Electromagnetic scattering and emission by a fixed multi-particle object in local thermal equilibrium: General formalism

Abstract

The majority of previous studies of the interaction of individual particles and multi-particle groups with electromagnetic field have focused on either elastic scattering in the presence of an external field or self-emission of electromagnetic radiation. In this paper we apply semi-classical fluctuational electrodynamics to address the ubiquitous scenario wherein a fixed particle or a fixed multi-particle group is exposed to an external quasi-polychromatic electromagnetic field as well as thermally emits its own electromagnetic radiation. We summarize the main relevant axioms of fluctuational electrodynamics, formulate in maximally rigorous mathematical terms the general scattering-emission problem for a fixed object, and derive such fundamental corollaries as the scattering-emission volume integral equation, the Lippmann-Schwinger equation for the dyadic transition operator, the multi-particle scattering-emission equations, and the far-field limit. We show that in the framework of fluctuational electrodynamics, the computation of the self-emitted component of the total field is completely separated from that of the elastically scattered field. The same is true of the computation of the emitted and elastically scattered components of quadratic/bilinear forms in the total electromagnetic field. These results pave the way to the practical computation of relevant optical observables.

Keywords: Electromagnetic scattering; Fluctuational electrodynamics; Multi-particle scattering–emission equations; Scattering–emission volume integral equation; Thermal emission.

Fig. 1

Schematic representation of the standard scattering–emission problem. The unshaded exterior region V_EXT is unbounded in all directions, whereas the shaded areas collectively represent the interior region of the object V_INT.