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A Riemann–Hilbert Problem for Propagation of Electromagnetic Waves in an Inhomogeneous, Dispersive Ω Waveguide

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Abstract

We consider the inverse scattering problem for a model of electromagnetic wave propagation in a rectangular waveguide filled with dispersive Ω material. The waveguide is inhomogeneous in the longitudinal direction but homogeneous in the transverse directions. Dispersive properties of the material are described by a single-resonance Lorentz model. By reformulating the scattering problem in the frequency domain as a Riemann–Hilbert problem, we prove that the constitutive parameters of the inhomogeneous waveguide are reconstructed uniquely from the scattering data.

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  1. Mathematical Division, Institute for Low Temperature Physics, 47 Lenin Avenue, 310164, Kharkov, Ukraine

    Dmitry Shepelsky

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  1. Dmitry Shepelsky
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Shepelsky, D. A Riemann–Hilbert Problem for Propagation of Electromagnetic Waves in an Inhomogeneous, Dispersive Ω Waveguide. Mathematical Physics, Analysis and Geometry 3, 179–193 (2000). https://doi.org/10.1023/A:1009826621082

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  • DOI: https://doi.org/10.1023/A:1009826621082

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