In one minute

Buhmann, Butcher and Scheel formulate macroscopic quantum electrodynamics for the most general linear absorbing media, without assuming Onsager reciprocity. Such responses matter because cross-susceptibilities arise naturally in chiral metamaterials, topological insulators and moving media. For nonlocal media, they base field quantisation on the conductivity tensor and the electromagnetic Green tensor. For local media, permittivity, permeability and magnetoelectric susceptibilities give an explicitly duality-invariant scheme. They work out explicitly how the fields, the response functions and the Green tensor behave under duality transformations. Duality invariance holds as a continuous symmetry only when non-reciprocal responses are allowed, whereas simple isotropic media keep only a discrete duality symmetry.

Macroscopic quantum electrodynamics in nonlocal and nonreciprocal media