| CPC B23K 26/53 (2015.10) [B23K 26/009 (2013.01); B23K 26/0622 (2015.10); B23K 26/0643 (2013.01); B23K 26/0648 (2013.01); B23K 26/38 (2013.01); B23K 2103/54 (2018.08)] | 13 Claims |

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1. A method for processing a transparent workpiece, the method comprising:
directing a laser beam oriented along a beam path and propagating in a beam propagation direction into the transparent workpiece such that a portion of the laser beam directed into the transparent workpiece comprises a laser beam focal arc and generates an induced absorption within the transparent workpiece, the induced absorption producing a defect within the transparent workpiece, wherein the laser beam focal arc comprises:
curvature;
a wavelength λ;
a spot size w0; and
a Rayleigh range ZR that is greater than
![]() where FD is a dimensionless divergence factor comprising a value of 10 or greater, wherein the curvature is produced by impinging the laser beam on a phase-altering optical element, wherein the phase-altering optical element comprises a phase function
![]() wherein xp(z) and yp(z) are line shift functions quantifying a line shift direction that determines the curvature of the laser beam focal arc.
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