The plane wave expansion method for investigating the dispersion properties of metallic photonic crystals

Original method for studying the dispersion characteristics of photonic crystals – media with a dielectric constant that varies periodically in space is considered. The based on representation wave functions and permittivity periodic medium form Fourier series their subsequent substitution into equation, which leads to formulation equation. Using latter, each value vector it possible determined set eigen frequencies. Each frequency forms separate curve as continuous function number. expansion coefficients permittivity, depend vectors reciprocal lattice crystal, are basis data geometric elements electrophysical properties density crystal. solution equation found makes obtain complete information about number modes propagating structure at different frequencies, possibility forming band gaps, i.e. ranges within propagation through crystal impossible. focus this work application analysis metallic crystals. difficulties arise case due presence intrinsic metals overcome by an analytical description model free electrons. As result, formulated, numerical easily algorithmized. That determine arbitrary parameters. Obtained results calculation diagrams, characterize two-dimensional metal crystals, compared experimental obtained using self-consistent equations. Their good agreement demonstrated.