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.