Inverse medium scattering from periodic structures with fixed-direction incoming waves. (English) Zbl 1507.65224
Summary: This paper is concerned with inverse time-harmonic acoustic and electromagnetic scattering from an infinite biperiodic medium (diffraction grating) in three dimensions. In the acoustic case, we prove that the near-field data of fixed-direction plane waves incited at multiple frequencies uniquely determine a refractive index function which depends on two variables. An analogous uniqueness result holds for time-harmonic Maxwell’s system if the inhomogeneity is periodic in one direction and remains invariant along the other two directions. Uniqueness for recovering (non-periodic) compactly supported contrast functions are also presented.
MSC:
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 76Q05 | Hydro- and aero-acoustics |
| 78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |
Keywords:
uniqueness; inverse scattering; multi-frequency data; periodic media; acoustic waves; electromagnetic wavesReferences:
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