Transmission problems in contrasting chiral media

Time harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle embedded in a homogeneous chiral environment. The corresponding transmission problem is reduced, with the use of Beltrami fields, to an integral equation over the interface between the obstacle and the surrounding medium. This integral equation is known to be weakly uniquely solvable except for a discrete set of electromagnetic parameters of the obstacle. We establish classical solvability, and in some interesting cases (mirror conjugated and isoimpedant chiral media) it is shown that unique solvability is established without the exception of any set of electromagnetic parameters.