Inverse medium scattering from periodic structures with fixed-direction incoming waves. (29th May 2018)

• Record Type: Journal Article
• Authors: Gibson, Peter; Hu, Guanghui; Zhao, Yue
• Is Part Of: Inverse problems. Volume 34:Number 7(2018:Jul.)
• Publication Date: 2018-05-29
• Subjects: uniqueness -- inverse scattering -- multi-frequency data -- periodic media -- acoustic waves -- electromagnetic waves; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aac3ad
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This paper is concerned with inverse time-harmonic acoustic and electromagnetic scattering from an infinite biperiodic medium (diffraction grating) in three dimensions. In the acoustic case, we prove that the near-field data of fixed-direction plane waves incited at multiple frequencies uniquely determine a refractive index function which depends on two variables. An analogous uniqueness result holds for time-harmonic Maxwell's system if the inhomogeneity is periodic in one direction and remains invariant along the other two directions. Uniqueness for recovering (non-periodic) compactly supported contrast functions are also presented.