A novel method in determining a layered periodic structure

Abstract

Abstract This paper is concerned with the inverse scattering of time-harmonic waves by a penetrable structure. By applying the integral equation method, we establish the uniform L α p ( 1 < p ≤ 2 ) $L^{p}_{\alpha }\ (1< p\leq 2)$ estimates for the scattered and transmitted wave fields corresponding to a series of incident point sources. Based on these a priori estimates and a mixed reciprocity relation, we prove that the penetrable structure can be uniquely identified by means of the scattered field measured only above the structure induced by a countably infinite number of quasi-periodic incident plane waves.

Keywords

• Inverse scattering
• Uniqueness
• L α p $L^{p}_{\alpha }$ estimate
• Periodic structures