A method for laser processing a transparent workpiece includes forming a contour line having defects in the transparent workpiece, which includes directing a pulsed laser beam oriented along a beam pathway through a beam converting element and through a phase modifying optical element such that the portion of the pulsed laser beam directed into the transparent workpiece includes a phase shifted focal line having a cross-sectional phase contour that includes phase contour ridges induced by the phase modifying optical element and extending along phase ridge lines. Moreover, the phase shifted focal line generates an induced absorption within the transparent workpiece to produce a defect within the transparent workpiece including a central defect region and a radial arm that extends outward from the central defect region in a radial defect direction oriented within 20° of the phase ridge lines of the phase shifted focal line.