Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case
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Published:2023-03-27
Issue:5
Volume:39
Page:055004
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ISSN:0266-5611
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Container-title:Inverse Problems
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language:
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Short-container-title:Inverse Problems
Author:
Xiang JianliORCID,
Hu GuanghuiORCID
Abstract
Abstract
We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a rectangular grating profile together with the refractive index beneath it can be uniquely determined by the near-field observation data incited by a single plane wave and measured on a line segment above the grating. Our approach relies on the expansion of solutions to the Helmholtz equation and the corner singularity analysis of solutions to the inhomogeneous Laplace equation with a piecewise continuous source term in a sector. This paper also contributes to corner scattering theory for the Helmholtz equation in a special non-convex domain.
Funder
Natural Science Foundation of Hubei Province
Fundamental Research Funds for Central Universities in China
National Natural Science Foundation of China
Subject
Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science
Cited by
1 articles.
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