Core Concepts
Uniqueness and existence in time-harmonic scattering by Dirichlet periodic curves.
Abstract
The article discusses the well-posedness of time-harmonic scattering by locally perturbed periodic curves of Dirichlet kind. It explores properties of the Green’s function, proving new results for scattering of plane waves at a propagative wave number. Uniqueness in forward scattering is ensured through an orthogonal constraint condition. The inverse problem of determining defects is addressed with uniqueness results using point source and plane waves. The TE polarization case is modeled by the Dirichlet boundary value problem of the Helmholtz equation. Mathematical analysis includes radiation conditions, numerical approximations, and inverse scattering problems.
Introduction: Concerns TE polarization of electromagnetic scattering from conducting gratings with a localized defect.
Radiation Conditions: Describes mathematical model for TE polarization electromagnetic scattering.
Properties of Green’s Function: Discusses properties and decomposition of Green's function for perturbed and unperturbed problems.
Scattering of Plane Waves: Addresses uniqueness and existence in time-harmonic scattering at propagative wave numbers.
Stats
2π-periodic domain with Lipschitz curve boundary Γ.
Uniqueness assumption on forward scattering model for plane wave incidences.
Guided/Floquet wave modes to homogeneous problem decay exponentially orthogonal to periodicity direction.