Plasmonic cavity modes: Black-hole phenomena captured by perfectly matched layers

We study a 2D dielectric cavity with a metal inclusion and we assume that, in a given frequency range, the metal permittivity ε = ε(ω) is a negative real number. We look for the plasmonic cavity resonances by studying the linearized eigenvalue problem (dependence in ω of ε frozen). When the inclusion is smooth, the linearized problem operator has a discrete spectrum which can be computed numerically with a good approximation, e.g., by a classical Finite Element Method. However, when the inclusion has corners, due to very singular phenomena, we loose the operator properties and numerical approximations are not stable. Paradoxically there is a theoretical and a numerical need to take into account these singularities in order to compute the modes, even the regular ones. Then we propose an original use of PMLs (Perfectly Matched Layers) at the corners to capture these plasmonic waves.