A general perturbation formula for electromagnetic fields in presence of low volume scatterers (Q2839153)

The paper is devoted to the asymptotic behavior of scattered electromagnetic fields, i.e. the difference between the fields with and without scatterer, as the volume of the scatterer tends to zero. The only regularity assumptions on the scatterer are that it is measurable and well separated from the boundary of the homogeneous background medium. The author derives a general formula for the leading order term in the corresponding asymptotic expansion. This formula generalizes and unifies earlier results for small conductivity inhomogeneities and yields new asymptotic expressions for practically important cases like thin tubes or thin penetrable cracks. The results can also be extended to unbounded domains.