Mathematical analysis of plasmonic resonance for 2D 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 quasiperiodic layer potential techniques and the spectral theorem of quasiperiodic NeumannPoincar{é} operator, the quasistatic 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 DOI:
 10.48550/arXiv.1701.07687
 arXiv:
 arXiv:1701.07687
 Bibcode:
 2017arXiv170107687Z
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs