A Geometrical Approach to Duality Transformations for Tellegen Media

Duality transformations are of key importance in the study of Tellegen (i.e., achiral and nonreciprocal biisotropic) media: they often can reduce electromagnetic problems with both Tellegen media and simple isotropic media (SIMs), to simpler problems just with SIMs. Here, we generalize known results and derive the most general classes of Tellegen media that can be reduced, under the same duality transformation, to SIMs. Furthermore, it is shown that a family of isorefractive Tellegen media can be completely mapped onto the Riemann sphere where duality transformations are conformal mappings. Depending on their geometrical action in the Riemann sphere the duality transformations are then classified as: 1) generalized rotations; 2) Lorentz boosts; or 3) Galilean boosts. Applications include a wide range of structures containing Tellegen media: from (open and closed) waveguides to photonic crystals.