A NEW COMPACTNESS RESULT FOR ELECTROMAGNETIC WAVES. APPLICATION TO THE TRANSMISSION PROBLEM BETWEEN DIELECTRICS AND METAMATERIALS

We consider the time-harmonic Maxwell equations, involving wave transmission between media with opposite sign dielectric and/or magnetic coefficients. We prove that, in the case of sign-shifting dielectric coefficients, the space of electric fields is compactly embedded in L2. We build a three-field variational formulation equivalent to Maxwell system for sign-shifting magnetic coefficients and show that, under some suitable conditions, the formulation fits into the coercive plus compact framework.