Emitter near an arbitrary body: Purcell effect, optical theorem and the Wheeler-Feynman absorber

TL;DR

This paper explores how an emitter's spontaneous emission is affected by nearby bodies using classical electromagnetic energy balance, revisiting classical theories and generalizing the Purcell effect for complex geometries.

Contribution

It introduces a classical framework connecting the Purcell effect, optical theorem, and Wheeler-Feynman absorber theory, providing new insights into emission modification near arbitrary bodies.

Findings

Total decay rate can include both radiative and non-radiative components.

The classical approach offers alternative perspectives on the Purcell effect.

Generalizes emission enhancement and inhibition in complex geometries.

Abstract

The altered spontaneous emission of an emitter near an arbitrary body can be elucidated using an energy balance of the electromagnetic field. From a classical point of view it is trivial to show that the field scattered back from any body should alter the emission of the source. But it is not at all apparent that the total radiative and non-radiative decay in an arbitrary body can add to the vacuum decay rate of the emitter (i.e.) an increase of emission that is just as much as the body absorbs and radiates in all directions. This gives us an opportunity to revisit two other elegant classical ideas of the past, the optical theorem and the Wheeler-Feynman absorber theory of radiation. It also provides us alternative perspectives of Purcell effect and generalizes many of its manifestations, both enhancement and inhibition of emission. When the optical density of states of a body or a material is difficult to resolve (in a complex geometry or a highly inhomogeneous volume) such a generalization offers new directions to solutions.