A method and device for separating a substrate with a laser beam. The duration of the laser beam's effect is extremely short, so the substrate is only modified concentrically about the laser beam axis (Z) without it degrading the substrate material. While the laser beam acts upon the substrate, the substrate moves relative to a laser machining head, producing plural filament-type modifications along a separating surface to be incorporated. The laser beam is initially diverted by a transmission medium having a higher intensity dependent refractive index than air, then reaches the substrate. The non-constant pulsed laser intensity increases to a maximum over the temporal course of the single pulse, then reduces, and the refractive index changes. The laser beam focus point moves between the substrate's outer surfaces along the beam axis (Z), reaching the desired modification along the beam axis (Z) without correcting the laser machining head in the z-axis.