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Modal expansion is an attractive technique for solving electromagnetic scattering problems. With the one set of resonator modes, calculated once and for all, any configuration of near-field or far-field sources can be obtained almost…

Optics · Physics 2020-09-08 Parry Y. Chen , Yonatan Sivan , Egor A. Muljarov

Plasmonic devices with feature sizes of a few nanometers exhibit effects which can be described by the nonlocal hydrodynamic Drude model. We demonstrate how to exploit contour integral methods for computing eigenfrequencies and resonant…

The idea of the modal expansion in electromagnetics is derived from the research on electromagnetic resonators, which play an essential role in developments in nanophotonics. All of the electromagnetic resonators share a common property:…

Optics · Physics 2020-10-28 Minh Duy Truong

The interaction of light with photonic resonators is determined by the eigenmodes of the system. Modal theories based on quasinormal modes provide a natural tool to calculate and understand light scattering by nanoresonators. We show that,…

Optics · Physics 2025-11-06 Christophe Sauvan

We derive a closed-form expression that accurately predicts the peak frequency-shift and broadening induced by tiny perturbations of plasmonic nanoresonators without critically relying on repeated electrodynamic simulations of the spectral…

Optics · Physics 2015-05-20 Jianji Yang , Harald Giessen , Philippe Lalanne

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…

Mathematical Physics · Physics 2021-02-11 Lorenzo Baldassari , Pierre Millien , Alice L. Vanel

This paper is concerned with efficient representations and approximations of the solution to the scattering problem by a system of strongly coupled plasmonic particles. Three schemes are developed: the first is the resonant expansion which…

Numerical Analysis · Mathematics 2017-09-26 Habib Ammari , Matias Ruiz , Sanghyeon Yu , Hai Zhang

Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…

Optics · Physics 2023-09-28 S. F. Almousa , E. A. Muljarov

Modal analysis based on the quasi-normal modes (QNM), also called resonant states, has emerged as a promising way for modeling the resonant interaction of light with open optical cavities. However, the fields associated with QNM in open…

Optics · Physics 2018-08-21 Rémi Colom , Ross McPhedran , Brian Stout , Nicolas Bonod

We study the possible expansion of the electromagnetic field scattered by a strictly convex metallic nanoparticle with dispersive material parameters placed in a homogeneous medium in a low-frequency regime as a sum of modes oscillating at…

Mathematical Physics · Physics 2021-05-20 Habib Ammari , Pierre Millien , Alice L. Vanel

Quasi-normal modes (QNMs) are ubiquitous throughout photonics and are utilized in a wide variety of applications, but determining these modes remains a formidable task in general. Here we show that by exploiting the structure of Maxwell's…

Optics · Physics 2020-07-15 Jörn Zimmerling , Rob Remis

A quasimodal expansion method (QMEM) is developed to model and understand the scattering properties of arbitrary shaped two-dimensional (2-D) open structures. In contrast with the bounded case which have only discrete spectrum (real in the…

All electromagnetic systems, in particular resonators or antennas, have resonances with finite lifetimes. The associated eigenstates, also called quasinormal modes, are essentially non-Hermitian and determine the optical responses of the…

Computational Physics · Physics 2022-12-20 T. Wu , D. Arrivault , W. Yan , P. Lalanne

In this Review, the theory and applications of optical micro and nanoresonators are presented from the underlying concept of their natural resonances, the so-called quasi-normal modes (QNMs). The latter are the basic constituents governing…

The dispersive resonant-state expansion, developed for an accurate calculation of the resonant states in open optical systems with frequency dispersion, is applied here to realistic materials, such as metallic nanoparticles and…

Optics · Physics 2020-01-29 Hame Sehmi , Wolfgang Langbein , Egor Muljarov

Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light…

Analysis of PDEs · Mathematics 2015-06-03 Habib Ammari , Pierre Millien , Matias Ruiz , Hai Zhang

It is proven that in the lossless case the electrodynamics of a generic inhomogeneous possibly bianisotropic and nonreciprocal system may be described by an augmented state-vector whose time evolution is determined by a Hermitian operator.…

Optics · Physics 2019-01-10 Mario G. Silveirinha

In photonics, Dispersive Quasi-Normal Modes (DQNMs) refer to optical resonant modes, solutions of spectral problems associated with Maxwell's equations for open photonic structures involving dispersive media. Since these DQNMs are the…

We present exact modal expansions for photonic systems including highly dispersive media. The formulas, based on a simple version of the Keldysh theorem, are very general since both permeability and permittivity can be dispersive,…

Optics · Physics 2018-12-26 Frédéric Zolla , André Nicolet , Guillaume Demésy

In this paper we provide a mathematical framework for localized plasmon resonance of nanoparticles. Using layer potential techniques associated with the full Maxwell equations, we derive small-volume expansions for the electromagnetic…

Mathematical Physics · Physics 2015-10-28 Habib Ammari , Youjun Deng , Pierre Millien
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