Abstract
We theoretically investigate the multipolar effects on the dipole-forbidden transitions of a semiconductor quantum dot. An approximated expression for the decay rate of these transitions is derived. Unlike the general theory of the spontaneous emission beyond the dipole approximation, the distinct roles of the emitter and the vacuum electric field in the transition rate are here clearly recognizable and can be separately optimized. We illustrate the potential of this formalism by calculating the spontaneous emission decay rate of an InAs/GaAs quantum dot embedded into two realistic nanostructures---an L3 photonic crystal cavity and a plasmonic dimer antenna. The obtained results show that, although the two structures provide an enhancement of the same order of magnitude, the plasmonic antenna constitutes a more promising candidate for the experimental observation of the dipole-forbidden transitions of a quantum dot.
Highlights
Semiconductor quantum dots (QDs) have become a subject of intensive research [1] in the recent years for both fundamental and applicative purposes
In Appendix B, we discuss the influence of these effects on the decay rate of the DF transitions and we show that, for this case, they constitute a higher-order correction with respect to the term related to the envelope function
We have theoretically investigated the multipolar effects on the DF transitions of a semiconductor QD
Summary
Semiconductor quantum dots (QDs) have become a subject of intensive research [1] in the recent years for both fundamental and applicative purposes. When describing the light-matter interaction, one usually assumes that the emitter can be considered pointlike with respect to the spatial variation of the electromagnetic field This approach constitutes the well-known dipole approximation, which is an excellent approximation for atoms emitting in the visible part of the spectrum, since their dimensions are several orders of magnitude smaller than the optical wavelength. In artificial photonic nanostructures the aforementioned criterion is not applicable anymore, since the electromagnetic field at a certain frequency can feature spatial variations corresponding to |k| values larger than the plane wave in a bulk material These situations can introduce non-negligible corrections, as recently demonstrated in an experimental work [7] where the decay rate of QDs in close proximity to a metallic mirror has been shown to differ from the dipole approximation predictions.
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