Modal analysis using Quasi-Normal Modes (QNM) is now an essential tool to interpret the behavior of open photonic devices based on their intrinsic resonances. When dealing with frequency dispersive media, which is unavoidable in optics, the eigenvalue problem to be considered becomes non-linear due to the dependence of the permittivity with respect to the eigenvalue. The same situation occurs when dealing with frequency dependent boundary conditions at infinity, such as dispersive Perfectly Matched Layers (PMLs), Absorbing Boundary Conditions (ABC), or higher order approximations of the Dirichletto-Neumann operator. In this talk, we will present the various numerical tools recently introduced allowing to perform the QNM expansion with dispersive media in open geometries: (i) Starting with a general causal rational function as a permittivity model [1], (ii) we will review various linearization schemes to tackle the non-linear eigenvalue problem using finite elements, (iii) to finally show a general frame based on the Keldysh theorem to expand [3] the solution of direct problems.
In collaboration with Carmen Campos (Universitat Politècnica de València), Christophe Geuzaine (University of Liège) , Boris Gralak (Institut Fresnel), André Nicolet (Institut Fresnel), Jose E. Roman (Universitat Politècnica de València), Frédéric Zolla (Institut Fresnel).[-]