Title: Mathematical analysis of plasmonic resonance for 2-D photonic crystal,
Abstract: In this article, we study the plasmonic resonance of infinite photonic
crystal mounted by the double negative nanoparticles in two dimensions. 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{é} operator, the quasi-static expansion of the near field in
the presence of nanoparticles is derived. Furthermore, when the magnetic
permeability of nanoparticles satisfies 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. It indicates that one can appropriately
control the bulk electron relaxation rate or filling factor of nanoparticle in
photonic crystal structure such that the near field energy attains its maximum,
and enhancing the efficiency of energy utilization.