A method for processing a transparent workpiece includes directing a pulsed laser beam into the transparent workpiece such that a portion of the pulsed laser beam directed into the transparent workpiece generates an induced absorption within the transparent workpiece, thereby forming a damage line within the transparent workpiece, and the portion of the pulsed laser beam directed into the transparent workpiece includes a wavelength λ, a spot size w0, and a Rayleigh range ZR that is greater than F D ⁢ π ⁢ w 0 2 λ , where FD is a dimensionless divergence factor comprising a value of 10 or greater. Further, the method for processing the transparent workpiece includes etching the transparent workpiece with an etching vapor to remove at least a portion of the transparent workpiece along the damage line, thereby forming an aperture extending through the at least a portion of the thickness of the transparent workpiece.