The paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium, which widely occur in practical applications. The case where the obstacle is buried in a two-layered piecewise homogeneous medium is considered but the results can be extended to the multi-layered case. The well-posedness of the corresponding direct problem is established by means of the integral equation method.
It was proved previously [see X. Liu and B. Zang, Appl. Anal. 88, No. 9, 1339–1355 (2009; Zbl 1176.78010)], under the condition that the wave numbers in the innermost and outmost homogeneous layers coincide and is known in advance, that the obstacle with its physical property can be uniquely determined from knowledge of the electric far-field pattern for incident plane waves. In the present paper this restriction is removed by establishing a new mixed reciprocity relation. It is proved that the penetrable interface between layers can also be uniquely determined.