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Zbl 1219.35363
Liu, Xiaodong; Zhang, Bo; Yang, Jiaqing
The inverse electromagnetic scattering problem in a piecewise homogeneous medium. (English)
[J] Inverse Probl. 26, No. 12, Article ID 125001, 19 p. (2010). ISSN 0266-5611

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. \par It was proved previously [see {\it X. Liu} and {\it 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 $S_0$ 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.
[Elena V. Tabarintseva (Chelyabinsk)]

MSC 2000:: *35R30 Inverse problems for PDE
78A46 Inverse scattering problems

Keywords: inverse scattering problem; piecewise homogeneous medium; uniqueness of the solution

Citations: Zbl 1176.78010

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