Phase-modified quasi-non-diffracting laser beams for high angle laser processing of transparent workpieces

A method for processing a transparent workpiece that includes directing a laser beam the transparent workpiece. The laser beam incident to the impingement surface has an oblong angular spectrum and portion of the laser beam directed into the transparent workpiece is a laser beam focal line and generates an induced absorption to produce a defect within the transparent workpiece. The laser beam focal line includes a wavelength λ, a spot size wo, a Rayleigh range ZR that is greater thanFD⁢π⁢⁢wo2λ,where FD is a dimensionless divergence factor comprising a value of 10 or greater, and an internal beam angle of greater than 10° relative to a plane orthogonal to an impingement surface at an impingement location, such that the defect has a defect angle within the transparent workpiece of greater than 10° relative to a plane orthogonal to the impingement surface at the impingement location.