Electromagnetic Inverse Problems and Generalized Sommerfeld Potentials

In this article we study the inverse boundary value problem for Maxwell’s equation; that is, we determine the scalar permeability, permissibility, and conductivity of a body from electromagnetic field measurements outside the body. In this paper, the problem is approached by using certain generalized Sommerfeld potentials that are shown to satisfy a vector-valued Schrödinger equation. By using these potentials, the inverse boundary value problem is reduced to the problem of determining the potential of this second-order operator. Further, it is shown that the electromagnetic material parameters can be determined by using electric or magnetic dipole point sources only.