Reciprocity and equivalence in reciprocal and non-reciprocal media through reflection transformations of the current distributions

The electromagnetic wave fields generated by arbitrary electric and equivalent magnetic current distributions are expressed by means of a Maxwell operator in anisotropic, gyrotropic or bianisotropic media. Provided that the constitutive tensorK(r), (which relates the wave-field vectorsD andB toE andH), has in each case the appropriate symmetry in its spatial variation, Lorentz-type reciprocity relations are obtained connecting the given current distributions and their wave fields with a transformed (reflected) set of current distributions and their fields. Reflections are with respect to a plane, a line or a point, depending on the symmetry structure of the constitutive tensor. Modified Lorentz reciprocity appears as a special case of the reflection transformations. A related set of reflection transformations yields equivalence (rather than reciprocity) relationships, in which mirrored current distributions generate mirrored wave fields. Various applications are discussed.