Unified position-dependent photon-number quantization in layered structures

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.

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

“…(1). After integration, the LDOS can also be expressed in the more familiar form in terms of the imaginary part of the Green's function [4]. Using this definition, the NLDOS ρ NL (x,ω,x ) accounts for both the electric-field (term |G| 2 ) and the magnetic-field (term |∂G/(k∂x)| 2 ) contributions.…”

“…This requirement leads to conceptually simple definitions for the position-dependent ladder and photon-number operators as a weighted sum over the incident fields and the noise. For the expectation value of the photon-number operator, for instance, this weighted sum reads as [4] n(…”

“…Originally these anomalies were argued to bear no physical significance, but recently it has been shown that the anomalous commutation relations lead to the existence of a threshold for second harmonic generation when it occurs inside microcavities [1,2]. In addition, anomalies in the commutation relations have also been shown to prevent systematic description of the local thermal balance between the field and interacting media [3,4,10]. Experimental measurements of the onset of the second harmonic generation or the thermal balance formation in microcavities could therefore confirm the theoretical predictions that the conventional mode normalization introducing these anomalies is not sufficient for field quantization of resonant structures.…”

“…To shed more light on the anomalous commutation relations, we have very recently developed a quantized fluctuational electrodynamics (QFED) scheme based on generalizing the fluctuational electrodynamics to quantum optical fields [3,4,10]. Using the QFED approach we were able to formulate the canonical commutation relations preserving ladder and photon-number operators for the total electromagnetic (EM) field [3,4,10].…”

“…Using the QFED approach we were able to formulate the canonical commutation relations preserving ladder and photon-number operators for the total electromagnetic (EM) field [3,4,10]. However, even in the QFED framework, it has not been evident how to separate the ladder and photon-number operators to left and right propagating parts, which is also essential for the final resolution of the anomalies and for bridging the classical propagating wave descriptions and the commutation-relation-preserving quantum descriptions.…”