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

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.

Photoluminescence decay rate engineering of CdSe quantum dots in ensemble arrays embedded with gold nano-antennae

“…Also very large Q factors and mode volumes imply both acute specificity of the spectral range of operation and relatively larger size of these devices, which may not be advantageous. Hence recently, Purcell effect mediated decay rate engineering using plasmonic nano-antenna [26][27][28][29][30][31][32][33][34] or even metallodielectric antenna 35 has been suggested as an alternative with the advantage that although the Q factors are smaller than the corresponding photonic crystal based cavities, huge reduction in mode volumes can be obtained leading to possibility of very high F p . In addition, such coupling can also be enhanced by reducing the separation between an emitter or quantum dot with a metal nano-antenna.…”

Influence of localized surface plasmon in a lens-shaped metal cluster on the decay dynamics of a point-dipole emitter

“…Then it can be separated to radiative part that corresponds to light scattering to far field and nonradiative part that is transferred to the plasmon mode and thus absorbed by the metal particle. Both decay channels are affected by the particle presence and contribute to the modified emitter dynamics [14].…”

The optical theorem for local source excitation of a particle near a plane interface

“…The first term in the right part of (9) already appeared in [23] the second one corresponds to the total dipole radiation cross-section. Let us consider the representation for the electric dipole field in D 0 extracting the singular part as ( here η 2 0;1 ¼ λ 2 Àk 2 0;1 ; k 0;1 ¼ k U n 0;1 and…”

“…We already mentioned that the first term in the right part of (17) already appeared in [23]. Let us introduce the conventional scattering cross-section С 7…”

“…The OT was extended to the case of seismic wave propagation [18,19], as well as rough surfaces and beam excitation [20,21]. Excitation by a point sources on the other hand needs a new approach, and the OT has up to now been extended to point source excitation of a particle located in free space only [22,23].…”