).

[0195] Now referring to Figure 10 , an optical design is shown where the line focus generated by the axicon is magnified by a 2F / 2F objective pair (e.g., a telescope). This optical system can be used to generate a Bessel beam for glass cutting. The magnification of the telescope located after (downstream of) the axicon is given by M = F2 / F1 and can then be varied by changing the focal length F1 or the focal length F2. The numerical aperture of the Bessel beam emerging from the telescope will scale with the magnification of the telescope. Correspondingly, this means that the transverse profile (diameter) of the focused Bessel beam along the Z-direction in a given plane scales linearly with the magnification of the telescope. However, as derived from the axial magnification characteristics of a telescope commonly known in the art, it should be noted that the length of the line focus is proportional to the square of the magnification.

[0196] Now referring to Figure 11 , an embodiment is shown that includes magnifying the size (1 / e 2 radius, R z ) of the input Gaussian beam by a factor of N upstream of the axicon. For the Figure 11 configuration shown, according to Equation (B) and Equation (C), the only key output parameter affected by the change in the size (1 / e 2 radius, R z ) of the input Gaussian beam is the length of the line focus, which scales with the input Gaussian beam magnification N (the size (1 / e 2 radius, R z ) of the input beam at the incident surface of the axicon compared to the size (1 / e 2Radius, R z ) increases linearly. Since the numerical aperture of the focused light remains constant, as can be seen from equation (B), the diameter of the line focus is not affected. In contrast, when using a Gaussian laser beam that is not modified by an axicon, the depth of focus (Rayleigh range) and the focused core diameter are inherently coupled and cannot be varied independently. Using an input telescope to modify the input Gaussian beam size (1 / e 2 Radius, R z ) is a convenient way to control a line-focus (Bessel-like) cutting / drilling system because it allows only the line focal length to be changed while keeping the core diameter constant. To set the line length to be suitable for processing a textured glass substrate with a thickness of about 2.5 - 3 mm using Gaussian-Bessel beams with different numerical apertures, in some embodiments, the input Gaussian beam size used is as large as 2.75 mm (1 / e 2 Radius, R z ), in other embodiments, it is made 2.5 mm, and in some cases, it is made as small as 1.5 mm.

[0197] In one example, the optical setup employs a 1064 nm laser that has a Gaussian beam profile incident on an axicon fabricated with a 9.615-degree cone angle. The Gaussian-Bessel beam emerging from the axicon is directed to a telescope. The first lens (F1) of the telescope consists of a pair of elements with a combined effective focal length of 134 mm. This creates an annular ring with a diameter of approximately 22 mm at the second lens F2 of the telescope. For lens F2, various focal lengths are used to convert the annular ring generated by the first lens F1 into a focused Gaussian-Bessel beam. The various focal lengths of lens F2 provide different telescope magnifications and thus focus Gaussian-Bessel beams with different numerical apertures. In each case, the distance by which the second lens F2 is separated from the first lens F1 is equal to the sum of the effective focal length of the first lens F1 and the focal length of the second lens F2. Table 1 details a set of optical configurations explored. The telescope magnification refers to the ratio of the focal length of the second lens F2 to the effective focal length (134 mm) of the first lens F1. The final beam NA refers to the numerical aperture of the beam generated by the second lens F2 and is determined by equation (A), where the medium is air (refractive index = 1) and β is the cone angle of the axicon (9.615 degrees). The core diameter is determined by equation (B), where the medium is air (refractive index = 1).

[0198] Table 1

[0199] Now refer to Figures 4 to 5 B, when using, for example, according to Figures 3 to 6In one embodiment of the embodiments, after forming the profile 170 of the defect 172 along the profile line 142 in the transparent workpiece 120, the transparent workpiece 120 can be further acted on in a subsequent separation step to induce the separation of the transparent workpiece 122 along the profile line 142 (i.e., along the profile 170 of the defect 172). In an embodiment, the subsequent separation step includes directing an infrared laser beam 212 onto the transparent workpiece 120 to apply a thermal stress to the transparent workpiece 120. The applied thermal stress induces a separation extending between adjacent defects 172 in the transparent workpiece 120 along the profile line 142. In the transparent workpiece 120, such separation can include the propagation of cracks along the profile line 142.

[0200] Without being limited by theory, the infrared laser beam 212 is a controlled heat source that rapidly increases the temperature of the transparent workpiece 120 at or near the profile line 142, modifies the material of the transparent workpiece 120 along or near the profile line 142 to induce the separation of the material extending between adjacent defects 172. Additionally, this rapid heating can build compressive stress in the transparent workpiece 120 on or near the profile 170. Since the area of the heated surface of the transparent workpiece 120 is relatively small and shallow compared to the total surface area of the transparent workpiece 120, the heated area cools relatively rapidly. The resulting temperature gradient induces tensile stress in the transparent workpiece 120 sufficient to propagate cracks along the profile 170 and through the depth of the transparent workpiece 120, resulting in the complete separation of the transparent workpiece 120. Without being limited to theory, it is believed that the tensile stress can be caused by the expansion (i.e., changing density) of the glass in the portion of the workpiece having a higher local temperature induced by the infrared laser beam 212.

[0201] Figure 12 An optical component 200 is depicted, and the optical component 200 includes an infrared beam source 210 configured to generate an infrared laser beam 212. The infrared beam source 210 can include a carbon dioxide laser (“CO 2 laser”), a carbon monoxide laser (“CO laser”), a solid-state laser, a laser diode, or a combination thereof. The infrared laser beam 212 includes a wavelength that is readily absorbed by the transparent workpiece 120, for example, a wavelength in the range of 1.2 μm to 13 μm, such as a wavelength in the range of 4 μm to 12 μm. The power of the infrared laser beam 212 can range from about 10 W to about 4000 W, for example, 100 W, 250 W, 500 W, 750 W, 1000 W, etc. Additionally, the infrared beam source 210 can include a continuous-wave laser or a pulsed laser. The optical component 200 further includes a lens assembly 230, and the lens assembly 230 includes a lens 232 for focusing the infrared laser beam 212 to create a specific core diameter (1 / e 2Twice the radius or equivalent). The core diameter at the surface of the workpiece is typically greater than or equal to 1 mm and less than or equal to 15 mm, such as greater than or equal to 2 mm and less than or equal to 10 mm, or greater than or equal to 4 mm and less than or equal to 8 mm. It is desirable to keep the spot size small enough so that the local temperature of the glass increases significantly and thermal stress is generated as well as cracks are generated, but not to make the spot size too small and the laser intensity too high so that the glass is locally ablated or damaged in an uncontrolled manner. The infrared laser spot is passed along the defect profile 170, which propagates the crack from one defect 172 to the next. The infrared beam spot size at the transparent workpiece 120 and the available infrared laser power define the speed at which the infrared laser beam 212 can be translated to affect crack propagation, and a higher laser power allows the infrared laser beam to be translated at a higher speed. In operation, the infrared laser beam 212 propagates along the infrared beam path 211 and is directed such that the infrared laser beam 212 can be, for example, directed onto the transparent workpiece 120, and a desired spot size is formed on the textured surface 123 of the transparent workpiece 120 using the lens 232.

[0202] Now referring to Figure 13 , a cross-section of the transparent workpiece 120 having the profile 170 with the defect 172 is schematically depicted during laser machining using the infrared laser beam 212. In Figure 13 , the infrared laser beam 212 is directed onto the transparent workpiece 120 using the optical assembly 200 of Figure 12 and includes a Gaussian intensity distribution at the transparent workpiece 120. Further, in Figure 13 , the infrared laser beam 212 is directed onto the transparent workpiece 120 and aligned with the profile 170 of the defect 172 and thus with the profile line 142. Because the infrared laser beam 212 includes a Gaussian energy distribution, the interaction of the infrared laser beam 212 with the transparent workpiece 120 forms a heat-affected zone 140. The heat-affected zone 140 corresponds to the portion of the transparent workpiece 120 that absorbs the infrared laser beam 212 and receives sufficient energy to generate thermal stress sufficient to induce separation of the transparent workpiece 120 along the profile 170. That is, the heat-affected zone 140 includes a portion of the transparent workpiece 120 in which thermal energy sufficient to induce separation of the profile 170 of the defect 172 is applied. In an embodiment, the heat-affected zone 140 induces propagation of the crack 150 in the transparent workpiece 120. In the depicted example, the crack 150 extends through the entire thickness of the transparent workpiece 120 such that the heat-affected zone 140 is sufficient to induce separation of the transparent workpiece 120 along the crack 150.

[0203] As depicted in Figure 13 , as herein with respect to Figures 3 to 6The defect 172 formed by the described machining result does not always extend through the entire transparent workpiece 120. Even if the focal line 113 of the pulsed laser beam has a length greater than the thickness of the transparent workpiece 120, such a defect 172 may be caused. For example, the textured surface 123 can distort and scatter the focal line 113 of the pulsed laser beam, thereby modifying the energy density distribution of the focal line 113 of the pulsed laser beam. As a result of such distortion, after traveling through a part of the transparent workpiece 120, the focal line 113 of the pulsed laser beam may not have the energy density required to modify the transparent workpiece 120, such that at least a part of the transparent workpiece 120 is not modified by the focal line 113 of the pulsed laser beam. This unmodified part of the transparent workpiece 120 makes the propagation of the crack 150 unpredictable. In the example, the crack 150 significantly deviates from the profile 170 in the part of the transparent workpiece 120 where the depicted defect 172 does not extend.

[0204] The distortion of the focal line 113 of the pulsed laser beam caused by the textured surface 123 can also cause the defect 172 to have a non-uniform cross-sectional shape (e.g., in the X-Y plane) as a function of the distance from the textured surface 123 (e.g., in the Z direction). Such a cross-sectional deviation can cause the crack 150 to propagate between adjacent defects 172 (e.g., separated in the Y direction in the depicted example) in the defect 172 in a manner deviating from the profile 170. Thus, although applying the infrared laser beam 212 may cause the separation of the transparent workpiece 120, the separation line (e.g., the crack 150) may significantly deviate from the profile 170 in an unpredictable manner. This unpredictability results in machining waste because the transparent workpiece 120 can be machined using a profile that provides a margin for such crack deviation.

[0205] Figure 14 A perspective view of the transparent workpiece 120 during its separation is depicted. As depicted, the transparent workpiece 120 includes a plurality of defects 172. At the textured surface 123, the plurality of defects 172 have an elliptical cross-section (e.g., in the X-Y plane). For example, in an embodiment, the optical component 100 described herein can impart an elliptical cross-sectional shape to the pulsed laser beam 112 such that the focal line 113 of the pulsed laser beam has an elliptical cross-section in the X-Y plane. In an embodiment, the plurality of defects 172 can have an alternative shape (e.g., having an asymmetry such that the defect 172 is larger in size along the extension direction of the profile 170 or in Figure 5 the Y direction). In the depicted example, the defect 172 has a major axis extending along the profile 170. The defect 172 having such a shape advantageously guides the propagation of the stress-induced crack 150 along the profile 170 (e.g., via Figure 14 and Figure 12 and Figure 13The described infrared laser beam 212), thereby reducing the threshold amount of stress that induces crack propagation. Guiding the propagation of crack 150 along profile 170 also beneficially improves the edge strength of the separated portion of the transparent workpiece 120 by reducing the amount of crack 150 propagating in a direction perpendicular to profile 170 (e.g., in the X direction).

[0206] However, as described herein with respect to Figure 13 When the pulse laser beam focal line 113 propagates through the transparent workpiece 120, the textured surface 123 can change the cross-sectional shape of the pulse laser beam focal line 113. Thus, the defect 172 may not have the Figure 14 oval profile depicted in. This cross-sectional deviation can reduce the crack guiding tendency of the defect 172, thereby causing a deviation 152 in the crack 150 in a direction perpendicular to the profile 170 (e.g., the X direction). Thus, the textured surface 123 can cause the transparent workpiece 120 to separate along a separation line that significantly deviates from the expected separation line. Additionally, multiple defects 172 may not extend through the entire thickness of the transparent workpiece 120. Thus, the propagation of the crack 150 through the thickness of the transparent workpiece 120 (e.g., in the Z direction) may also deviate from the profile 170.

[0207] Figure 15 Depicts a cross-sectional view of the separated portion 300 of the transparent workpiece 120. For example, the separated portion 300 can be produced by separating the transparent workpiece 120 along the crack 150 with respect to Figure 14 described. The separated portion 300 includes a cutting edge 156 that can correspond to the crack 150. The cutting edge 156 includes a cantilever curl 158, where the cutting edge 156 deviates from the desired separation line 154 by a thickness Tc. The cantilever curl 158 is produced by the defect 172 not extending through the entire thickness of the transparent workpiece 120 and failing to guide the crack 150 when the crack 150 propagates through the thickness of the transparent workpiece 120. In an example, the thickness Tc of the cantilever curl in a direction perpendicular to the desired separation line 154 can be greater than or equal to 100 μm (e.g., greater than or equal to 100 μm and less than or equal to 150 μm). Thus, a significant amount of post-processing may be required to provide a cutting edge 156 corresponding to the desired separation line 154. Given the likelihood of such a large deviation from the desired separation line 154, laser processing of the transparent substrate 120 by directing the pulse laser beam 112 directly onto the textured surface 123 can utilize a contour line that is significantly offset from the desired separation line 154, increasing material waste.

[0208] As another example, Figure 16FIG. 0 depicts a top view of a separated portion 500 of a transparent workpiece processed by the laser machining method described herein. The separated portion 500 includes a textured surface 508 and a cutting edge 502 including a curved profile. Since the defects generated by the laser machining method described herein do not extend through the entire thickness of the separated portion 500, the cutting edge 502 includes a chip 504, wherein the cutting edge 502 extends inwardly from the curved profile by about 100 μm, and the adherent glass 506 extends outwardly from the curved profile by about 150 μm. Such chips 504 and adherent glass 506 can be specifically generated by a profile whose profile direction changes rapidly with position, such as a curved profile having a radius of curvature less than or equal to 10 mm. In order to provide the separated portion 500 with a relatively robust outer edge at the cutting edge 502, the cutting edge 502 can be ground and polished to remove the chip 504 and the adherent glass 506. Removing more than 100 μm of material from the cutting edge 502 represents a material removal amount significantly exceeding the typical subsurface damage (e.g., less than or equal to 30 μm) associated with the laser machining of transparent substrates. Therefore, when a curved profile is desired, the textured surface can result in additional material waste.

[0209] Now refer to Figure 17 and Figure 18 , by passing a laser beam across a glass sheet and emitting laser pulses at a controlled time, these nanopores are coherently joined together to outline the profile of the desired part. The spacing between nanopores is typically from a few micrometers to dozens of micrometers, and can be formed at a rate of hundreds of thousands per second. The nanopores serve as sites for initiating and guiding crack propagation in the glass sheet. Once stress is applied, the glass sheet will separate along the nanopore profile.

[0210] The stress can be applied by mechanically bending the sheet or by applying thermally induced stress. The preferred way to apply thermal stress is to use a mid-infrared laser such as a CO 2 laser as described above to track the nanopore profile. The mid-infrared light is absorbed at the glass surface and creates local heating. This heat generates local expansion of the glass sheet, and the local expansion of the glass sheet propagates cracks along the nanopore sites, separating the glass into discrete fragments. The CO 2 laser spot size and dwell time at any given location must deposit sufficient energy to generate sufficient thermal stress to propagate the crack, but the energy cannot be too large so as to cause melting, ablation, or other undesirable damage to the glass surface. Typical processing requires modulating the duty cycle or continuous wave laser beam with an optical power of 50 - 400 W (e.g., 200 W) to be focused to a spot size of 1 - 15 mm diameter (1 / e 2 ) at the glass surface (e.g., 6 mm), and passing the spot around the nanopore profile at a speed of 50 - 1000 mm / second (e.g., 200 mm / second).

[0211] For optimal results, the nanopores should satisfy two conditions. First, the cracks emanating from each nanopore site should point towards adjacent nanopores. In other words, even at the submillimeter scale (100 μm scale), the cracks should follow the expected part profile and not propagate into the body of the desired part. Second, the nanopores should extend through the entire depth (thickness) of the transparent workpiece.

[0212] Now referring to Figure 19 , guiding the cracks to adjacent nanopores ensures easy crack propagation, meaning that a minimum amount of stress can be applied to separate the glass piece. It also ensures high edge strength of the resulting separated part because when the part is bent or flexed, cracks that go directly into the body of the part (perpendicular to the cut or separation edge) will fail at low applied stress. Guiding the cracks to adjacent nanopores can be achieved by imparting some asymmetry to the shape of the light beam, such as by making the beam focus core have an elliptical shape or the shape of multiple light spots aligned along a particular axis. This asymmetry will cause the stress from each nanopore to be maximum along a particular axis, such that the cracks will preferentially align in a given direction. In the case of an elliptical light spot, the cracks generally align in the same direction as the long axis of the ellipse. This direction can be oriented parallel to the desired outer contour of the part. Methods for generating such asymmetric quasi-non-diffracting light beams, and their benefits for reducing separation stress and increasing edge strength, are described in detail in U.S. Patent Nos. 10,435,796 and 9,758,876 and U.S. Application Publication No. 2020 / 0061750, which are incorporated herein by reference.

[0213] Now referring to Figure 20 and Figure 21 , nanopores that extend through the entire depth of the glass sheet ensure that the oriented or guided cracks pass through the entire thickness of the part following the expected edge profile. Incomplete nanopores may cause the glass part to separate in an uncontrolled or inconsistent manner. In the case of a straight cut, typically the edge of the glass piece is intended to be a 90° edge, i.e., a single plane. These uncontrolled areas result in deviation from this plane. In the case of separating glass around a rounded corner profile, these deviations cause the glass part to potentially protrude from the expected radius (adhering glass), or be recessed into the expected part, which, if at the part surface, results in fragmentation.

[0214] Now referring to Figures 22 to 25 , a textured glass substrate is shown, such as those formed by a rolling process. The textured glass substrate may have a surface roughness Ra of about 0.5 - 5 μm. The surface roughness Ra can be alleviated by a light etch (about 5 μm of surface removal). However, this etching may increase cost and may not completely planarize the surface.

[0215] Due to the non-planar surface of the textured glass substrate, light deviates from its intended path, and the focal line of the Bessel beam may not be formed with sufficient intensity. This effect is strongest for light focused to the deepest part of the glass. The focal line will typically form with sufficient intensity near the surface where the laser beam enters the glass sheet, but the intensity can decay rapidly as a function of depth, as Figure 26 and Figure 27 shown. Even in this case of partial bulk nanoporation, the glass piece may still separate. In fact, if the entrance surface is under tension, then compared to full bulk nanoporation, no additional force may be required to separate the glass. However, the crack may no longer be well-controlled across the entire thickness of the glass. When stress is applied to separate the glass piece, this lack of nanoporation may cause the glass edge to deviate from the desired straight edge.

[0216] Now referring to Figure 15 and Figure 28 , this deviation phenomenon is called "cantilever curl". This cantilever curl does not necessarily occur along the entire length of the separation edge of the glass piece. It can vary in magnitude (distance from the ideal straight edge) and height (depth at which it starts), where the variation is a strong function of the way and consistency of the applied mechanical or thermal separation stress. Due to this cantilever curl, the grinding and polishing required to achieve the final part shape increases because the amount removed must account for all the variability of the part edge. For the glass thickness examined here (e.g., about 1.0 mm), partial bulk nanoporation typically results in a cantilever curl of about 100 - 150 μm. This requires about 5 times the additional removal compared to the requirement of only removing the lower layer damage, thus reducing some of the economic advantages provided by laser cutting.

[0217] Now referring to Figure 29 , although showing stronger laser damage, using multiple laser exposures at different focus heights still results in nanoporations that do not extend through the thickness of the glass sheet. The surface texture still inhibits the beam from focusing well at the farthest depth of the glass sheet. Some damage is seen at the laser exit because the ablation threshold at the interface is typically less than the ablation threshold inside the glass sheet. Additionally, the multiple-pass method also has the challenge that the nanoporations from each pass may not align well laterally, which can lead to variability in the crack direction or separation plane.

[0218] Now referring to Figure 30 , in one example, the sample surface was mechanically polished and laser cut. The mechanical polishing flattened the glass and removed any surface inclusions (such as boron nitride). The nanoporations fully extended through the depth of the glass, illustrating that the challenge of cutting a textured glass substrate is due to surface effects, rather than volume or material effects. Figure 30It is also shown that the laser focal line itself is long enough and strong enough to modify materials greater than 1 mm, provided that it does not become distorted due to surface texture.

[0219] It should also be noted that the texture problem may not be easily solved by simply applying more laser energy. More laser energy will generate damage or nanopores deeper into the depth of the glass sheet. However, for optimal crack guidance, the line focus needs to form both a high-intensity core and preferably an appropriate cross-sectional shape, such as an elliptical Bessel-like beam. The textured surface of the glass not only attenuates the energy but also distorts the beam. As a result, the light may no longer form the expected Bessel-like beam cross-sectional profile. For textured glass, it is generally observed that nanopores will be well formed and cracks will be well controlled near the incident surface of the glass sheet. However, at greater depths, such as 500 μm below the incident surface, there may be laser damage, but the nanopores may no longer exhibit the same shape / cross-sectional profile. It can be observed that the core of the Bessel beam splits into multiple spots due to optical aberration, and the direction of the resulting cracks emerging from each nanopore will become difficult to control and no longer follow the expected part profile.

[0220] In addition, the side lobes of the Bessel-like beam can contain sufficient intensity to induce plasma absorption effects, and cause the resulting material modification to no longer be determined by the shape of the core (central lobe) of the beam. The additional material damage from the side lobes may make the cracks difficult to control because the effect is intensity-dependent and may occur stronger or weaker (depending on the precise beam focusing or the depth into the material).

[0221] Given the problems described herein, the laser processing method described herein allows the laser to completely penetrate through the thickness of the textured glass without the need for any additional steps (e.g., etching or coating), resulting in near-net shape parts that can be precisely cut with subsurface damage less than 30 μm at their edges, allowing a significant reduction in grinding and polishing removal / time in downstream final part edge finishing steps.

[0222] In particular, a method of cutting textured glass includes using a low numerical aperture quasi-non-diffracting beam to nanopore through the coating into the glass, tracing the profile of the desired part. Then, by mechanical (e.g., bending) or thermal (e.g., with CO 2Stress is applied by a laser to separate the glass around the nano-perforation profile. The light beam directed onto the substrate should have a numerical aperture between 0.10 and 0.25, between 0.12 and 0.23, or even between 0.15 and 0.20. The beam can be incident on a material with a textured surface having a surface roughness (Ra) greater than 0.5 μm. Laser processing may require a single pass of the laser beam through the substrate or multiple passes, each pass having a different focusing setting.

[0223] In addition to the textured glass substrate, the described method can also be applied to cutting 3D-formed glass or glass-ceramic articles, where the substrate can have a smooth surface, but local regions have a small radius of curvature (e.g., a radius of curvature less than 20 mm, or less than 15 mm, or less than 10 mm, or less than 5 mm), which can inhibit standard nano-perforation cutting. The same numerical aperture range cited above enables strong nano-perforation through the thickness of the substrate in those highly curved regions.

[0224] Furthermore, the article can include a cut glass sheet having a surface texture, but the profile edges of the cut glass sheet are defined nano-perforations extending through the entire thickness of the glass sheet. The surface texture (i.e., surface roughness Ra) on at least one side of the glass sheet can be greater than 0.5 μm. The textured glass sheet can also have boron nitride inclusions present at the glass surface. The thickness of the glass sheet can be greater than 1 mm.

[0225] The textured surface of the rolled material includes non-periodic deformations. The texture level of each piece can be generally the same, but the exact surface deviations are local and irregular, so the refractive changes imposed on each ray in the Bessel beam will depend on the exact location where the beam strikes a given piece. For the purpose of simulating the effect of the texture on the Bessel beam, a periodic surface is used so that the effects of amplitude and spatial frequency (the spacing of the height deviations) can be seen. For a Bessel beam with a numerical aperture = 0.37 incident on the glass surface, the simulation of these effects based on ray tracing is as Figure 31 shown.

[0226] In Figure 32 and Figure 33 the simulation results for two specific surface texture amplitudes are shown. In both cases, the periodicity (spacing) and shape (substrate width) of the height distortion remain the same, but the magnitude of the deviation changes from 0.125 μm to 5 μm. While the effect of the smaller height deviation on the on-axis intensity distribution of the Gaussian-Bessel beam in the beam propagation direction can be negligible ( Figure 32 ), it is clear that the larger deviation introduces significant distortion and complex structures into the on-axis intensity distribution of the Gaussian-Bessel beam ( Figure 33 ).

[0227] Now referring to Figures 34 to 38 , a comparison is depicted of the effects of the amplitude and spacing of a surface texture on the on-axis intensity distribution in the beam propagation direction of a Gaussian-Bessel beam having a numerical aperture of 0.37. In all cases, the ratio of the base width of the simulated feature to the spacing is held constant at a value of 0.27. It can be seen most clearly by observing the Spacing = 3.14 mm graph ( Figure 35 ) that the amplitude of the height deviation is the main driver of Bessel beam distortion. However, the spacing of the height deviation is also important. For the maximum spacing (6.28 mm, Figure 34 ), the beam remains undistorted for all height amplitudes modeled. Features having a spacing of approximately 1.0 - 1.6 mm cause the greatest distortion to this Bessel beam ( Figure 36 and 37 ), where a feature spacing of 0.78 mm causes slightly less distortion ( Figure 38 ). This can be understood by considering the spatial dimensions of the Bessel beam cone interacting with the glass surface, which has a diameter of approximately 2 mm. Thus, for very large spacings, the Bessel beam samples very few surface features and most of the surface of the sample is flat. As the spacing decreases (i.e., 3.1 mm to 1.6 mm to 1.0 mm), the Bessel beam interacts with more surface features and causes more distortion. The distortion is random and will depend on the position of the Bessel beam relative to the surface feature pattern. However, when the spacing becomes smaller, the distortion effect becomes less random because all azimuthal parts of the Bessel cone impinging on the surface will sample similar surface features. Thus, for the case of Spacing = 0.78 mm, the distortion tends to exhibit a moderately uniform attenuation of the on-axis intensity distribution of the Gaussian-Bessel beam (intensity vs. z), with a reduced amplitude of fluctuations compared to those seen at larger spacings.

[0228] Now referring to Figures 39A to 39E 、 Figures 40A to 40E 、 Figures 41A to 41E 、 Figures 42A to 42E 、 Figures 43A to 43E 、 Figures 44A to 44E and Figure 4 , the effects of a range of numerical apertures are depicted. ​ Shows a modeled data set of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the optical axis including beams having a range of numerical apertures (0.15, 0.16, 0.18, 0.21, 0.26) interacting with air (i.e., no glass substrate). In all cases, the focal line length is held constant at a value of approximately 4.1 mm. ​ Respectively show the on-axis intensity distributions of the modeled data of Figures 39A to 39E , which exhibit a sharp rise on the left and a slower decay on the right.

[0229] Figures 41A to 41E shows a modeling data set including a Bessel beam having the same numerical aperture and focal line length as and interacting with a flat glass substrate (i.e., surface roughness less than Figures 39A to 39E ), the modeling data set indicating that the flat glass substrate does not cause significant beam profile distortion. ) Figures 42A to 42E Respectively show the on-axis intensity distributions of the modeling data of Figures 41A to 41E , which maintain the expected on-axis intensity distribution of the Gaussian-Bessel beam.

[0230] Figures 43A to 43E shows a modeling data set of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including a beam having the same numerical aperture and focal line length as Figures 39A to 39E , the beam interacting with a textured glass substrate (i.e., surface roughness greater than 1 μm), which indicates that the Bessel beam with the lowest numerical aperture ( Figure 43A with NA = 0.15 in Figures 44A to 44E ) has the least beam profile distortion. Figures 43A to 43E Respectively show the on-axis intensity distributions of the modeling data of Figure 44A , indicating that the beam with the lowest numerical aperture ( Figure 45 with NA = 0.15 in Figures 44A to 44E ) has the least truncation in the shape of the expected on-axis intensity distribution. Figures 39A to 39E , Figures 40A to 40E , Figures 41A to 41E , Figures 42A to 42E , Figures 43A to 43E , Figures 44A to 44E and Figure 45 show that a beam with a relatively low numerical aperture is less distorted by the textured glass substrate.

[0231] The lateral position at which the Bessel beam interacts with the periodic texture of the glass substrate affects beam cutting. Now refer to Figures 46A to 46E , Figures 47A to 47E , Figure 48 , Figures 49A to 49E , Figures 50A to 50E , Figure 51 , Figures 52A to 52E , Figures 53A to 53E , Figure 54 , Figures 55A to 55E , Figures 56A to 56E , Figure 57 , Figures 58A to 58E , Figures 59A to 59E and Figure 60, depicting the effects of various spatial periods of the textured glass surface and a range of numerical apertures. Figure 46A Figures B to E show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) Figures 39A to 39E Figures B to E show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) 6 Figures B to E show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) Figures 47A to 47E Figures B to E show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) Figures 46A to 46E Figures B to E show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) Figure 48 Figures B to E show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) Figures 47A to 47E Figures B to E show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y))

[0232] Figures 49A to 49E Figures F to I show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) Figures 39A to 39E Figures F to I show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) 6 Figures F to I show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) Figures 50A to 50E Figures F to I show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) Figures 49A to 49E Figures F to I show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) Figure 51 Figures F to I show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y)) Figures 50A to 50E Figures F to I show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 5μm*(Sin(2x)+Sin(2y))

[0233] Figures 52A to 52E Figures J to M show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 10μm*(Sin(2x)+Sin(2y)) Figures 39A to 39E Figures J to M show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 10μm*(Sin(2x)+Sin(2y)) 6 Figures J to M show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 10μm*(Sin(2x)+Sin(2y)) Figures 53A to 53E Figures J to M show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 10μm*(Sin(2x)+Sin(2y)) Figures 52A to 52E Figures J to M show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 10μm*(Sin(2x)+Sin(2y)) Figure 54 Figures J to M show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 10μm*(Sin(2x)+Sin(2y)) Figures 53A to 53E Figures J to M show modeled datasets of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including beams having the same numerical aperture and focal line length, the beams interacting with a textured glass surface having a height defined by an amplitude of 10μm*(Sin(2x)+Sin(2y))

[0234] Figures 55A to 55E shows a modeled data set of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including a beam having the same numerical aperture and focal line length as Figures 39A to 39E and interacting with a textured glass surface having a height defined by an amplitude of 10 μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y-offset) of 0.35 mm. Figures 56A to 56E Respectively show the Figures 55A to 55E on-axis intensity distribution of the modeled data. Figure 57 Graphically depicts the Figures 56A to 56E length of the Gaussian-Bessel on-axis intensity distribution shown as a function of the numerical aperture.

[0235] Figures 58A to 58E shows a modeled data set of the cross-sectional intensity of a Gaussian-Bessel beam versus the propagation distance along the optical axis, the Gaussian-Bessel beam including a beam having the same numerical aperture and focal line length as Figures 39A to 39E and interacting with a textured glass surface having a height defined by an amplitude of 10 μm*(Sin(2x)+Sin(2y)) 6 and a lateral offset (i.e., y-offset) of 1.0 mm. Figures 59A to 59E Respectively show the Figures 58A to 58E on-axis intensity distribution of the modeled data. Figure 60 Graphically depicts the Figures 59A to 59E length of the Gaussian-Bessel intensity distribution shown as a function of the numerical aperture.

[0236] As Figures 46A to 46E , FIGS. 47 to Figure 47E , Figure 48 , Figures 49A to 49E , Figures 50A to 50E , Figure 51 , Figures 52A to 52E , Figures 53A to 53E , Figure 54 , Figures 55A to 55E , Figures 56A to 56E , Figure 57 , Figures 58A to 58E , Figures 59A to 59E and Figure 60 shown, Gaussian-Bessel beams with relatively low numerical apertures are less distorted by the various spatial periods of the textured glass substrate.

[0237] Now refer to Figure 61, using the optical system described above in connection with Table 1, the work of cutting textured materials was accomplished with two Bessel beams having numerical apertures of 0.37 (f = 30 mm lens) and 0.28 (f = 40 mm lens). A high-energy psec pulsed laser was used for cutting and was capable of delivering approximately 160 W of power or approximately 1.5 mJ / pulse train of energy to the substrate at 110 kHz. In both cases, a single pass was unable to create a nanoperforation of sufficient length within the glass to fully perforate the material. Therefore, multiple passes were then attempted at different focal heights. Figure 61 The two images in

[0238] show the results for each numerical aperture, where two passes were used and the focus was adjusted to attempt to achieve maximum coverage within the substrate. For numerical aperture = 0.37 (30 mm lens), only 70%-75% of the material was nanoperforated. For numerical aperture = 0.28 (40 mm lens), the coverage was more complete, reaching approximately 1.75 mm or approximately 60% of the substrate thickness within the nanoperforation during a single pass. By two passes at different focal heights, the nanoperforations could extend through the entire depth of the substrate, but with significantly small discontinuous regions. These regions may be caused by the nanoperforation beam being distorted by local surface features that vary spatially across the substrate. Figure 62 and Figure 63 , an optical system for generating a beam with a lower numerical aperture as described in Table 1 was also evaluated, using the same laser and pulse train energy as used in Figure 61 . Single-pass nanoperforation samples using a 50 mm lens (numerical aperture = 0.22) and a 58 mm lens (numerical aperture = 0.19) are shown. In both cases, the nanoperforations failed to form near the bottom side of the sheet. The nanoperforations now extend, on average, to 2 mm, or approximately 75% of the glass thickness. It can be seen that, on average, the nanoperforations penetrate slightly deeper in the case of using a beam with a numerical aperture of 0.19.

[0239] Now referring to Figure 64 , two passes at different focal heights using a beam with a numerical aperture of 0.19 were used to cut a glass sheet. The nanoperforations extended through the entire thickness of the glass sheet, with reduced discontinuous regions compared to those seen when cutting with a beam having a numerical aperture of 0.28.

[0240] Now referring to Figure 65 and Figure 66, using the optical system described above in connection with Table 1, the work of cutting a 2.75 mm thick textured glass substrate was completed with a Bessel beam using a 58 mm lens (numerical aperture = 0.19), a focal length of 2.3 mm, and 1.5 μJ / pulse train. As shown, the use of a lower numerical aperture results in most of the cut edges including uniform nanopores that penetrate the entire thickness of the textured glass substrate.

[0241] When using a lower numerical aperture, an increase in the core diameter and the focal line length of the focal line needs to be considered, both of which can reduce the beam intensity. If the intensity is reduced too much, the focal line may no longer be able to modify the glass. However, since the length of the Bessel beam can be independently controlled by changing the size of the beam entering the axicon, a reduced input beam size can be used to shorten the focal line and thus increase the intensity. When cutting a transparent substrate with a Bessel beam in a nonlinear process, the ability of the Bessel beam to vary the focal line length independently of the core diameter is an important degree of freedom.

[0242] Another consideration when using a Bessel beam with a lower numerical aperture is that laser energy no longer flows into the focal line from rays oriented at high angles. The ability of energy to flow in from the side and cause the Bessel beam core (central lobe) to (re)form downstream of the obscuring element is an effect called "self-healing", and it can restore the intensity of the central lobe after being interrupted by the obscuring element. Therefore, if there are shadow effects from debris on the substrate surface or from the plasma created by the laser-material interaction, self-healing may not occur when a Bessel beam with a lower numerical aperture is used for cutting, and the penetration depth of the nanopores formed in the substrate is limited. In practice, it has been experimentally observed that when the numerical aperture of the Bessel beam is less than about 0.10, the ability of the Bessel beam to reliably form deep nanopores in glass and glass-ceramic materials is significantly impaired. The preferred numerical aperture range for cutting textured or curved (including 3D) surfaces with a Bessel beam can be 0.10 < NA < 0.25, or 0.12 < NA < 0.23, or 0.15 < NA < 0.20.

[0243] Regarding surface tilt, when a Bessel beam converges and impinges on a piece of glass, the rays are refracted at the air-glass interface. If the Bessel beam propagates perpendicular to the glass surface, this refraction is azimuthally uniform around the optical axis of the beam. The Bessel beam will be extended along the optical axis by this refraction, but it will still focus onto a Bessel profile inside the glass - creating a high-intensity core that ultimately produces "nanopores". However, when the Bessel beam is incident on a tilted glass piece, due to the breakdown of azimuthal symmetry, aberrations are induced during surface refraction - in other words, the rays on one side of the converging beam enter the glass surface at a different angle than the rays on the other side of the beam. As Figure 67As shown, a series of nano-perforations are made in a thick polished glass piece, where the angle of the nano-perforations gradually changes from -20° to 20° in 1° increments from left to right in the figure. At higher angles, the length of the nano-perforations decreases sharply.

[0244] Now refer to Figure 68 , which gives the quantification of the tests described for Figure 67 . Figure 68 The test results of Bessel beams with NA = 0.19 (f = 58 mm lens) and NA = 0.28 (f = 40 mm lens) using the optical system described above in combination with Table 1 are compared. For each substrate tilt angle, the depth of the nano-perforations of each beam is measured in 1° increments from -20° to 20°. The results show that when using a Bessel beam with a numerical aperture = 0.19, the length of the nano-perforations remains constant over a wider range of angles. Therefore, the numerical aperture plays a role in the tolerance of the air-glass surface aberration.

[0245] The numerical aperture of the Bessel beam plays a role not only in the tolerance of the substrate tilt but also in the tolerance of the curved glass surface. Such curvature may be encountered when glass is used to form non-planar products (such as for handheld electronic devices with curved edges, augmented or virtual reality headsets, or cover glasses for glass tubes). Figure 69 A modeling data set comparing Bessel beams with a series of NAs (0.104, 0.149, 0.452) interacting with a series of surface curvatures from 5 mm (small radius) to 200 mm (large radius) is shown. As the numerical aperture increases, the radius of curvature decreases, or the depth into the substrate increases, the Bessel beam becomes more aberrated.

[0246] Now refer to Figures 70 to 72 , where an example uses Bessel beams with two different numerical apertures to nano-perforate a Pyrex glass tube with a diameter of 10 mm (radius of curvature of 5 mm). A 1064 nm pulsed laser (about 10 psec pulse, 8 pulses / burst) is used to provide an energy incident on the substrate of about 400 μJ / burst. A spatial light modulator is used as an adjustable axicon. The beam numerical apertures generated by the spatial light modulator are 0.20 and 0.31, and the beam measurements of the focal line are as shown in Figure 70 and 71 . The cross-section of the nano-perforated glass tube is shown in Figure 72Shown in. Focus adjustments are made to find the conditions under which each beam produces the deepest nano-perforations. With three tests (not all depicted) performed with each beam NA, the beam with NA = 0.20 provides an average perforation depth of approximately 766 μm (767, 767, 764 μm), while the beam with NA = 0.31 provides an average perforation depth of approximately 504 μm (574, 460, 478 μm). Thus, in the presence of a curved surface, the lower-NA beam produces deeper nano-perforations, despite the fact that its energy density is lower due to its larger core diameter and longer line length.

[0247] The methods of cutting textured glass articles described herein enable high-edge-quality and high-precision laser cutting of glass and glass-ceramics formed by a rolling process. Despite the fact that such rolled materials have a significant surface texture that tends to distort and scatter the laser beam being cut. Specifically, the method allows the laser beam to create laser-modified sites or nano-perforations through the entire depth or thickness of the glass sheet. This means that for textured glass, all the benefits of laser cutting with low subsurface damage can be achieved. Only a small amount of grinding and polishing (e.g., less than 30 μm) may be required to achieve high strength. These nano-perforations define the plane of severance or crack propagation within the glass sheet. Without such definition across the entire thickness of the sheet, the crack may deviate and the cut edge will not precisely follow the intended path, forming a "cantilever curl" that may extend approximately 100 to 150 μm from the cut edge, requiring additional grinding of the part in the final finishing.

[0248] Unless otherwise expressly stated, no method set forth herein is to be construed as requiring its steps to be performed in a particular order, nor any apparatus to be specifically oriented. Accordingly, where a method claim does not actually recite an order to be followed by its steps, or any apparatus claim does not actually recite an order or orientation of components, or where the claims or description do not otherwise specifically state that the steps are limited to a particular order, or do not recite a specific order or orientation of the components of the apparatus, no inference of order or orientation is to be made in any respect. This applies to any possible non-explicit basis for interpretation, including: logical matters regarding step arrangement, operational flow, order of components, or orientation of components; ordinary meaning derived from grammatical organization or punctuation; and the number or type of embodiments described in the specification.

[0249] It will be apparent to those skilled in the art that various modifications and variations can be made to the embodiments described herein without departing from the spirit and scope of the claimed subject matter. Accordingly, it is intended that the specification cover various modifications and variations of the embodiments described herein, provided that such modifications and variations fall within the scope of the appended claims and their equivalents.

Claims

1. A method for processing a transparent workpiece, the method comprising: Directing a defect-forming laser beam onto an impact surface of the transparent workpiece, the defect-forming laser beam having a numerical aperture of 0.10 to 0.25, the transparent workpiece having a textured surface, the textured surface having an Ra value greater than or equal to 0.5 μm.

2. The method according to claim 1, wherein, The defect-forming laser beam forms a laser beam focal line within the transparent workpiece, and the laser beam focal line forms a defect in the transparent workpiece.

3. The method according to claim 1 or 2, wherein, The defect-forming laser beam is quasi-non-diffracting.

4. The method according to any one of claims 1-3, wherein, The defect-forming laser beam is a Gaussian-Bessel beam.

5. The method according to any one of claims 1-4, wherein, The defect formed by the defect-forming laser beam extends through the entire thickness of the transparent workpiece.

6. The method according to claim 5, wherein, The thickness of the transparent workpiece is greater than or equal to 1.0 mm.

7. The method according to claim 5, wherein, The thickness of the transparent workpiece is greater than or equal to 3.0 mm.

8. The method according to any one of claims 1-7, wherein the textured surface has an Ra value greater than or equal to 2.0 μm.

9. The method according to any one of claims 1-8, wherein, The impact surface of the transparent workpiece is curved.

10. A method for separating a transparent workpiece, the method comprising: Directing a defect-forming laser beam onto a curved impact surface of the transparent workpiece, the defect-forming laser beam having a numerical aperture of 0.10 to 0.

25.

11. The method according to claim 10, wherein, The defect-forming laser beam forms a laser beam focal line within the transparent workpiece, and the laser beam focal line forms a defect in the transparent workpiece.

12. The method according to claim 11, wherein, The length of the laser beam focal line is greater than or equal to the thickness of the transparent workpiece.

13. The method according to any one of claims 10-12, wherein, The defect-forming laser beam is quasi-non-diffracting.

14. The method according to any one of claims 10-13, wherein, The defect-forming laser beam is a Gaussian-Bessel beam.

15. The method according to any one of claims 10-14, wherein the defect formed by the defect-forming laser beam extends through the entire thickness of the transparent workpiece, and the thickness of the transparent workpiece is greater than or equal to 1.0 mm.

16. The method according to any one of claims 10-15, wherein the curved impact surface is a textured surface, the textured surface having an Ra value greater than or equal to 0.5 m.

17. The method according to any one of claims 10-16, wherein, The defect formed by the defect-forming laser beam extends through the entire thickness of the transparent workpiece.

18. A glass article in its as-cut original state, the glass article comprising: A textured surface having an Ra value greater than or equal to 0.5 μm; A second surface, the second surface being spaced from the textured surface by a thickness that is greater than or equal to 500 μm; and An edge, the edge extending from the textured surface and the second surface, the edge including a cantilever curl that extends from the edge a distance of less than 150 μm.

19. The glass article according to claim 18, wherein the thickness is greater than or equal to 1.0 mm.

20. The glass article according to claim 18 or 19, wherein the edge has a subsurface damage that is less than or equal to 30 μm.

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