Green’s function application to photonic crystal waveguides analysis

Abstract

The paper considers application of the Green's tensor functions to analysis of the multilayer magneto-dielectric structures in relation to photonic crystals of the microwave range. The solution of the problem of electromagnetic wave propagation in rectangular and flat waveguides, as well as in unlimited space is presented. Efficiency of application of the Green's functions to calculation of transmission coefficients through the regular and perturbed structure of a photonic crystal is shown. It was proposed to solve the problem of diffraction of electromagnetic waves by the layered structures as the problem of equivalent electric and magnetic currents radiation. These currents are determined on the illuminated layered media surface by the Equivalence Theorem. The magnitude of the current is related to the electric field intensity, and, also, the direction of the incident wave is defined by the current phase distribution. The radiation of the equivalent currents behind the layered structure is considered as a transmitted wave. Radiation of these currents in the same region is treated as a reflected wave. So, transmission and reflection coefficients are defined. Application of this approach to analysis of the periodic structures of the photonic crystals is shown in this paper.