Surface plasmons in metamaterial cavities: Scattering by obstacles with negative wave speed

TL;DR

This paper investigates surface plasmons in metamaterial cavities with negative refraction indices, analyzing their existence, localization, and resonance properties in non-trapping geometries.

Contribution

It characterizes conditions for surface plasmons in non-trapping cavities and provides asymptotic estimates for their resonances and localization.

Findings

Resonances lie super-polynomially close to the real axis.

Surface plasmons are highly localized at cavity boundaries.

The paper provides an asymptotic formula for the number of resonances.

Abstract

We study scattering by metamaterials with negative indices of refraction, which are known to support \emph{surface plasmons} -- long-lived states that are highly localized at the boundary of the cavity. This type of states has found uses in a variety of modern technologies. In this article, we study surface plasmons in the setting of non-trapping cavities; i.e. when all billiard trajectories outside the cavity escape to infinity. We characterize the indices of refraction which support surface plasmons, show that the corresponding resonances lie super-polynomially close to the real axis, describe the localization properties of the corresponding resonant states, and give an asymptotic formula for their number.