Analytical description of the electrodynamic properties of metallic photonic crystals

Abstract

We consider the excitation by a dipole of metallic photonic crystals—systems of infinitely extended parallel-oriented metallic cylinders with a small circular cross section. Based on the rigorous statement of the problem, analytical expressions are obtained that make it possible to give a simple estimate of frequencies that determine the band gap edges in the spectrum of eigenstates of such a crystal and, also, to describe the amplitude characteristics of radiation in the low-frequency range, in which the approximations used in our study are correct. We compare our results with those obtained by strictly numerical simulation.