Quantizing polaritons in inhomogeneous dissipative systems

In this article we provide a a general analysis of canonical quantization for polaritons in dispersive and dissipative electromagnetic media. We compare several approaches based either on the Huttner Barnett model [B. Huttner, S. M. Barnett, Phys. Rev. A $\mathbf{\text{46}}$, 4306 (1992)] or the Green function, Langevin noise method [T. Gruner, D.-G. Welsch, Phys. Rev. A $\mathbf{\text{53}}$, 1818 (1996)] which includes only material oscillators as fundamental variables. We show in order to preserve unitarity, causality and time symmetry one must necessarily include with an equal footing both electromagnetic modes and material fluctuations on the evolution equations. This becomes particularly relevant for all nanophotonics and plasmonics problems involving spatially localized antennas or devices.