Coherent Radiation by a Spherical Medium of Resonant Atoms

TL;DR

This paper extends the analysis of cooperative radiation from resonant atomic media to three-dimensional spherical geometries, revealing complex mode structures, superradiance, and rich spectral features in emitted radiation.

Contribution

It introduces a multipole expansion approach for spherical media, providing new insights into the eigenmodes and radiation dynamics of such systems.

Findings

Large spheres exhibit temporal oscillations in radiation.

Small spheres tend to radiate superradiantly.

The emission spectrum has a rich structure with frequency gaps and peaks.

Abstract

Radiation by the atoms of a resonant medium is a cooperative process in which the medium participates as a whole. In two previous papers \cite{PG00,GP00}, we treated this problem for the case of a medium having slab geometry, which, under plane wave excitation, supports coherent waves that propagate in one dimension. We extend the treatment here to the three-dimensional problem, focusing principally on the case of spherical geometry. By regarding the radiation field as a superposition of electric and magnetic multipole fields of different orders, we express it in terms of suitably defined scalar fields. The latter fields possess a sequence of exponentially decaying eigenmodes corresponding to each multipole order. We consider several examples of spherically symmetric initial excitations of a sphere. Small uniformly excited spheres, we find, tend to radiate superradiantly, while the radiation from a large sphere with an initially excited inner core exhibits temporal oscillations that result from the participation of a large number of coherently excited amplitudes in different modes. The frequency spectrum of the emitted radiation possesses a rich structure, including a frequency gap for large spheres and sharply defined and closely spaced peaks caused by the small frequency shifts and even smaller decay rates characteristic of the majority of eigenmodes.