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arXiv:1501.04834 · Scientific Reports

An antenna model for the Purcell effect

Alex Krasnok, Alexey P. Slobozhanyuk, Constantin R. Simovski, Sergei Tretyakov, Alexander N. Poddubny, Andrey E. Miroshnichenko, Yuri S. Kivshar, Pavel A. Belov

Published Aug 10, 2015• 210 citations
arXivHTMLPDF

Abstract

The Purcell effect is defined as a modification of the spontaneous emission rate of a quantum emitter at the presence of a resonant cavity. However, a change of the emission rate of an emitter caused by an environment has a classical counterpart. Any small antenna tuned to a resonance can be described as an oscillator with radiative losses, and the effect of the environment on its radiation can be modeled and measured in terms of the antenna radiation resistance, similar to a quantum emitter. We exploit this analogue behavior to develop a general approach for calculating the Purcell factors of different systems and various frequency ranges including both electric and magnetic Purcell factors. Our approach is illustrated by a general equivalent scheme, and it allows resenting the Purcell factor through the continuous radiation of a small antenna at the presence of an electromagnetic environment.

DOI
10.1038/srep12956

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The Purcell effect is defined as a modification of the spontaneous emission rate of a quantum emitter at the presence of a resonant cavity. However, a change of the emission rate of an emitter caused by an environment has a classical counterpart. Any small antenna tuned to a resonance can be described as an oscillator with radiative losses, and the effect of the environment on its radiation can be modeled and measured in terms of the antenna radiation resistance, similar to a quantum emitter. We exploit this analogue behavior to develop a general approach for calculating the Purcell factors of different systems and various frequency ranges including both electric and magnetic Purcell factors. Our approach is illustrated by a general equivalent scheme, and it allows resenting the Purcell factor through the continuous radiation of a small antenna at the presence of an electromagnetic environment.
Standard cavity cooling of atoms or dielectric particles is based on the action of dispersive optical forces in high-finesse cavities. We investigate here a complementary regime characterized by large cavity losses, resembling the standard Doppler cooling technique. For a single two-level emitter a modification of the cooling rate is obtained from the Purcell enhancement of spontaneous emission in the large cooperativity limit. This mechanism is aimed at cooling quantum emitters without closed transitions, which is the case for molecular systems, where the Purcell effect can mitigate the loss of population from the cooling cycle. We extend our analytical formulation to the many-particle case governed by small individual coupling, but exhibiting large collective coupling. Published by the American Physical Society 2024
Abstract Inhibition and enhancement of spontaneous emission rate, first proposed by Purcell, is discussed in terms of altered density-of-modes in various types of solid-state cavities and the Purcell factor is derived for two-level atomic system. The conditions for observing Purcell factor and experimental findings in micropillars embedded with Quantum Dots (QD)s are discussed. The strong interaction between photons and matter in the form of QD excitons, dispersion relations for ground and excited states separated by Rabi splitting are discussed. Experimental photoluminescence spectra showing anticrossing of exciton lines and cavity lines by temperature and other tuning methods are used to illustrate the strong light-matter interaction. The Jayness–Cummins model based on second quantization is presented to point out Rabi oscillation, Purcell effect, and other novel features. Microcavity structures for observing cavity quantum electrodynamics effects are mentioned. Microcavity lasers predicting thresholdless operation for unity spontaneous emission coupling factors are discussed.
The rate of spontaneous emission is known to depend on the environment of a emitter, and the enhancement of one-photon emission in a resonant cavity is known as the Purcell effect. Here we develop a theory of spontaneous two-photon emission for a general electromagnetic environment including inhomogeneous dispersive and absorptive media. This theory is used to evaluate the two-photon Purcell enhancement in the vicinity of metallic nanoparticles and demonstrates that the surface-plasmon resonances supported by these particles can increase the emission rate by more than two orders of magnitude. The control over two-photon Purcell enhancement given by tailored nanostructured environments could provide an emitter with any desired spectral response and may serve as an ultimate route for designing light sources with novel properties.
Abstract We provide a pedagogical introduction to the concept of the local density of optical states (LDOS), illustrating its application to both the classical and quantum theory of radiation. We show that the LDOS governs the efficiency of a macroscopic classical antenna, determining how the antenna’s emission depends on its environment. The LDOS is shown to similarly modify the spontaneous emission rate of a quantum emitter, such as an excited atom, molecule, ion, or quantum dot that is embedded in a nanostructured optical environment. The difference between the number density of optical states, the LDOS, and the partial LDOS is elaborated and examples are provided for each density of states to illustrate where these are required. We illustrate the universal effect of the LDOS on emission by comparing systems with emission wavelengths that differ by more than 5 orders of magnitude, and systems whose decay rates differ by more than 5 orders of magnitude. To conclude we discuss and resolve an apparent difference between the classical and quantum expressions for the spontaneous emission rate that often seems to be overlooked, and discuss the experimental determination of the LDOS.
Several methods have been developed to calculate the spontaneous emission rate for extended emitters in the vicinity of a nanophotonic structure.While taking the emitter's spatial extension, these methods have taken approximations regarding the full interaction, either by coupling to one single plasmonic mode or adding higher order rates individually thus neglecting interference terms.Here we apply a new framework [1] to extended emitters, by which, all these interactions can be considered, and we show both under, and over-estimation of the Purcell Factor when using a point-dipole.
We develop a theory of cooperative emission mediated by cooperative energy transfer (CET) from an ensemble of quantum emitters (QE) to plasmonic antenna at a rate equal to the sum of individual QE-plasmon energy transfer rates. If the antenna radiation efficiency is sufficiently high, the transferred energy is radiated away at approximately the same cooperative rate that scales with the ensemble size. We derive explicit expressions, in terms of local fields, for cooperative Purcell factor and enhancement factor for power spectrum valid for plasmonic structures of any shape with characteristic size smaller than the radiation wavelength. The radiated power spectrum retains the plasmon resonance lineshape with overall amplitude scaling with the ensemble size. If QEs are located in a region with nearly constant plasmon local density of states (LDOS), e.g., inside a plasmonic nanocavity, we demonstrate that the CET rate scales linearly with the number of excited QEs, consistent with the experiment, and can be tuned in a wide range by varying the excitation power. For QEs distributed in an extended region saturating the plasmon mode volume, we show that the cooperative Purcell factor has universal form independent of the system size. The CET mechanism incorporates the plasmon LDOS enhancement as well, giving rise to possibilities of controlling the emission rate beyond field enhancement limits.