Optical diffraction by two-dimensional photonic structures with hexagonal symmetry

Photonic structures with hexagonal symmetry have been prepared by the additive technology of two-photon laser lithography, and their optical properties have been investigated. The structure of the samples has been examined using scanning electron microscopy. The calculations have been performed for the optical diffraction in the Born approximation of the scattering theory for structures with a limited number of scatterers. The images formed in the monochromatic light on a flat screen located behind the sample have been calculated. The diffraction patterns on the screen have $C_{6v}$ symmetry and consist of three straight lines intersecting at an angle of 120$^\circ$ and hyperbolas, the number of which is a multiple of six. An important feature of these diffraction patterns is the superstructure, i.e., the partition of straight lines and hyperbolas into individual diffraction reflections, the number of which is determined by the number of scatterers of a particular sample. The results of the experimental investigation of the diffraction patterns completely coincide with the calculated data, including the number and arrangement of the superstructure reflections.