Principe d'absorption limite pour l'opérateur de Maxwell dans un milieu bihomogène

Abstract

We consider the Maxwell operator A that describes 3D electromagnetic wave propagation in an infinite cylindrical wave guide with a rectangular section, where the medium is made of two homogeneous parts separated by a vertical interface. The spectral analysis of this operator points out a countable family of real numbers in the spectrum called thresholds, and the resolvent operator R A (z) = ( A − z) −1, Im (z)) ≠ 0, can be extended (‘limiting absorption principle’) continuously to the lower or upper half-planes (origin excepted) in a suitable weighted L 2-topology. In particular, this continuity holds at the thresholds.