Quasinormal mode solvers for resonators with dispersive materials

Abstract

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.

Modeling electromagnetic resonators using quasinormal modes

“…The explicit correspondence between QNM calculations with an integral equation formulation and with PML truncations was illustrated in Ref. [17], and Maes et al [100], de Lasson et al [101] and Lalanne et al [102] recently compared a number of different calculation methods commonly in use in the literature. In addition to direct numerical solutions, numerous approximate methods exist, which may be used to device simple analytical descriptions of the QNM fields as well as insight to the physical mechanisms responsible for the partial trapping of the electromagnetic field.…”

Bound states in the continuum in symmetric and asymmetric photonic crystal slabs

“…Numerical calculations in this work are performed with the rigorous coupled-wave analysis (RCWA) 45 . The modes are calculated by searching for the poles of the scattering matrix in the complex frequency plane 46,47 . The number of Fourier harmonics retained in the expansion of the electromagnetic field is 2M + 1 with M = 30.…”

An auxiliary field approach for computing optical resonances in dispersive media

“…We revisit an experimentally realized setup supporting plasmonic resonances [17]. This system has been recently numerically investigated [18]. The geometry is sketched in Fig.…”

“…We apply the auxiliary field approach using the FEM solver JCMsuite to compute the resonant state which corresponds to an absorption peak near the wavelength λ = 650 nm [18]. For the relative permittivity of the gold grating, a one-pole Drude model…”