Abstract: Process and apparatus for deep cutting a material covering a substrate, the material absorbing laser radiation, enables the transforming of a beam from a laser source into a thin pencil of rays to create a focussing field having a thin blade shape including a large focussing depth spanning several millimeters and having variations in energy density of laser radiation less than a predetermined value so that the laser radiation is sufficient to remove an entire thickness of the material, by fusion or ablation, within the focussing field. The focussing field and the material are movable relative to each other to expose varying portions of the material to the focussing field while maintaining the focussing field substantially perpendicular to an external surface of the material or to a generating line of the external surface of the material.