Commutation-relation-preserving ladder operators for propagating optical fields in nonuniform lossy media

TL;DR

This paper introduces a quantum electrodynamics formalism that accurately separates left and right propagating optical fields in nonuniform lossy media, resolving longstanding anomalies in field commutation relations.

Contribution

The work develops a generalized QFED model with a density of states concept to unambiguously distinguish propagating fields and resolve commutation anomalies.

Findings

Successfully separates left and right propagating fields in complex media

Resolves the anomaly in commutation relations of confined propagating fields

Provides a unified quantum description of interference effects

Abstract

We have recently developed a quantized fluctuational electrodynamics (QFED) formalism to describe the quantum aspects of local thermal balance formation and to formulate the electromagnetic field ladder operators so that they no longer exhibit the anomalies reported for resonant structures. Here we show how the QFED can be used to resolve between the left and right propagating fields to bridge the QFED and the quantum optical input-output relations commonly used to describe selected quantum aspects of resonators. The generalized model introduces a density of states concept describing interference effects, which is instrumental in allowing an unambiguous separation of the fields and related quantum operators into left and right propagating parts. In addition to providing insight on the quantum treatment of interference, our results also provide the conclusive resolution of the long-standing enigma of the anomalous commutation relations of partially confined propagating fields.