Inverse electromagnetic diffraction by biperiodic dielectric gratings. (19th June 2017)

• Record Type: Journal Article
• Authors: Jiang, Xue; Li, Peijun
• Is Part Of: Inverse problems. Volume 33:Number 8(2017:Aug.)
• Publication Date: 2017-06-19
• Subjects: Maxwell's equations -- inverse diffraction -- near-field imaging -- biperiodic gratings; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa76b9
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Consider the incidence of a time-harmonic electromagnetic plane wave onto a biperiodic dielectric grating, where the surface is assumed to be a small and smooth perturbation of a plane. The diffraction is modeled as a transmission problem for Maxwell's equations in three dimensions. This paper concerns the inverse diffraction problem which is to reconstruct the grating surface from either the diffracted field or the transmitted field. A novel approach is developed to solve the challenging nonlinear and ill-posed inverse problem. The method requires only a single incident field and is realized via the fast Fourier transform. Numerical results show that it is simple, fast, and stable to reconstruct biperiodic dielectric grating surfaces with super-resolved resolution.