Propagation of waves in metallic photonic crystals at low frequencies and some theoretical aspects of left-handed materials

TL;DR

This paper develops an analytical theory for low-frequency electromagnetic wave propagation in metallic photonic crystals with small metal volume fractions, providing exact dispersion relations and exploring conditions for left-handed material behavior.

Contribution

It presents an exact dispersion equation and analytical permittivity expression, clarifying the conditions under which metallic photonic crystals can or cannot exhibit left-handed properties.

Findings

Derived an exact dispersion relation for low-frequency waves

Calculated an analytical permittivity expression

Showed that embedding in negative mu medium prevents propagation

Abstract

An analytical theory of low frequency electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. The evidence of the existence of such waves has been found recently via experiments and computations. We have obtained an exact dispersion equation for omega (k) and studied the cutoff frequency omega_0 = omega(0) as a function of parameters of the photonic crystal. An analytical expression for the permittivity epsilon is calculated. It is shown, that if the crystal is embedded into a medium with negative mu, it has no propagating modes at any frequency. Thus, such a compound system is not a left-handed material (LHM). The recent experimental results on the LHM are discussed.