Quasinormal mode solvers for resonators with dispersive materials.

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 raises 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 two-dimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, with the perspective to elaborate standards for the computation of resonance modes.

Extracting an accurate model for permittivity from experimental data: hunting complex poles from the real line.

In this Letter, we describe a very general procedure to obtain a causal fit of the permittivity of materials from experimental data with very few parameters. Unlike other closed forms proposed in the literature, the uniqueness of this approach lies in its independence on the material or frequency range at stake. Many illustrative numerical examples are given, and the accuracy of the fitting is compared to other expressions in the literature.

Tessellated and stellated invisibility.

We derive the expression for the anisotropic heterogeneous matrices of permittivity and permeability associated with two-dimensional polygonal and star shaped cloaks. We numerically show using finite elements that the forward scattering worsens when we increase the number of sides in the latter cloaks, whereas it improves for the former ones. This antagonistic behavior is discussed using a rigorous asymptotic approach. We use a symmetry group theoretical approach to derive the cloaks design.

Duality relation for the Maxwell system.

This paper is intended to establish a link between the vector Maxwell system for three-dimensional (3D) and 2D finite photonic crystals in the low-frequency limit. For this, we generalize the classical results of Keller and Dykhne (chessboard problem) to periodic media described by piecewise continuous permittivity profiles: our theorem enlights the result of Mendelson (polycrystalline and multiphase media) in the framework of homogenization theory of elliptic operators. In fine, we give illustrative examples by using both integral equation and variational approaches via the so-called method of fictitious charges and finite-element method.