Optimality of T-coercivity for scalar interface problems between dielectrics and metamaterials

Anne-Sophie Bonnet-Ben Dhia (1) , Lucas Chesnel (1) , Patrick Ciarlet (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative parameters when dissipation is neglected. They are usually called metamaterials. We study a scalar wave transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of R^d, with d = 2, 3. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or coercive + compact) framework. For that, we build some criteria, based on the geometry of the interface between the dielectric and the metamaterial. The proofs rely on localization techniques, together with the theory of T-coercivity introduced by the first and third authors and co-worker. In particular, we establish the optimality of the criteria, when the dielectric permittivity is piecewise constant.

Mots clés: Meta-material; Left-handed material; Interface problem; T-coercivity

Domaines: Equations aux dérivées partielles [math.AP]

Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Patrick Ciarlet. Optimality of T-coercivity for scalar interface problems between dielectrics and metamaterials. 2011. ⟨hal-00564312v1⟩