Reciprocity-based compound symmetries in inhomogeneous chiral and Tellegen media [Invited]

We show that a very wide class of inhomogeneous structures consisting of materials with Tellegen coupling possesses compound symmetries. These symmetries are combinations of reciprocity and a geometric operation, such as spatial inversion, mirror, or rotation operations. We show that these compound symmetries strongly constrain the scattering matrix and the band structure of Tellegen structures. The symmetry analysis also provides a unified treatment of chiral and Tellegen media on an equal footing. To illustrate our results, we provide numerical studies of transmission, reflection, and band structure for one-dimensional multilayer systems as well as scattering from a sphere in three dimensions. Our findings show that many known results for Tellegen and chiral media can be obtained using this compound symmetry framework, and also predict new results based on such symmetry.