Electromagnetic waves in a three-dimensional asymmetric dielectric slab waveguide
type: Item
instance of: scholarly article
title: Electromagnetic waves in a three-dimensional asymmetric dielectric slab waveguide
zbMATH Open document ID: 0585.35081
DOI: 10.1016/0022-247X(85)90175-1
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35P10
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 78A40
zbMATH DE Number: 3937696
zbMATH Keywords: Maxwell equations
zbMATH Keywords: spectral analysis
zbMATH Keywords: explicit representation for the Green's function
zbMATH Keywords: resolvent kernel
zbMATH Keywords: Parseval identity
zbMATH Keywords: eigenfunctions
author: D. S. Gilliam
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3937696