The present invention relates to a method of laser processing a glass substrate, the method comprising: focusing a pulsed laser beam into a laser beam focal line, which is formed via an optical arrangement and oriented along the beam propagation direction and directed into the glass substrate, the glass substrate having a feature formed on a first surface of the glass substrate, the laser beam focal line generating an induced absorption within the glass substrate, and the induced absorption producing a defect line along the laser beam focal line within the substrate, wherein a first portion of the laser beam focal line is focused at the first surface of the glass substrate and a second portion of the laser beam focal line is focused at a second surface of the glass substrate that is opposite the first surface, wherein a first set of rays exiting the optical arrangement at a first radius R1, as measured from a center of the optical arrangement forms the first portion of the laser beam focal line with a deflection angle of θ1, wherein a second set of rays exiting the optical arrangement at a second radius R2, as measured from the center of the optical arrangement forms the second portion of the laser beam focal line with a deflection angle of θ2, wherein R1 is less than R2; and wherein θ1 is greater than θ2, and wherein θ1 decreases to θ2 from R1 to R2 in one of a step-wise decrease or a graded decrease; and translating the glass substrate and the laser beam relative to each other along a first contour, thereby laser forming a plurality of defect lines along the first contour within the substrate.