Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies.For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This rises a difficulty that is only scarcely documented in the literature. We review our recent efforts for implementing efficient and accurate QNM-solvers for computing and normalizing the QNMs of micro-and nanoresonators made of highly-dispersive materials. We benchmark several methods for three geometries, a twodimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, in the perspective to elaborate standards for the computation of resonance modes.
Grating spectra exhibit sharp variations of the scattered light, known as grating anomalies. The latter are due to resonances that have fascinated specialists of optics and physics for decades and are nowadays used in many applications. We present a comprehensive theory of grating anomalies, and develop a formalism to expand the field scattered by metallic or dielectric gratings into the basis of its natural resonances, thereby enabling the possibility to reconstruct grating spectra measured for fixed illumination angles as a sum over every individual resonance contribution with closed-form expressions. This gives physical insights into the spectral properties and a direct access to the resonances to engineer the spectral response of gratings and their sensitivity to tiny perturbations.The efficiencies of gratings as a function of the wavelength may present peaks, dips or anomalies generated by the excitation of leaky photonic of plasmonic modes. Yet another example is found in Fig. 1. This is well known since U. Fano introduced a surface-plasmon model to analyze light diffraction by metallic gratings and explained Wood's anomalies [1]. Nowadays, grating resonances have many applications for biosensing, photodetectors, photovoltaics, light emission, optical processing, metamaterials … and their theoretical analysis for harnessing light-matter interaction remains of great importance.The theory of grating anomalies was pioneered by a milestone work by Hessel and Oliner [2] and was then followed by a series of works summarized in Refs. [3][4][5], which contributed to the systematic development of a phenomenological study of grating anomalies through the poles and zeros of the scattering operator, the so-called "polology". Poles were indifferently computed by considering a real frequency ω (equal to the driving laser frequency) and looking for complex in-plane wave-vectors ̃( ) or angles of incidence sin (̃( )), or by considering a fixed angle of incidence , and looking for complex frequencies ̃( ). Great insight in the physics of grating anomalies was achieved by tracking the pole trajectories in the complex plane as some parameters, e.g. the grating depth, are tuned [4]. The frequency poles ̃, i.e. the natural resonances, have a profound meaning (these poles correspond to the quasinormal-modes or QNMs hereafter). They define important quantities such as the resonance frequency, Re(̃), or the inverse of the mode lifetime, 2Im(̃). The theory of grating anomalies changed little during several decennia, and the polology has been used to analyze or engineer various
Any optical structure possesses resonance modes, and its response to an excitation can be decomposed onto the quasinormal and numerical modes of a discretized Maxwell operator. In this paper, we consider a dielectric permittivity that is an N-pole Lorentz function of the frequency. Even for discretized operators, the literature proposes different formulas for the coefficients of the quasinormal-mode expansion, and this comes as a surprise. We propose a general formalism, based on auxiliary fields, which explains why and evidences that there is, in fact, an infinity of mathematically sound possible expansion coefficients. The nonuniqueness is due to a choice of the linearization of Maxwell’s equations with respect to frequency and of the choice of the form of the source term. Numerical results validate the different formulas and compare their accuracy.
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