Global uniqueness in determining rectangular periodic structures by scattering data with a single wave number

DOI10.1515/156939403769237024zbMath1038.78014OpenAlexW2037113093MaRDI QIDQ4432576

Johannes Elschner, Gunther Schmidt, Masahiro Yamamoto

Publication date: 27 October 2003

Published in: Journal of Inverse and Ill-posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/156939403769237024

zbMATH Keywords

Helmholtz equationinverse scattering problemglobal uniquenesstransverse electric polarizationnear-field observationsrectangular periodic structurestransverse magnetic polarization

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

Related Items (10)

Uniqueness results in the inverse scattering problem for periodic structures ⋮ An inverse scattering problem for a layered periodic structure ⋮ Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case ⋮ A linear sampling method for inverse problems of diffraction gratings of mixed type ⋮ Uniqueness in Inverse Diffraction Grating Problems With Infinitely Many Plane Waves at a Fixed Frequency ⋮ Some recent progress on inverse scattering problems within general polyhedral geometry ⋮ Uniqueness in determining polygonal periodic structures ⋮ Unique determination of periodic polyhedral structures by scattered electromagnetic fields II: The resonance case ⋮ Uniqueness in inverse elastic scattering from unbounded rigid surfaces of rectangular type ⋮ Unique determination of periodic polyhedral structures by scattered electromagnetic fields

Cites Work

• Diophantine approximation
• Inverse acoustic and electromagnetic scattering theory.
• Inverse problems for scattering by periodic structures
• Inverse scattering for periodic structures: stability of polygonal interfaces
• A uniqueness theorem for an inverse problem in periodic diffractive optics
• Schiffer's theorem in inverse scattering theory for periodic structures
• An Inverse Problem in Periodic Diffractive Optics: Reconstruction of Lipschitz Grating Profiles
• An inverse problem in diffractive optics: conditional stability

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