Glass cutting systems and methods using non-diffracting laser beams

Abstract

Embodiments are directed to systems for laser cutting at least one glass article comprising a pulsed laser assembly and a glass support assembly configured to support the glass article during laser cutting within the pulsed laser assembly, wherein the pulsed laser assembly comprises at least one non-diffracting beam (NDB) forming optical element configured to convert an input beam into a quasi-NDB beam; and at least one beam transforming element configured to convert the quasi-NDB beam into multiple quasi-NDB sub-beams spaced apart a distance of about 1 m to about 500 m; wherein the pulsed laser assembly is oriented to deliver one or more pulses of multiple quasi-NDB sub-beams onto a surface of the glass article, wherein each pulse of multiple quasi-NDB sub-beams is operable to cut a plurality of perforations in the glass article.

Claims

1. A system for laser cutting at least one glass article comprising a pulsed laser assembly and a glass support assembly configured to support the glass article during laser cutting within the pulsed laser assembly, wherein the pulsed laser assembly comprises at least one non-diffracting beam forming optical element configured to convert an input beam into a quasi-non-diffracting beam; and at least one beam transforming element configured to convert the quasi-non-diffracting beam into multiple quasi-non-diffracting sub-beams spaced apart a distance of about 1 m to about 500 m; wherein the pulsed laser assembly is oriented to deliver one or more pulses of the multiple quasi-non-diffracting sub-beams onto a surface of the glass article, wherein each of the one or more pulses of multiple quasi-non-diffracting sub-beams is operable to cut a plurality of perforations in the glass article.

2. The system of claim 1 further comprising at least one collimating lens configured to narrow the quasi-non-diffracting beam from the at least one non-diffracting beam forming optical element.

3. The system of claim 2 wherein the beam transforming element is oriented downstream of the collimating lens.

4. The system of claim 3 wherein the beam transforming element is oriented proximate a Fourier-transform plane produced by the collimating lens.

5. The system of claim 1 further comprising at least one additional collimating lens downstream of the beam transforming element and configured to focus the multiple quasi-non-diffracting sub-beams.

6. The system of claim 5 wherein the beam transforming element is oriented within a focal length of the additional collimating lens.

7. The system of claim 1 wherein the input beam is a Gaussian beam.

8. The system of claim 1 wherein the multiple quasi-non-diffracting sub-beams are parallel to one another and spaced apart a distance of about 1 m to about 20 m.

9. The system of claim 1 wherein the beam transforming element is chosen from a phase grating, an amplitude grating, or combinations thereof, and the non-diffracting beam forming optical element is chosen from an axicon, a spatial light modulator, an elliptical lens, or combinations thereof.

10. The system of claim 1 wherein the beam transforming element is configured to shift a phase of at least one of the multiple quasi-non-diffracting sub-beams from about /4 to about 2.

11. The system of claim 1 wherein the quasi-non-diffracting beam is a Bessel beam, an Airy beam, a Weber beam, or a Mathieu beam.

12. A system for laser cutting at least one glass article comprising a pulsed laser assembly and a glass support assembly configured to support the glass article during laser cutting within the pulsed laser assembly, wherein the pulsed laser assembly comprises at least one axicon configured to convert a Gaussian beam into a Bessel beam; first and second collimating lenses disposed downstream of the axicon; and at least one beam transforming element oriented between the first and second collimating lenses, wherein the at least one beam transforming element is configured to convert the Bessel beam into multiple sub-Bessel beams which are parallel and spaced apart a distance of about 1 m to about 500 m; wherein the pulsed laser assembly is oriented to deliver one or more pulses of multiple sub-Bessel beams onto a surface of the glass article, wherein each of the one or more pulses of multiple sub-Bessel beams is operable to cut a plurality of perforations in the glass article.

13. The system of claim 12 wherein the beam transforming element is a phase grating, an amplitude grating, or combinations thereof.

14. The system of claim 12 wherein the multiple sub-Bessel beams are spaced apart a distance about 1 m to about 20 m.

15. The system of claim 12 wherein the beam transforming element is oriented proximate a Fourier-transform plane produced by the first collimating lens.

16. The system of claim 12 wherein the beam transforming element is oriented within a focal length of the second collimating lens.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The following detailed description of specific embodiments of the present disclosure can be best understood when read in conjunction with the drawings enclosed herewith.

(2) FIG. 1 is a schematic view of a Gaussian beam passing through the axicon to produce a quasi-NDB Bessel beam.

(3) FIG. 2A is a schematic view of a glass cutting system in accordance with one or more embodiments of the present disclosure.

(4) FIG. 2B is a close-up view of FIG. 2A depicting the laser cutting of the glass article in accordance with one or more embodiments of the present disclosure.

(5) FIG. 3A is a graphical illustration of a computer simulation, the graphical illustration depicting a single-axis scan across the center of two Bessel sub-beams separated by 5.84 m.

(6) FIG. 3B is a graphical illustration of a computer simulation, the graphical illustration depicting a two-dimensional cross-section of the two Bessel sub-beams of FIG. 3A.

(7) FIG. 4A is a graphical illustration of a computer simulation, the graphical illustration depicting a single-axis scan across the center of two Bessel sub-beams separated by 3.23 m, wherein a phase shift is added to one beam.

(8) FIG. 4B is a graphical illustration of a computer simulation, the graphical illustration depicting a two-dimensional cross-section of the two Bessel sub-beams of FIG. 4A.

(9) FIG. 5A is a graphical illustration of a computer simulation, the graphical illustration depicting a single-axis scan across the center of three Bessel sub-beams separated by 5.85 m.

(10) FIG. 5B is a graphical illustration of a computer simulation, the graphical illustration depicting a two-dimensional cross-section of the three Bessel sub-beams of FIG. 5A.

(11) FIG. 6A is a graphical illustration of a computer simulation, the graphical illustration depicting a single-axis scan across the center of three Bessel sub-beams separated by 3.23 m, wherein a phase shift is added to one beam.

(12) FIG. 6B is a graphical illustration of a computer simulation, the graphical illustration depicting a two-dimensional cross-section of the three Bessel sub-beams of FIG. 6A.

(13) FIG. 7 is a schematic depiction of an optical assembly used in the pulsed laser assembly wherein the beam transforming element is oriented proximate the Fourier-transform plane of an upstream collimating lens according to one or more embodiments of the present disclosure.

(14) FIG. 8 is a schematic depiction of an optical assembly used in the pulsed laser assembly wherein the beam transforming element is oriented within a focal length of a downstream collimating lens according to one or more embodiments of the present disclosure.

(15) FIG. 9 is a schematic depiction of an alternative optical assembly with smaller optical elements according to one or more embodiments of the present disclosure.

(16) FIG. 10 is a schematic depiction of yet another optical assembly with a reflective optical element according to one or more embodiments of the present disclosure.

(17) FIG. 11 is a schematic depiction comparing damage spots produced by one, two, and three beam systems.

(18) The embodiments set forth in the drawings are illustrative in nature and not intended to be limiting of the invention defined by the claims. Moreover, individual features of the drawings will be more fully apparent and understood in view of the detailed description.

DETAILED DESCRIPTION

(19) Referring to the embodiments of the FIGS. 2A and 2B, a system 1 for laser cutting at least one glass article is shown. The system 1 comprises a pulsed laser assembly 10 and a glass support assembly 50 which supports the glass article 5 during laser cutting by the pulsed laser assembly 10. As shown in FIGS. 2A and 2B, the pulsed laser assembly 10 delivers one or more pulses of multiple quasi-NDB sub-beams 18A, 18B onto a surface of the glass article 5. Referring to FIG. 2B, the pulse (or complex beam) 18 of multiple quasi-NDB sub-beams 18A, 18B may cut a plurality of perforations 6A, 6B or in the glass article 5. As shown in the embodiment of FIG. 2A, the glass support assembly 50 is merely depicted as a conveyor; however, various other components such as a spindle chuck, robotic arm, etc are contemplated as suitable herein. These contemplated embodiments may cause the pulsed laser assembly 10 and the glass support assembly 50 to be moveable relative to one another during the laser cutting process.

(20) Referring to FIG. 7, the pulsed laser assembly 10 comprises at least one NDB forming optical element 20 that converts an input beam 7 (e.g., a Gaussian beam) into a quasi-NDB beam 12 (See also FIG. 1), and at least one beam transforming element 40 which converts the quasi-NDB beam 12 into multiple quasi-NDB sub-beams 18A, 18B, 18C spaced apart a distance of about 1 m to about 500 m.

(21) As used herein, quasi-NDB beam means a created non-diffracting beam, typically a nondiffracting beam created from the conversion of an input beam (e.g., a Gaussian beam) to a non-diffracting beam. The quasi-NDB beam could encompass many beam types. As used herein, input beam may include any beam having a substantially uniform optical phase. In one embodiment, the input beam is a Gaussian beam. For example, the quasi-NDB may include a Bessel beam, an Airy beam, a Weber beam, or a Mathieu beam. In the embodiments described below, the quasi-NDB beam is a Bessel beam. The conversion of a Gaussian beam 7 by an axicon NDB forming optical element 20 to a Bessel quasi-NDB beam 12 is shown in FIG. 1. FIG. 1 depicts a single pulse Gaussian beam; however, the Gaussian beam source may also deliver the Gaussian beam in multiple pulses. In addition to axicons, various other NDB forming optical elements are contemplated, for example, a spatial light modulator, an elliptical lens, or combinations thereof. Bessel beams may be readily produced by axicons; however, other quasi-NDB beams are produced with other NDB forming elements 20.

(22) Further as used herein, multiple quasi-NDB sub-beams does not mean separate NDB laser beams. Multiple quasi-NDB sub-beams means a complex beam having a plurality of spots. Referring to FIG. 3A, the two peaks 18A and 18B are two quasi-NDB sub-beams in the complex Bessel beam depicted therein. As shown in FIG. 1, Bessel beams tend to have a central peak at zero, which would constitute its beam spot. However, in accordance with the present embodiments, the Bessel beam is converted in the beam transforming element 40, such that the Bessel beam with a single spot is transformed into a modified Bessel beam having two spots corresponding to peaks 18A and 18B. These two spots or two quasi-NDB sub-beams are depicted in cross-section in FIG. 3B. FIGS. 4A and 4B depict another embodiment having 2 quasi-NDB sub-beams, and FIGS. 5A-6B depict embodiments with 3 quasi-NDB sub-beams 18A, 18B, and 18C. While not shown, multiple quasi-NDB sub-beams encompasses complex beams having more than 2 or 3 quasi-NDB sub-beams.

(23) Referring to FIGS. 7 and 8, the beam transforming element 40 converts a quasi-NDB beam 12 into multiple quasi-NDB sub-beams 18A, 18B, and 18C. The beam transformation essentially re-shapes the high intensity single quasi-NDB beam into multiple lower intensity sub-beams, which in most embodiments are spaced apart from one another. As shown in FIGS. 3A-6B, the multiple quasi-NDB sub-beams are depicted as being in parallel; however, it is contemplated that the multiple quasi-NDB sub-beams 18 could be angled such that they overlap with one another. In addition to generating the multiple quasi-NDB sub-beams, the beam transforming element 40 may optimize the spacing between the beams, and optionally may shift the phase of one or more of the multiple quasi-NDB sub-beams. By phase shifting the phase of at least one of the multiple quasi-NDB sub-beams, the intensity of the multiple quasi-NDB sub-beams may be added coherently. Depending on the glass cutting application, various spacings between sub-beams may be sought. For example, the spacing may be from about 1 m to about 500 m, or about 1 m to about 200 m, or about 1 m to about 100 m, or about 1 m to about 50 m, or about 1 m to about 20 m, or about 1 m to about 10 m, or about 1 m to about 5 m. Similarly, the degree of phase shift may vary with phase shifts ranging from about /4 to about 2, or about /2 to about being contemplated.

(24) The beam transforming element 40 may comprise various components. For example and not by way of limitation, the beam transforming elements may comprise is a phase grating or phase plate, an amplitude grating, or combinations thereof. In specific embodiment, it may be beneficial to include a beam transforming element 40 which is a combination of a phase element and an amplitude grating element. These gratings may be square wave or sinusoidal; however, other complex shapes are contemplated herein. A further discussion of beam transforming elements 40 is provided below.

(25) An amplitude-only grating may be defined by the following equation:

(26) $\begin{array}{cc}{P}_{\mathrm{tot}}\left(u,v\right)=0.5+0.5*\cos \left(\frac{2u}{T}\right)& \left(3\right)\end{array}$

(27) Physically, this would be a much easier grating to make, because no phase shift is required; however, such a grating may produces many order sub-beams, for example, a zeroth-order sub-beam and two first-order sub-beams. Thus, in some embodiments, a phase shift may be utilized to substantially limit the sub-beams to a single order.

(28) Phase-only gratings may be formed from a thickness or index grating in glass or using a programmable spatial light modulator. A square phase-only grating can more efficiently couple light into the sub-beams. For two sub-beams, the most efficient phase-only grating may be defined by:

(29) $\begin{array}{cc}{P}_{\mathrm{tot}}\left(u,v\right)=e^{i{}_o\mathrm{rect}\left(\begin{array}{c}2u\\ T\end{array}\right)}& \left(4\right)\end{array}$
Where

(30) ${}_o=\frac{}{2}\mathrm{and}\mathrm{rect}\left(\frac{2u}{T}\right)$
is a square-wave function of u oscillating between 1 and +1 with a period of T. With the square grating, additional diffraction orders may be present, but with the correct choice of phase amplitude they can be minimized. With the sinusoidal amplitude grating, there are only the two first-order sub-beams.

(31) To generate a third sub-beam, it is possible to use

(32) ${}_o=a\tan \left(\frac{}{2}\right)~1\mathrm{rad}$
to give:

(33) $\begin{array}{cc}{P}_{\mathrm{tot}}\left(u,v\right)=e^{\mathrm{irect}\left(\frac{2u}{T}\right)}& \left(5\right)\end{array}$
which results in three sub-beams.

(34) In one or more embodiments, static phase elements can be made to various scales. However, it may be desirable to use programmable phase elements such as acousto-optic modulators (AOM), electro-optic modulators (EOM), spatial light modulators (SLM) and digital micro-mirror arrays (DMA).

(35) Without being bound by theory, sub-beam spacings that preserve the characteristics of the input beam 7 are beneficial. As an example, a discussion regarding combining two zeroth-order Bessel sub-beams is provided below. This approach can be used for finding the optimal spacings for other quasi-NBD sub-beams

(36) As shown in FIG. 1, the Bessel function J.sub.0(x) is an oscillatory function (positive and negative) about zero. If two Bessel functions are added coherently with a lateral offset, they will interfere destructively when a positive peak in one function overlaps with a negative peak in the second function. Similarly, the beams will add constructively when two positive peaks add. The locations of the positive maxima and negative minima of the function J.sub.0(x) are given by the zeros of the higher-order Bessel function J.sub.1(x) (through a well-known relationship that dJ.sub.0(x)/dx=J.sub.1(x)). These zeros .sub.j are well known and the first few are given in Table 1 below. For roots beyond those shown in Table 1, the roots become equally spaced by , so simply add multiples of =3.14159 to the 7.sup.th root.

(37) The equation for optimal x.sub.opt that optimizes the peak intensity of the sub-beams may be defined as:

(38) $\begin{array}{cc}{x}_{\mathrm{opt},j}=\frac{{}_j}{k_r}\mathrm{where}\text{:}& \left(6\right)\\ k_r=k.Math.\mathrm{NA}=\frac{2n_o}{{}_o}.Math.\mathrm{NA}=\frac{2n_o}{{}_o}.Math.\sin \left(\right).& \left(7\right)\end{array}$

(39) For .sub.0=1.06 m in air with numerical aperture (NA)=0.2 (or =11.5), we find k.sub.r=1.1855 m.sup.1 and the resulting optimal spacing is given in the 4.sup.th column of Table 1 while column 5 gives the spacing for NA=0.1 (narrow cone angle of =5.7). When the sub-beams are added with no phase shift between them, we use the odd roots j=3, 5, etc.

(40) An alternative approach for generating two sub-beams would be to add the two coherent sub-beams with a phase shift between them. If we add a shift to the relative optical phase, this is equivalent to multiplying one of the sub-beams by a minus sign. Thus the positive peaks of one sub-beam will add coherently to the negative peaks of the second sub-beam. This allows for efficient sub-beam separations at the spacings labeled N in the third column of Table 1, corresponding to the even roots j=2, 4, etc.

(41) TABLE-US-00001 TABLE 1 Example x.sub.opt Example x.sub.opt (m) (m) j.sup.th J1 zero, NA = 0.2 NA = 0.1 Root .sub.j Peak sign k.sub.r = 1.1855 m.sup.1 k.sub.r = 0.5928 m.sup.1 1 0 P 0.00 0.00 2 3.8317 N 3.23 6.46 3 7.0156 P 5.92 11.84 4 10.1735 N 8.58 17.16 5 13.3237 P 11.24 22.48 6 16.4706 N 13.89 27.79 7 19.6159 P 16.55 33.09

(42) For illustration, FIG. 3A depicts two spaced quasi-NDB sub-beams, and FIG. 4A shows the two spaced quasi-NDB sub-beams but with a 7C phase shifted added to one of the beams. Both FIGS. 3A and 4A show optimal separations for which the sub-beam intensity is locally maximized. The out-of-phase beams in FIG. 4A can be placed very close together (3 microns). This is important in the cutting of transparent substrates for creating nearly continuous damage zones. Similarly, FIG. 5A depicts three spaced quasi-NDB sub-beams 18A, 18B, and 18C, and FIG. 6A shows three spaced quasi-NDB sub-beams but with a phase shift added to the central beam 18B.

(43) For non-optimal spacing, the peak intensity is not maximized, but such spacings may still produce acceptable cutting behavior as long as sufficient laser power is available to achieve nonlinear material damage.

(44) Referring to the embodiments of FIG. 7-10, specific optical assembly 11 arrangements for the pulsed laser assembly 10 are depicted therein. As shown in FIGS. 7 and 8, the optical assembly 11 may comprise at least one collimating lens 31 configured to narrow the quasi-NDB beam 12 from the at least one NDB forming optical element 20.

(45) Further as shown in FIG. 7, the beam transforming element 40 may be oriented downstream of the collimating lens 31. In a further embodiment, the beam transforming element 40 may be oriented proximate a Fourier-transform plane 41 produced by the collimating lens 31. It is also contemplated to place the beam transforming element 40 at a location not proximate or within the Fourier-transform plane 41. Moreover as shown in FIG. 7, the optical assembly 11 may further comprise at least one additional collimating lens 32 downstream of the beam transforming element 40 which focus the multiple quasi-NDB sub-beams 18A, 18B, and 18C.

(46) Referring again to the embodiment of FIG. 7, when the beam transforming element 40 is oriented behind the Fourier-transform plane 41 of collimating lens 31, the field A(u,v) at Fourier-transform plane 41 is multiplied by a transfer function P(u,v) to produce a new field A(u,v) with two new angular components which are then imaged by collimating lens 32 to an image plane 17 to produce three quasi NDB sub-beams 18A, 18B, and 18C. The rays after beam transforming element 40 are depicted with dashed lines to indicate that the optical field in this region is a function beam transforming element 40

(47) As shown in the embodiment of FIG. 7, the focus 8 of the input beam 7 is placed in front of the first collimating lens 31 at a distance f.sub.1, where f.sub.1 is the focal length of the first collimating lens 31. A second lens 32 with a second focal length f.sub.2 is placed a distance of f.sub.1+f.sub.2 behind the first lens 31. The Fourier-transform plane 41 at a distance of f.sub.1 behind the first lens 31 is the Fourier-transform plane of the first lens 31 and the optical field at this plane is known to be the optical Fourier transform A(u,v) of the input field a(x,y) at a distance f.sub.1 in front of collimated lens 31:

(48) $\begin{array}{cc}A\left(u,v\right)={}_{-}^{}\frac{a\left(x,y\right)}{i{f}_1}{e}^{\frac{-2\mathrm{ni}}{f_1}\left(\mathrm{xu}+\mathrm{yv}\right)}\mathrm{dxdy}& \left(8\right)\end{array}$

(49) The purpose of the second lens 32 is to take the inverse Fourier transform of the optical field A(u,v) in Fourier-transform plane 41 and form an image b(x,y) of the input beam in image plane 17. It can be shown that:

(50) 0$\begin{array}{cc}b\left(x^{},y^{}\right)={}_{-}^{}\frac{A\left(u,v\right)}{i{f}_2}{e}^{\frac{-2\mathrm{ni}}{f_2}\left({\mathrm{ux}}^{}+{\mathrm{vy}}^{}\right)}\mathrm{dudv}& \left(9a\right)\\ =\frac{f_1}{f_2}a\left(-\frac{f_1}{f_2}{x}^{},-\frac{f_1}{f_2}{y}^{}\right)& \left(9b\right)\\ =Ma\left(-M{x}^{},-M{y}^{}\right)& \left(9c\right)\end{array}$
If f.sub.1f.sub.2, the image will have a magnification M1 and the quasi NDB sub-beams may not be parallel. If f.sub.1=f.sub.2, the image will have a magnification M=1 and the quasi NDB sub-beams will be parallel.

(51) Introducing the beam transforming element 40 in the Fourier-transform plane 41 has the effect of multiplying the Fourier-transform of the input field by the transfer function of this element:

(52) $\begin{array}{cc}{b}^{}\left(x^{},y^{}\right)={}_{-}^{}\frac{A^{}\left(u,v\right)}{i{f}_2}{e}^{\frac{-2\mathrm{ni}}{f_2}\left({\mathrm{ux}}^{}+{\mathrm{vy}}^{}\right)}\mathrm{dudv}& \left(10a\right)\\ ={}_{-}^{}\frac{A\left(u,v\right)P\left(u,v\right)}{i{f}_2}{e}^{\frac{-2\mathrm{ni}}{f_2}\left({\mathrm{ux}}^{}+{\mathrm{vy}}^{}\right)}\mathrm{dudv}& \left(10b\right)\end{array}$

(53) It is known that certain optical elements can shift an input beam in an arbitrary direction, can impart a tilt to the focal region, and can scale the amplitude of the output beam. Other elements and apertures can be used to filter unwanted spatial frequencies from the beam in order to mitigate or create impairments to the optical beam. In this disclosure, we will focus on the lateral shifting of quasi-NDB sub-beams to generate multiple quasi NDB sub-beams.

(54) The phase transformation to accomplish a lateral shift (x,y) is:

(55) $\begin{array}{cc}P\left(u,v\right)=e^{\frac{2\mathrm{ni}}{f_2}\left(u{x}^{}+v{y}^{}\right)}& \left(11\right)\end{array}$

(56) From above it can be seen that:

(57) $\begin{array}{cc}{b}^{}\left(x^{},y^{}\right)={}_{-}^{}\frac{A\left(u,v\right)P\left(u,v\right)}{i{f}_2}{e}^{\frac{-2\mathrm{ni}}{f_2}\left({\mathrm{ux}}^{}+{\mathrm{vy}}^{}\right)}\mathrm{dudv}& \left(12a\right)\\ ={}_{-}^{}\frac{A\left(u,v\right)}{i{f}_2}{e}^{\frac{2\mathrm{ni}}{f_2}\left(ux+vy\right)}{e}^{\frac{-2\mathrm{ni}}{f_2}\left(u{x}^{}+v{y}^{}\right)}\mathrm{dudv}& \left(12b\right)\\ =Ma\left\{-M\left(x^{}-x\right),-M\left(y^{}-y\right)\right\}& \left(12c\right)\end{array}$

(58) Thus, the output field b(x,y) in image plane 17 is a scaled and shifted version of the input field a(x,y).

(59) It is also known that multiple quasi-NDB sub beams can be produced by summing different phase shifts:

(60) $\begin{array}{cc}{P}_{\mathrm{tot}}\left(u,v\right)=\frac{1}{\underset{j=1}{\overset{N}{.Math.}}.Math.c_j.Math.}\underset{j=1}{\overset{N}{.Math.}}{c}_j{e}^{\frac{2ni}{f_2}\left(u{x}_j+v{y}_j\right)}& \left(13\right)\end{array}$

(61) For the special case of two equal beams, N=2 spaced by x.sub.o:

(62) $\begin{array}{cc}{P}_{\mathrm{tot}}\left(u,v\right)=\frac{1}{2}\left[e^{\frac{2\mathrm{ni}}{f_2}\left(u\frac{x_0}{2}\right)}+e^{\frac{-2\mathrm{ni}}{f_2}\left(u\frac{x_0}{2}\right)}\right]& \left(14a\right)\\ =\cos \left(\frac{2n}{f_2}\left(u\frac{x_0}{2}\right)\right)& \left(14b\right)\\ =\cos \left(\frac{2u}{T}\right)& \left(14c\right)\end{array}$
where

(63) $T=\frac{2f_2}{n{x}_0}.$
In this instance, P.sub.tot(u,v) is simply a cosinusoidal amplitude diffraction grating of period T. When a phase shift is introduced between the two beams we find:

(64) $\begin{array}{cc}{P}_{\mathrm{tot}}\left(u,v\right)=\frac{1}{2}\left[e^i{e}^{\frac{2ni}{f_2}\left(u\frac{x_0}{2}\right)}+e^{\frac{-2ni}{f_2}\left(u\frac{x_0}{2}\right)}\right]& \left(15a\right)\\ =\cos \left(\frac{2u}{T}+\frac{}{2}\right)& \left(15b\right)\end{array}$

(65) So that a phase shift of = between the sub-beams adds a phase of /2 to the cosine which makes it a sine function. Practically, this corresponds to a lateral shift of the grating by a quarter of a period or T/4.

(66) In addition to the arrangement of FIG. 7, the NBD forming optical element 20 (e.g., axicon) may be at a distance greater or less than the focal length f1 of lens 31. This may lead to an uncollimated region between the collimating lenses 31 and 32, and thus may impact the choice of the beam transforming element 40. Additionally, various distances are contemplated between collimating lenses 31 and 32. For example, the distance between collimating lenses 31 and 32 differ may be greater or less than f1+f2.

(67) Alternatively, the embodiments above describe the positioning of the beam transforming element 40 after lens 31; however, various other positions are also contemplated. For example, and not by way of limitation, the beam transforming element 40 may be positioned before collimating lens 31 or after collimating lens 32.

(68) Various additional optical assemblies are also contemplated herein. In the embodiment of FIG. 8, the optical assembly may also include the beam transforming element 40 within the focal length (f.sub.2) of collimating lens 32, which is downstream of the beam transforming element 40. As shown, this may be achieved by placing the beam transforming element 40 in close proximity to collimating lens 31, which is upstream of the beam transforming element 40.

(69) In an additional embodiment depicted in FIG. 9, the optical assembly 11 may comprise comprising multiple collimated regions 30 and 35. In the embodiment of FIG. 9, the multiple collimated regions 30 and 35 include a large collimated region 30 and a small collimated region 35 downstream of the large collimated region 30. The large collimated region 30 may include one or multiple collimating lenses 31 and 32 that narrow the NDB beam from the at least one NDB forming optical element 20. Moreover, the optical assembly 11 may include a small collimated region 35 downstream of the large collimated region 30 which narrows the quasi-NDB beam from the prior to splitting in the beam transforming element 40. The small collimated region 35 includes one or a plurality of collimating lenses 36 and 37. While the beam transforming element 40 is disposed in the small collimated region 35 in the embodiment of FIG. 9, it is contemplated that the beam transforming element 40 may be disposed in the large collimated region 30.

(70) Without being bound by theory, having two collimating regions 30 and 35 as shown in FIG. 9 is useful to accommodate a Bessel beam Rayleigh range optimized for large diameter beams with large numerical apertures. For example, the diameter of the beam between collimating lens 31 and collimating lens 32 is large e.g., 10-30 mm. Thus, to provide small focal spots, it may be necessary to include the small collimated region 35 that is small in diameter.

(71) Referring to FIG. 10, an alternative optical assembly may include a reflective beam transforming element 40. In this instance, after the input beam 7 is converted by an axicon 20 into a quasi-NDB beam 12, it is linearly polarized and passes through a polarizing beam splitter 48 in the collimating region between collimating lenses 31 and 32. The quasi-NDB beam 12 then passes through a quarter wave plate 46 to become circularly polarized before being recollimated with demagnification by collimating lenses 32 and 33. The quasi-NDB beam 12 is converted into multiple quasi-NDB-beams, which are then retroreflected off the reflective beam transforming element 40 and back through collimating lenses 33 and 32. The multiple quasi-NDB-beams are further rotated in polarization by the quarter wave plate 46 and thereby achieve the opposite linear polarization to input beam 7. This new polarization is reflected by beam splitter 48 and the beam is focused to its final size by collimating lens 38.

(72) As stated above, it is also anticipated that the optical assemblies may have apertures to block unwanted light from reaching the image plane 17. This may be the case with phase only gratings that have higher-order diffraction patterns. The magnification of the final image is dependent on the choice of focal lengths. Without being bound by theory, the target beam spacing is specified in the image plane and can thus be tuned by both the grating and the optical magnification.

(73) Turning now to glass cutting applications, the present embodiments may yield improved formation of single lines of damage (i.e., perforations) and improved formation of multiple lines to form arrays of damage sites.

(74) In the case of the single damage line, the multiple sub-beams are aligned with the scan direction of the laser. For example, if a 100 kHz laser system is used to create damage sites spaced at 3 microns, a single beam optical system could be scanned 3 microns every 10 microseconds for a cutting speed of 0.5 m/s. However, with 3 sub-beams, the same system could run at 1.5 m/s by moving the compound beam spot by 9 microns in the same 10-microsecond time interval.

(75) In the case of the multiple damage lines for array applications as depicted in FIG. 11, the multiple sub-beams are aligned orthogonally to the scan direction of the laser. For example as depicted in FIG. 11, if a 100 kHz laser system is used to create a 10,00010,000 damage sites spaced at 10 microns, a single beam optical system would require 1000 seconds to create the array. A three sub-beam system could finish the same task in 334 seconds.

(76) As would be familiar to one of skill in the art, various other components are contemplated for the laser cutting assembly. For example, the laser cutting assembly may include some mechanism for separating the glass article along the perforations to yield a laser cut glass article. This may include thermal shock devices, cracking beams, etc.

(77) It is further noted that terms like preferably, generally, commonly, and typically are not utilized herein to limit the scope of the claimed invention or to imply that certain features are critical, essential, or even important to the structure or function of the claimed invention. Rather, these terms are merely intended to highlight alternative or additional features that may or may not be utilized in a particular embodiment of the present disclosure.

(78) It will be apparent that modifications and variations are possible without departing from the scope of the disclosure defined in the appended claims. More specifically, although some aspects of the present disclosure are identified herein as preferred or particularly advantageous, it is contemplated that the present disclosure is not necessarily limited to these aspects.