Resonant effects in random dielectric structures
Abstract
Recently, a theory for artificial magnetism in two-dimensional photonic crystals has been developed for large wavelength using homogenization techniques. In this paper we pursue this approach within a rigorous stochastic framework: dielectric parallel nanorods are randomly disposed, each of them having, up to a large scaling factor, a random permittivity \epsilon(\omega) whose law is represented by a density on a window \Delta=[a,b]x[0,h] of the complex plane. We give precise conditions on the initial probability law (permittivity, radius and position of the rods) under which the homogenization process can be performed leading to a deterministic dispersion law for the effective permeability with possibly negative real part. Subsequently a limit analysis h->0, accounting a density law of \epsilon, which concentrates on the real axis, reveals singular behavior due to the presence of resonances in the microstructure.
Cite
@article{arxiv.1305.7129,
title = {Resonant effects in random dielectric structures},
author = {Guy Bouchitte and Christophe Bourel and Luigi Manca},
journal= {arXiv preprint arXiv:1305.7129},
year = {2013}
}