Microscopic calculation of noise current operators for electromagnetic field quantization in absorbing material systems

Abstract

We present a microscopic quantization scheme for the electromagnetic field in dispersive and lossy dielectrics of arbitrary geometry. This method also describes anisotropic media and media driven by light field via a spatially nonlocal permittivity. The method removes the need for complicated diagonalization of material, reservoir and field variables and allows us to include the effect of all the material excitations. Dissipation inside the medium is described by considering the coupling of the polarization quanta of the system with the reservoir oscillators in the usual Langevin approach.

QED of excitons with nonlocal susceptibility in arbitrarily structured dielectrics

“…͑45͔͒ and commutation relation ͓Eq. ͑48͔͒ are just the ones discussed by Savasta and co-workers 39,40 and they also have the same forms as those of Raabe et al 17 Further, Eq. ͑48͒ can be understood as a natural result from the fluctuation theorem, as discussed in Refs.…”

“…II, the QED of media with the nonlocality has already been discussed in a few studies. From the viewpoint of practical applications, we compare our theory with the studies of Di Stefano and co-workers [38][39][40] and Raabe et al 17 Di Stefano et al discussed the quantum-well structures of dispersive and absorptive dielectrics with the nonlocality in Ref. 38, and their theory is generalized to enable the consideration of arbitrary structures in Refs.…”

“…5 As a pioneering study on a full-quantum theory with the nonlocality, Jenkins and Mukamel 37 discussed molecular crystals in d dimensions ͑d =1,2,3͒, where the relative motion of excitons is localized at a single molecule and the center of mass moves between molecules due to the dipoledipole interaction. While their theory concentrates on treating the resonant polarization without nonradiative relaxation, recently, the nonlocality has been introduced into the field quantization in dispersive and absorptive media, 16,17,[38][39][40][41] and some studies have demonstrated the application of their theories for specific structures. 17,38 Di Stefano et al 38 discussed excitons with the nonlocality in media with spatial translation symmetries broken along one dimension, and they practically calculated the spatial and frequency dependences of the vacuum-field fluctuation in a semiconductor quantumwell structure.…”

“…17,38 Di Stefano et al 38 discussed excitons with the nonlocality in media with spatial translation symmetries broken along one dimension, and they practically calculated the spatial and frequency dependences of the vacuum-field fluctuation in a semiconductor quantumwell structure. Thereafter, they extended their theory to an arbitrary 3D structure 39 and discussed the input-output relations in scattering systems. 40 On the other hand, Bechler 41 performed the field quantization for homogeneous systems with the nonlocality by using the path-integral method, and Suttorp 16 performed the same for nonlocal, inhomogeneous, and anisotropic systems by using the diagonalization method.…”

Quantum electrodynamics near a dispersive and absorbing dielectric

“…In this approach, the field equations are solved by using the Green's function of the wave equation, and the noise-current operators and their properties play a major role in describing the dynamics of the coupled field-dielectric system. A few papers have provided an a posteriori microscopic justification of such a procedure by deriving the commutative properties of the noise-current operators that were otherwise introduced ad hoc [9][10][11].…”