Abstract
The Purcell effect, i.e., the modification of the spontaneous emission rate by optical interference, profoundly affects the light-matter coupling in optical resonators. Fully describing the optical absorption, emission, and interference of light hence conventionally requires combining the full Maxwell’s equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping and scattering coefficients derived from the recently introduced quantized fluctuational electrodynamics (QFED) framework. In addition to describing the nonlocal optical interference processes as local directionally resolved effects, this allows reformulating the well known and widely used radiative transfer equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices.
Highlights
The Purcell effect, i.e., the modification of the spontaneous emission rate by optical interference, profoundly affects the light-matter coupling in optical resonators
The connection between the quantized fluctuational electrodynamics (QFED) and the radiative transfer equation (RTE) model can be established by comparing pointwise the rate of change of the photon number due to the absorption and emission in both the RTE and QFED models
The approach involves deriving the quantum optically exact damping and scattering coefficients from the position dependent expectation values of the propagating photon-number operators provided by the QFED framework
Summary
The Purcell effect, i.e., the modification of the spontaneous emission rate by optical interference, profoundly affects the light-matter coupling in optical resonators. This limitation fundamentally arises from the challenge to separately attribute the interference induced modifications in the light-matter coupling[6,7,8] to the propagating modes of the system To overcome this limitation and to provide a physically transparent relation between the various optical density of states concepts[7, 9,10,11] and the local propagating field interactions, we derive quantum optically exact damping and scattering coefficients that allow including all interference related effects directly in the RTE model of stratified media. Where the terms ρσ and ρi,σ, i ∈ {IF, NL±} are the local and nonlocal densities of states presented in Supplemental Material and in ref. 9
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