Duality transformations and green dyadics for bi-anisotropic media

Duality transformation, defined as a linear transformation between electromagnetic six-vectors, is known to transform electromagnetic problems in a linear (bi-anisotropic) medium to electromagnetic problems in another linear medium. This gives a possibility to create analytical expressions for the Green dyadic for media which are dual to simpler media with known Green dyadic solutions. Different forms of the duality transformation of fields are considered and their properties in terms of eigenfunctions are discussed. After this, corresponding transformations to medium parameters are considered in terms of their eigenmedia, i.e., media which are transformed in a simple manner. As a particular example a nonreciprocal anisotropic medium is considered, for which the Green dyadic was recently constructed in analytic form. It is shown that when the medium is transformed to a nonreciprocal bi-anisotropic medium, its Green dyadic can be obtained through the same transformation.