MATHEMATICAL-ANALYSIS OF ELECTROMAGNETIC OPEN WAVE-GUIDES

The study of open electromagnetic waveguides amounts to the spectral a nalysis of selfadjoint operators with noncompact resolvents. In this a rticle, we are particularly interested in obtaining existence results for guided modes and in studying their properties. The noticeable feat ure of our work is that we consider the case where both the dielectric permittivity epsilon and the magnetic permeability mu may vary in the cross section of the waveguide. The originality of our approach, with respect to previous works is that it takes into account the divergenc e-free condition in the functional framework. In this paper we exhibit various existence results depending on various assumptions on epsilon and mu, we study the properties of the thresholds and we point out wh at happens at low and high frequencies.