Mathematical analysis of plasmonic resonance for 2-D photonic crystal

Guang-Hui Zheng

Published 2017-01-26Version 1

In this article, we study the plasmonic resonance in two dimensions infinite photonic crystal mounted by the double negative nanoparticles. The corresponding physical model is described by the Helmholz equation with so called Bloch wave condition in a periodic domain. By using the quasi-periodic layer potential techniques and the spectral theorem of quasi-periodic Neumann-Poincar{\'e} operator, the quasi-static expansion of the near field in the presence of nanoparticles is derived. Furthermore, when the magnetic permeability of nanoparticles satisfy the Drude model, we give the conditions under which the plasmonic resonance occurs, and the rate of blow up of near field energy with respect to nanoparticle's bulk electron relaxation rate and filling factor are also obtained.