The most general classes of Tellegen media reducible to simple reciprocal media: A geometrical approach

Duality mappings allow to transform a nonreciprocal achiral bi-isotropic medium (Tellegen medium) into a conventional reciprocal material leaving the free space invariant. In particular, the analytical solutions of electromagnetic problems involving a single Tellegen medium and a vacuum can be found by applying the inverse duality transformation to the solution of the duality transformed problem wherein the materials are conventional reciprocal media. Here, based on the geometrical interpretation of duality transformations in the Riemann sphere, we derive the most general classes of Tellegen media that are reducible to simple isotropic media (SIMs) under the same duality transformation. It is shown that Tellegen media can be identified with the points of the Riemann sphere. Moreover, duality transformations are classified into different categories according to their geometrical actions on the sphere. We apply the developed theory to periodic structures formed by Tellegen media showing how the wave propagation in these complex structures can be easily studied using duality transformations. Furthermore, to unveil the role of the nonreciprocal response, we investigate the wave propagation in Tellegen periodic structures wherein the pertinent materials cannot be reduced to conventional media.