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arXiv · 2402.11230

Time-harmonic scattering by locally perturbed periodic structures with Dirichlet and Neumann boundary conditions

Guanghui Hu·Andreas Kirsch
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Abstract

The paper is concerned with well-posedness of TE and TM polarizations of time-harmonic electromagnetic scattering by perfectly conducting periodic surfaces and periodically arrayed obstacles with local perturbations. The classical Rayleigh Expansion radiation condition does not always lead to well-posedness of the Helmholtz equation even in unperturbed periodic structures. We propose two equivalent radiation conditions to characterize the radiating behavior of time-harmonic wave fields incited by a source term in an open waveguide under impenetrable boundary conditions. With these open waveguide radiation conditions, uniqueness and existence of time-harmonic scattering by incoming point source waves, plane waves and surface waves from locally perturbed periodic structures are established under either the Dirichlet or Neumann boundary condition. A DtN operator without using the Green's function is constructed for proving well-posedness of perturbed scattering problems.

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Guanghui Hu, Andreas Kirsch. 2024-02-17. Time-harmonic scattering by locally perturbed periodic structures with Dirichlet and Neumann boundary conditions. https://arxiv.org/abs/2402.11230

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