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In this paper various extensions of the design strategy of transformationmedia are proposed. We show that it is possible to assign different transformedspaces to the field strength tensor (electric field and magnetic induction) andto the excitation tensor (displacement field and magnetic field), resp. In thisway, several limitations of standard transformation media can be overcome. Inparticular it is possible to provide a geometric interpretation ofnon-reciprocal as well as indefinite materials. We show that thesetransformations can be complemented by a continuous version ofelectric-magnetic duality and comment on the relation to the complementaryapproach of field-transforming metamaterials.

Generalized transformation optics from triple spacetime metamaterials