
The problem indicated in the title gives rise to a Maxwell problem. However, looking for guided waves in the \(x_3\)-direction and assuming the medium to be \(x_3\)-independent, the author is left with two scalar problems with periodic coefficients. The corresponding Green integral operators and their spectral properties are used for a characterization of guided modes. Some numerical experiments are included.
Integral operators, integral equations, Applied Mathematics, Green's function, Antennas, waveguides in optics and electromagnetic theory, Photonic crystals, wave guides, Maxwell equations, periodic coefficients, Photonic fibers, PDEs in connection with optics and electromagnetic theory, Integral equation
Integral operators, integral equations, Applied Mathematics, Green's function, Antennas, waveguides in optics and electromagnetic theory, Photonic crystals, wave guides, Maxwell equations, periodic coefficients, Photonic fibers, PDEs in connection with optics and electromagnetic theory, Integral equation
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