Extinction zones and scalability in N-beam interference lattices

The interference of N-beams was theoretically investigated. Both azimuthal and zenithal symmetry between incident beams using spherical coordinates were considered; zenithal and azimuthal polarization of the electric fields were studied, as well. In the analysis of the patterns in the θ − x plane for zenithal configuration of the electric field, extinction points, where all interference vanishes, is predicted. Choosing more than four beams to interfere resulted in the evolution of extinction points to extinction zones with modified frequency. Suitable numbers of the beams produced a specific geometry, and presented important scalability properties for its application in the etching of photosensitive materials.