A method for processing a transparent workpiece , the method comprising: directing a laser beam oriented along a beam pathway into the transparent workpiece , the transparent workpiece having an impingement surface , the laser beam passing through the impingement surface at an impingement location to enter the transparent workpiece , wherein: a portion of the laser beam directed into the transparent workpiece produces a laser beam focal line in the transparent workpiece and generates an induced absorption to produce a defect within the transparent workpiece , the laser beam focal line comprising: a wavelength λ; a spot size w o ; an internal focal line angle of greater than 10° relative to a plane orthogonal to the impingement surface at the impingement location; a circular angular spectrum, which refers to the distribution of the Fourier spectrum of the laser beam in the spatial frequency domain, within the transparent workpiece; and the method is characterized in that the laser beam focal line further comprises a Rayleigh range Z R that is greater than F D πw o 2 λ , where F D is a dimensionless divergence factor comprising a value of 10 or greater; and a length defined by a series of points, each of the points being formed from a plurality of intersecting rays from the laser beam , the intersecting rays being matched in phase. directing a laser beam oriented along a beam pathway into the transparent workpiece , the transparent workpiece having an impingement surface , the laser beam passing through the impingement surface at an impingement location to enter the transparent workpiece , wherein: a portion of the laser beam directed into the transparent workpiece produces a laser beam focal line in the transparent workpiece and generates an induced absorption to produce a defect within the transparent workpiece , the laser beam focal line comprising: a wavelength λ; a spot size w o ; an internal focal line angle of greater than 10° relative to a plane orthogonal to the impingement surface at the impingement location; a circular angular spectrum, which refers to the distribution of the Fourier spectrum of the laser beam in the spatial frequency domain, within the transparent workpiece; and the method is characterized in that the laser beam focal line further comprises a Rayleigh range Z R that is greater than F D πw o 2 λ , where F D is a dimensionless divergence factor comprising a value of 10 or greater; and a length defined by a series of points, each of the points being formed from a plurality of intersecting rays from the laser beam , the intersecting rays being matched in phase. a wavelength λ; a spot size w o ; an internal focal line angle of greater than 10° relative to a plane orthogonal to the impingement surface at the impingement location; a circular angular spectrum, which refers to the distribution of the Fourier spectrum of the laser beam in the spatial frequency domain, within the transparent workpiece; and the method is characterized in that the laser beam focal line further comprises a Rayleigh range Z R that is greater than F D πw o 2 λ , where F D is a dimensionless divergence factor comprising a value of 10 or greater; and a length defined by a series of points, each of the points being formed from a plurality of intersecting rays from the laser beam , the intersecting rays being matched in phase. <EOS>