Abstract
We study the electromagnetic field scattered by a metallic nanoparticle with dispersive material parameters in a resonant regime. We consider the particle placed in a homogeneous medium in a low-frequency regime. We define modes for the non-Hermitian problem as perturbations of electro-static modes, and obtain a modal approximation of the scattered field in the frequency domain. The poles of the expansion correspond to the eigenvalues of a singular boundary integral operator and are shown to lie in a bounded region near the origin of the lower-half complex plane. Finally, we show that this modal representation gives a very good approximation of the field in the time domain. We present numerical simulations in two dimensions to corroborate our results.
Highlights
When describing the interaction of light with a resonating particle, summing the natural resonant modes of the system is an intuitive and attractive approach
The goal of this paper is to obtain an approximation of the low-frequency part of the scattered field by a dispersive obstacle in the time domain as a finite sum of modes oscillating at complex frequencies
We show that even though they are irrelevant for frequency domain representation, quasi-normal modes can be used to approximate the field in the time domain
Summary
When describing the interaction of light with a resonating particle, summing the natural resonant modes of the system is an intuitive and attractive approach. The modes are computed as they are eigenmode solutions to a source-free problem. They are intrinsic quantities of the system and give insights to understand the underlying physics. Once they are calculated, the response of the system to any given excitation can be computed at a low com-. This article is part of the section “Applications of PDEs” edited by Hyeonbae Kang.
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