Method and apparatus for filamentation of workpieces not having a plan-parallel shape, and workpiece produced by filamentation

A dielectric workpiece comprising:

• a plurality of boundary surfaces delimiting the workpiece;
• the workpiece has a thickness between 0.5 and 20 mm, wherein the thickness varies spatially and/or at least one of the boundary surfaces has at least one curvature with a radius of curvature between 0.1 μm and 10 m,
• the workpiece has an edge having a roughness RMS from 1 to 5 μm determined by a roughness measurement using an atomic force microscope and/or a white light interferometer, wherein the edge has a material with a material property that differs from a remaining portion of the workpiece, wherein the edge is formed by determining a vector standing orthogonally on a local surface that is the mathematical surface normal vector so that a filament of the dielectric workpiece is aligned at an angle that is represented by the surface normal vector, wherein the filament is formed of a cavity, wherein the filament is a plurality of filaments that are produced in different height sections of the workpiece, and wherein one of the plurality of filaments has a starting point that is also an end point of another produced filament of the plurality of filaments, and wherein the starting point of the one of the plurality of filaments is identified by a scattering center in the workpiece.