Green functions and volumetric integro-differential equation methods for 2D and 3D photonic crystals analysis

摘要

The Green functions and corresponding integral and integro-differential equations for periodic structures are introduced. Some results based on this approach for 2D and 3D photonic crystals are presented. We consider the simplest photonic crystals, but the method is applicable to arbitrary shaped structure and may use the volumetric finite elements. The solutions of integral and integro-differential volumetric and combined surface-volumetric equations are considered and discussed. Also the method which reduces the kernel singularity is proposed and considered. The method is based on the transferring of differential operators from the kernel to the unknown functions under the integral. The dispersion equations is based on the variation formulation for integral and integro-differential equations and have been used to obtain the permittivity and permeability tensors for photonic crystal's equivalent complex media.