Two-dimensional planar photonic crystals: Calculation of coherent transmittance and reflectance at normal illumination under the quasicrystalline approximation

The technique to calculate coherent transmission and reflection coefficients of two-dimensional (2D) planar photonic crystal (PC) at the normal to layer plane illumination is proposed. It is based on the quasicrystalline approximation of the theory of multiple scattering of waves. At this approximation spatial particle correlations are characterized by the radial distribution function. We propose the method of the 2D planar PC radial distribution function simulation. It consists in the calculation of coordination circles of ideal crystal lattice and following blurring them into the “rings” with fuzzy edges to describe the crystal lattice of an actual crystal. The width of the “rings” depends on the distance from coordinate origin. The blurring technique is proposed and discussed. The method allows simulation of the PCs lattices with various ordering degrees and spatial particle correlations. The results of numerical calculations of coherent transmittance and reflectance of monolayers with different orderings and refractive indices of spherical monodisperse particles are displayed. ► Method of 2D photonic crystal radial distribution function simulation is proposed. ► Method allows simulation of different orderings of monolayers of particles. ► Triangular, square, hexagonal, and partially ordered layers are considered. ► Transmittance and reflectance of ordered monolayers of particles are calculated.