Unified position-dependent photon-number quantization in layered structures

TL;DR

This paper extends a position-dependent quantization scheme to include magnetic fields, enabling comprehensive analysis of electromagnetic fields, forces, and thermal distributions in layered structures with potential experimental verification.

Contribution

The authors develop a unified quantization framework for electric and magnetic fields in layered media, allowing detailed modeling of electromagnetic forces and thermal effects.

Findings

Electric and magnetic field temperatures oscillate spatially within cavities.

Effective photon number remains position-independent in lossless media.

Electromagnetic force direction varies with frequency, position, and thickness.

Abstract

We have recently developed a position-dependent quantization scheme for describing the ladder and effective photon-number operators associated with the electric field to analyze quantum optical energy transfer in lossy and dispersive dielectrics [Phys. Rev. A, 89, 033831 (2014)]. While having a simple connection to the thermal balance of the system, these operators only described the electric field and its coupling to lossy dielectric bodies. Here we extend this field quantization scheme to include the magnetic field and thus to enable description of the total electromagnetic field and discuss conceptual measurement schemes to verify the predictions. In addition to conveniently describing the formation of thermal balance, the generalized approach allows modeling of the electromagnetic pressure and Casimir forces. We apply the formalism to study the local steady state field temperature distributions and electromagnetic force density in cavities with cavity walls at different temperatures. The calculated local electric and magnetic field temperatures exhibit oscillations that depend on the position as well as the photon energy. However, the effective photon number and field temperature associated with the total electromagnetic field is always position-independent in lossless media. Furthermore, we show that the direction of the electromagnetic force varies as a function of frequency, position, and material thickness.