Quantizing polaritons in inhomogeneous dissipative systems

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

Figure 1

Integration path deformation leading to the proof that Eq. (A1) has no solution in the upper frequency half-plane (see Refs. [90, 103]).