Modal approximation for plasmonic resonators in the time domain: the scalar case

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.

Modal approximation for time-domain elastic scattering from metamaterial quasiparticles

“…We establish a polariton resonance expansion with sharp error estimates for the low-frequency part of the elastic field scattered by the aforementioned elastic quasiparticle. Our study shares a similar spirit to the recent works [4,6] which established the plasmon resonance expansion of the electromagnetic field scattered by nanoparticles with dispersive material parameters placed in a homogeneous medium in the low-frequency regime. However, it is remarked that the elastic waves in solid media where the coupled longitudinal and transverse waves bring challenging but richer wave phenomena.…”

“…To that purpose, we shall adopt the modal analysis, which is a powerful tool to understand complex wave physics; see [37] for a general presentation of resonance expansions. Notably, modal analysis for wave propagation in an unbounded domain [35,36] as well as from negative metamaterial structures [4,6,8,9] present significant challenges in either scenario, since many classical results from spectral theory do not apply, say e.g. the corresponding wave operator cannot be diagonalised with the classical spectral theorem.…”

Modal approximation for time-domain elastic scattering from metamaterial quasiparticles

“…Specifically, we show that the low-frequency part of the elastic scattered field can be well approximated by using the Minnaert resonant modal expansion. Our study is motivated by the recent works [2,4] and [7] on modal approximations. In [2,4], the authors established the plasmon resonant expansion of the electromagnetic field scattered by nanoparticles with dispersive material parameters placed in a homogeneous medium in the low-frequency regime.…”

“…Our study is motivated by the recent works [2,4] and [7] on modal approximations. In [2,4], the authors established the plasmon resonant expansion of the electromagnetic field scattered by nanoparticles with dispersive material parameters placed in a homogeneous medium in the low-frequency regime. In [7], the three authors of the present article established the polariton resonant expansion of the elastic field scattered by elastic metamaterial nanoparticles in the low-frequency regime.…”

Transmission properties of space-time modulated metamaterials

“…They are known to possess a subwavelength resonance called the Minnaert resonance [9]. Other examples of subwavelength resonators are Helmholtz resonators, plasmonic nanoparticles, and high-dielectric nanoparticles; see, for instance, [1,5,6,8,10,[23][24][25][26]37].…”