An inverse electromagnetic scattering problem for a bi-periodic inhomogeneous layer on a perfectly conducting plate

This article is concerned with uniqueness for reconstructing a periodic inhomogeneous medium sitting on a perfectly conducting plate. We deal with the problem in the framework of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation is obtained for two refractive indices and then used to prove that the refractive index can be uniquely identified from a knowledge of the incident fields and the total tangential electric field on a plane above the inhomogeneous medium, utilizing the eigenvalues and eigenfunctions of a quasi-periodic Sturm–Liouville eigenvalue problem.