Analysis of electromagnetic scattering from plasmonic inclusions beyond the quasi-static approximation and applications

¹ Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, P.R. China
² Department of Mathematics, Harbin University of Science and Technology, Harbin, P.R. China
³ Department of Mathematics, Harbin Institute of Technology, Harbin P.R. China

^* Corresponding author: hongyu.liuip@gmail.com, hongyuliu@hkbu.edu.hk

Received: 28 October 2018
Accepted: 24 January 2019

Abstract

This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the inclusions are allowed to be negative-valued. Using layer potential techniques for the full Maxwell system, the scattering problem is reformulated into a system of integral equations. We derive the complete eigensystem of the involved matrix-valued integral operator within spherical geometry. As applications, we construct two types of plasmonic structures such that one can induce surface plasmon resonances within finite frequencies and the other one can produce invisibility cloaking. It is particularly noted that the cloaking effect is a newly found phenomenon and is of different nature from those existing ones for plasmonic structures in the literature. The surface plasmon resonance result may find applications in electromagnetic imaging.