Methods for laser cutting glass substrates through narrow apertures

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 light rays exiting the optical arrangement at a first radius R1, as measured in a first direction 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 light rays exiting the optical arrangement at a second radius R2, as measured in a second direction opposite to the first direction 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.