Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: incandecence and luminescence in arbitrary geometries

TL;DR

This paper introduces a volume-current formulation for electromagnetic fluctuations in inhomogeneous media, enabling efficient calculations of thermal radiation, heat transfer, and luminescence in complex geometries using trace formulas and volume-integral equations.

Contribution

It extends previous heat exchange and Casimir interaction models to inhomogeneous media, employing volume-integral equations for efficient computation of electromagnetic fluctuations.

Findings

Trace formulas describe power and momentum transfer in inhomogeneous media.

Low-rank matrix properties enable fast iterative computations.

Method accurately predicts radiation in complex, spatially varying geometries.

Abstract

We describe a fluctuating volume--current formulation of electromagnetic fluctuations that extends our recent work on heat exchange and Casimir interactions between arbitrarily shaped homogeneous bodies [Phys. Rev. B. 88, 054305] to situations involving incandescence and luminescence problems, including thermal radiation, heat transfer, Casimir forces, spontaneous emission, fluorescence, and Raman scattering, in inhomogeneous media. Unlike previous scattering formulations based on field and/or surface unknowns, our work exploits powerful techniques from the volume--integral equation (VIE) method, in which electromagnetic scattering is described in terms of volumetric, current unknowns throughout the bodies. The resulting trace formulas (boxed equations) involve products of well-studied VIE matrices and describe power and momentum transfer between objects with spatially varying material properties and fluctuation characteristics. We demonstrate that thanks to the low-rank properties of the associatedmatrices, these formulas are susceptible to fast-trace computations based on iterative methods, making practical calculations tractable. We apply our techniques to study thermal radiation, heat transfer, and fluorescence in complicated geometries, checking our method against established techniques best suited for homogeneous bodies as well as applying it to obtain predictions of radiation from complex bodies with spatially varying permittivities and/or temperature profiles.