Electromagnetic waves in a three-dimensional asymmetric dielectric slab waveguide
The paper is concerned with an initial value problem for the Maxwell equations in the structure composed of a dielectric slab of finite thickness placed between two infinite dielectric half spaces. The study is based on an application of spectral analysis to the Maxwell operator defined in an appropriate Hilbert space. The author finds the explicit representation for the Green's function in the problem studied. It requires computation of the reflection and scattered matrices needed to satisfy interface conditions at the boundaries of the slab. While straightforward approach to this computation is a formidable task the author finds a simple method for constructing the matrices. It is shown that the resolvent kernel constructed in the paper does deliver the resolvent for the Maxwell operator. A complete set of generalized eigenfunctions is derived and is then used to obtain explicit representations of both the solution group and the Parseval identity. The eigenfunctions obtained are interpreted in terms of TE and TM parts of the plane wave, trapped wave and static modes.
explicit representation for the Green's function
scientific article; zbMATH DE number 3937696