Uniqueness in determining binary grating profiles and refractive indices with a single incoming wave

2021/11/23 by Jianli Xiang, Guanghui Hu, Xiang, Jianli +1
Materials Science · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical methods in inverse problems #Optical Coatings and Gratings

paper · pdf · doi:10.48550/arxiv.2111.11772

openalex publication_date 2021/11/23 · openalex created_date 2021/12/06 · openalex updated_date 2026/07/28

Abstract

We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary 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.

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