A laser cutting device for transparent material (23), which device is designed to focus the laser light (2) into a plurality of predetermined spots within the material (23), wherein the spots lie on a predetermined cutting line or cutting area (24) running substantially perpendicularly to the direction of incidence of the laser light (2), wherein the device comprises means for mode conversion (3) into laser light having a helical phase front (5), which means can be brought into and out of the beam path of the laser light (2).
