On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials

Eliane Bécache (1) , Patrick Joly (1) , Valentin Vinoles (2)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 EPFL - Ecole Polytechnique Fédérale de Lausanne

This work deals with Perfectly Matched Layers (PMLs) in the context of dispersive media, and in particular for Negative Index Metamaterials (NIMs). We first present some properties of dispersive isotropic Maxwell equations that include NIMs. We then demonstrate numerically the inherent instabilities of the classical PMLs applied to NIMs. We propose and analyse the stability of very general PMLs for a large class of dispersive systems using a new change of variable. We give necessary criteria for the stability of such models. For dispersive isotropic Maxwell equations, this analysis is completed by giving necessary and sufficient conditions of stability. Finally, we propose new PMLs that satisfy these criteria and demonstrate numerically their efficiency.

Mots clés: perfectly matched layer (PML); dispersive system; negative index metamaterial (NIM); stability; Maxwell equations

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Analyse numérique [math.NA]

Eliane Bécache, Patrick Joly, Valentin Vinoles. On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials. 2016. ⟨hal-01327315v2⟩