Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case. (1st May 2023)

• Record Type: Journal Article
• Authors: Xiang, Jianli; Hu, Guanghui
• Is Part Of: Inverse problems. Volume 39:Number 5(2023)
• Publication Date: 2023-05-01
• Subjects: inverse scattering -- uniqueness -- Helmholtz equation -- transmission conditions -- rectangular grating; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/acc41c
• Languages: English
• ISSNs: 0266-5611

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.