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Spontaneous emission mediated by cooperative energy transfer to a plasmonic antenna

Tigran V. Shahbazyan

Published Jun 5, 2018• 1 citation
OpenAlex

Abstract

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 (ET) rates. If the antenna radiation efficiency is sufficiently high, the transferred energy is radiated away at approximately 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 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 raising a possibility of controlling the emission rate beyond field enhancement limits.

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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 (ET) rates. If the antenna radiation efficiency is sufficiently high, the transferred energy is radiated away at approximately 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 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 raising a possibility of controlling the emission rate beyond field enhancement limits.
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.
We develop a theory of cooperative emission mediated by cooperative energy transfer (CET) from an ensemble of quantum emitters (QEs) 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 sizes 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.
Spontaneous emission from ensembles of quantum emitters (QEs) such as atoms, molecules or semiconductor quantum dots can be greatly enhanced by cooperative effects arising from electromagnetic correlations. We describe a cooperative mechanism for emission of light by an ensemble of QEs based upon cooperative energy transfer from QEs to localized surface plasmons in metal-dielectric structures followed by plasmon radiation at a rate that scales with the ensemble size. For large QE ensembles saturating the plasmon mode volume, we derive universal, i.e. independent of local field distribution, expression for cooperative Purcell factor that can by far exceed the field enhancement limits for individual QE in a hot spot. We also derive radiated power spectrum that retains the plasmon resonance lineshape and, in contrast to common cooperative mechanisms, is insensitive to natural variations of QEs' emission frequencies.
We develop a theory of cooperative emission of light by an ensemble of emitters, such as fluorescing molecules or semiconductor quantum dots, located near a metal nanostructure supporting surface plasmon. The primary mechanism of cooperative emission in such systems is resonant energy transfer between emitters and plasmons rather than the Dicke radiative coupling between emitters. We identify two types of plasmonic coupling between the emitters, (i) plasmon-enhanced radiative coupling and (ii) plasmon-assisted nonradiative energy transfer, the competition between them governing the structure of system eigenstates. Specifically, when emitters are removed by more than several nanometers from the metal surface, the emission is dominated by three superradiant states with the same quantum yield as a single emitter, resulting in a drastic reduction of ensemble radiated energy, while at smaller distances cooperative behavior is destroyed by nonradiative transitions. The crossover between two regimes can be observed in distance dependence of ensemble quantum efficiency. Our numerical calculations incorporating direct and plasmon-assisted interactions between the emitters indicate that they do not destroy the plasmonic Dicke effect.
We develop a theory of cooperative emission of light by an ensemble of emitters, such as fluorescing molecules or semiconductor quantum dots, located near a metal nanostructure supporting surface plasmon. The primary mechanism of cooperative emission in such systems is resonant energy transfer between emitters and plasmons rather than the Dicke radiative coupling between emitters. We identify two types of plasmonic coupling between the emitters, (i) plasmon-enhanced radiative coupling and (ii) plasmon-assisted nonradiative energy transfer, the competition between them governing the structure of system eigenstates. Specifically, when emitters are removed by more than several nm from the metal surface, the emission is dominated by three superradiant states with the same quantum yield as a single emitter, resulting in a drastic reduction of ensemble radiated energy, while at smaller distances cooperative behavior is destroyed by nonradiative transitions. The crossover between two regimes can be observed in distance dependence of ensemble quantum efficiency. Our numerical calculations incorporating direct and plasmon-assisted interactions between the emitters indicate that they do not destroy the plasmonic Dicke effect.
We develop a rigorous theory for nanophotonic cooperative spontaneous emission of an ensemble of quantum emitters near matter, which also incorporates absorption. Such theory is highly requested since one should expect that in the field of nanophotonics the close-by emitters will emit cooperatively simultaneously with strong interaction with the exotic metamaterial complex dielectric function. The closed-form model developed here considers the buildup both of interemitter correlation over time through emitter transitions via the mutual field and of geometry-induced spatial correlation. The presence of matter alters the local density of states (LDOS), resulting in modified decay rate and emission intensity for the entire ensemble relative to values of spontaneous emission in free space. The superradiant total emission is separable into a quantum-mechanical time-dependent part and a classical space-dependent part, both being functions of the LDOS. Two distinct radiative emitter--far-field coupling mechanisms, which together account for the superradiant emission, are obtained---the coupling of every individual emitter with the far field and the coupling of emitter pairs to the far field. The calculations for superradiating emitters near silver and near-zero epsilon (NZE) materials were performed with the following results: the silver sphere augments the superradiant far-field intensity and rate by up to 400 and 1000%, respectively, while the NZE sphere enhances the far-field intensity and rate of the superradiance by approximately 1400 and 400%, respectively.