Maxwell’s equations in a periodic structure
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- by Xinfu Chen and Avner Friedman PDF
- Trans. Amer. Math. Soc. 323 (1991), 465-507 Request permission
Abstract:
Consider a diffraction of a beam of particles in ${\mathbb {R}^3}$ when the dielectric coefficient is a constant ${\varepsilon _1}$ above a surface $S$ and a constant ${\varepsilon _2}$ below a surface $S$, and the magnetic permeability is constant throughout ${\mathbb {R}^3}$. $S$ is assumed to be periodic in the ${x_1}$ direction and of the form ${x_1} = {f_1}(s), {x_3} = {f_3}(s), {x_2}$ arbitrary. We prove that there exists a unique solution to the time-harmonic Maxwell equations in ${\mathbb {R}^3}$ having the form of refracted waves for ${x_3} \ll 1$ and of transmitted waves for $- {x_3} \gg 1$ if and only if there exists a unique solution to a certain system of two coupled Fredholm equations. Thus, in particular, for all the $\varepsilon$’s, except for a discrete number, there exists a unique solution to the Maxwell equations.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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