Quantizing polaritons in inhomogeneous dissipative systems

TL;DR

This paper analyzes the canonical quantization of polaritons in complex media, emphasizing the importance of including both electromagnetic modes and material fluctuations to ensure physical consistency, especially in nanophotonics.

Contribution

It compares different quantization approaches and demonstrates the necessity of incorporating both electromagnetic and material variables for accurate modeling.

Findings

Including both electromagnetic modes and material fluctuations preserves unitarity and causality.

The analysis is particularly relevant for nanophotonics and plasmonics applications.

Different quantization methods are contrasted and evaluated.

Abstract

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 \textbf{46}, 4306 (1992)] or the Green function, Langevin noise method [T. Gruner, D.-G. Welsch, Phys. Rev. A \textbf{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.