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

Abstract

We consider the Maxwell operator $\text{A}$ 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_$\text{A}$(z) = ($\text{A}$ − 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 L²-topology. In particular, this continuity holds at the thresholds.