Long wavelength limit of two dimensional photonic crystals

TL;DR

This paper analytically solves the multiple scattering equations for 2D photonic crystals in the long wavelength limit, clarifying plasmon-polariton band behavior and effects of wire radius on frequency.

Contribution

It provides a unified analytical approach to understanding the electromagnetic response of 2D photonic crystals in the long wavelength regime.

Findings

Analytical solutions for multiple scattering equations in 2D photonic crystals.

Clarification of plasmon-polariton band nature.

Discussion of frequency dependence on wire radius.

Abstract

We solve {\bf analytically} the multiple scattering (KKR) equations for the two dimensional photonic crystals in the long wavelength limit. Different approximations of the electric and magnetic susceptibilities are presented from a unified pseudopotential point of view. The nature of the so called plasmon-polariton bands are clarified. Its frequency as a function of the wire radius is discussed.