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This paper is concerned with analysis of electromagnetic wave scattering byan obstacle which is embedded in a two-layered lossy medium separated by anunbounded rough surface. Given a dipole point source, the direct problem is todetermine the electromagnetic wave field for the given obstacle and unboundedrough surface; the inverse problem is to reconstruct simultaneously theobstacle and unbounded rough surface from the electromagnetic field measured ona plane surface above the obstacle. For the direct problem, a new boundaryintegral equation is proposed and its well-posedness is established. Theanalysis is based on the exponential decay of the dyadic Green function forMaxwell's equations in a lossy medium. For the inverse problem, the globaluniqueness is proved and a local stability is discussed. A crucial step in theproof of the stability is to obtain the existence and characterization of thedomain derivative of the electric field with respect to the shape of theobstacle and unbounded rough surface.

Inverse obstacle scattering for Maxwell's equations in an unbounded structure