Generalized transformation optics from triple spacetime metamaterials

In this paper various extensions of the design strategy of transformation media are proposed. We show that it is possible to assign different transformed spaces to the field strength tensor (electric field and magnetic induction) and to the excitation tensor (displacement field and magnetic field), resp. In this way, several limitations of standard transformation media can be overcome. In particular it is possible to provide a geometric interpretation of non-reciprocal as well as indefinite materials. We show that these transformations can be complemented by a continuous version of electric-magnetic duality and comment on the relation to the complementary approach of field-transforming metamaterials.