Small perturbation of a surface: Full Maxwell's equations

In this paper, we derive high-order terms in the asymptotic expansions of the boundary perturbations of the electromagnetic fields resulting from small perturbations of the shape of an inhomogeneity with CdCd-boundary in RdRd, for d=2,3d=2,3. For such solutions we provide a rigorous derivation that extends those already derived for small volume conductivity inhomogeneities. Our formulas may be expected to develop effective algorithms, aimed at determining certain properties of the shape of an object based on electromagnetic boundary measurements.