Near-field imaging of periodic interfaces in multilayered media

Abstract

This paper is concerned with the inverse problem of scattering of time-harmonic electromagnetic waves by a penetrable multilayered periodic structure. The structure separates the whole space into three regions: the medium above and below the structure is assumed to be homogeneous but with different wave numbers, and the medium inside the structure is assumed to be inhomogeneous characterized by the refractive index. We prove, under certain conditions, that the factorization method can be used to reconstruct the upper interface from the scattered near-field data measured only above the structure and generated by a countably infinite number of downward propagating incident waves merely from the top region, leading to a fast imaging algorithm. A similar result can be obtained for reconstructing the lower interface from the scattered near-field data measured only below the structure, corresponding to a countably infinite number of upward propagating incident waves also merely from the bottom region. Thus, our approach is applicable, even if one merely has access to the object under investigation from one side. Finally, numerical examples are presented to illustrate the effectiveness of the inversion algorithm.