Macroscopic quantum electrodynamics and duality in non-local and   Onsager-violating media
  We formulate macroscopic quantum electrodynamics for the most general linear, absorbing media. In particular, Onsager reciprocity is not assumed to hold. For media with a non-local response, the field quantisation is based on the conductivity tensor and the Green tensor for the electromagnetic field. For a local medium response, we introduce the permittivity, permeability and magnetoelectric susceptibilities to obtain an explicitly duality-invariant scheme. We find that duality invariance only holds as a continuous symmetry when non-reciprocal responses are allowed for. 
Stefan Yoshi Buhmann, David T. Butcher, Stefan Scheel
quant-ph