Inside-Outside Duality and the Determination of Electromagnetic Interior Transmission Eigenvalues

We introduce an inside-outside duality approach for the determination of interior transmission eigenvalues of a possibly anisotropic dielectric electromagnetic scattering object using time-harmonic electromagnetic far field data. To this end, we exploit a self-adjoint factorization of the far field operator to link the electromagnetic interior transmission eigenvalues to the maximal or minimal phase of the eigenvalues of the corresponding far field operator, depending on whether the sign of the contrast function is positive or negative.