Electromagnetic wave propagation in almost periodic media

Citation

Mickelson, Alan Rolf (1978) Electromagnetic wave propagation in almost periodic media. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SZMY-A964. https://resolver.caltech.edu/CaltechTHESIS:03122012-112325331

Abstract

The problem of electromagnetic wave propagation in almost periodic media is investigated and a solution is obtained directly from Maxwell's equations. Techniques to evaluate this solution are developed. These techniques involve a generalization to almost periodic media of the Brillouin diagram of periodic media. The method of invariant imbedding is applied to the coupled mode equations which determine the Brillouin diagram for the purpose of transforming them to coupled Riccati equations. These coupled Riccati equations, when subjected to a single boundary condition, determine the solutions to both the periodic and almost periodic boundary value problems. These evaluation techniques are used to place in evidence similarities and differences of wave propagation in periodic and almost periodic media. It is shown that although the periodic and almost periodic theories agree in many cases of interest, there exist cases in which distinct differences appear. In cases of multi-tone perturbations, the almost periodic theory yields both simpler and more reasonable results than the periodic theory.

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