Maxwell's equations in a periodic structure

Authors:
Xinfu Chen and Avner Friedman

Journal:
Trans. Amer. Math. Soc. **323** (1991), 465-507

MSC:
Primary 35Q60; Secondary 35P25, 45B05, 78A45

DOI:
https://doi.org/10.1090/S0002-9947-1991-1010883-1

MathSciNet review:
1010883

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider a diffraction of a beam of particles in when the dielectric coefficient is a constant above a surface and a constant below a surface , and the magnetic permeability is constant throughout . is assumed to be periodic in the direction and of the form arbitrary. We prove that there exists a unique solution to the time-harmonic Maxwell equations in having the form of refracted waves for and of transmitted waves for if and only if there exists a unique solution to a certain system of two coupled Fredholm equations. Thus, in particular, for all the 's, except for a discrete number, there exists a unique solution to the Maxwell equations.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1991-1010883-1

Keywords:
Maxwell's equations,
transmission,
reflection,
Fredholm equations

Article copyright:
© Copyright 1991
American Mathematical Society