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

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.

Localization and geometrization in plasmon resonances and geometric structures of Neumann-Poincaré eigenfunctions

“…In fact, in many of the existing studies on plasmon resonances, the quasi-static approximation has played a critical role where the plasmonic inclusion is of a size much smaller than the wavelength. There are also several studies that go beyond the quasi-static limit [33,21,27,30,36]. In [33], double negative materials are employed in the shell and in [36], in addition to the employment of double negative materials, a so-called double-complementary medium structure is incorporated into the construction of the plasmonic device.…”

“…In [21], it is actually shown that resonance does not occur for the classical core-shell plasmonic structure without the quasistatic approximation as long as the core and shell are strictly convex. In [27,30], in order for the plasmon resonances to occur beyond the quasi-static approximation, the corresponding plasmonic configuration has to be designed in a subtle and delicate way. Nevertheless, we show that for a plasmonic structure that is resonant in the quasi-static regime but non-resonant out of the quasi-static regime, the resonance always occurs locally near a high-curvature boundary point of the plasmonic inclusion.…”

Asymptotic behavior of spectral of Neumann‐Poincaré operator in Helmholtz system

“…Recently, spectral of Neumann‐Poincaré operator has attracted much attention, for its applications in plasmon resonance, cloaking because of anomalous localized resonance, and enhancement of near cloaking . We also refer to Helsing, Kang, and Lim and Kang et al for analysis of spectral of Neumann‐Poincaré operator in domains with corners.…”

“…Most of the studies are based on the static (quasistatic) case, ie, conductivity problem. In the studies of Kang et al, Li et al, and Li and Liu, the authors consider the spectral of Neumann‐Poincaré operator in Helmholtz system with finite frequency and use the result to analyze plasmon resonance and cloaking because of anomalous localized resonance phenomena. Mathematically, one consider the following Helmholtz system.…”

Recent progress on the mathematical study of anomalous localized resonance in elasticity

“…The CALR has been extensively investigated. We refer to [4,6,9,11,15,20,21,29] for the relevant study in acoustics, [8,10,17,18,19,27,28,24] for elastic system and [3,2,1,7,13,14,15,25,26,31,32,33,34,36,37,38] for the Maxwell system.…”