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Spontaneous Emission in Systems of Reduced Dimension

Tyler A. Hill

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

Matter coupled to light can emit photons. In the absence of an external field this process is known as spontaneous emission. The radiation properties depends in detail the nature of the emitter. In this thesis we consider a two level point-source emitter, and examine how the emission is affected by engineering the local environment. We begin by studying analytically how embedding an emitter in a multi-layer cylindrical structure with radius much smaller than the emission wavelength alters the intensity of the emitted light. We find that for carefully chosen metal-dielectric interfaces, the emission can be strongly enhanced by the plasmonic effect. With this intuition, we experimentally study an InGaN semiconductor quantum dot-in-wire structure as our two level emitter, and manipulate the local field environment by coupling to a lossy plasmonic cavity. We find that the strong enhancement of the field around the quantum dot due to the metal more than compensates for the non-radiative losses, leading to order-of-magnitude increases in the radiative spontaneous emission rate, as well as overall brightness. We then examine how the emission of light can be affected by other nearby emitters. The cooperative effects are strongly dependent on the dimension of the system which controls the electromagnetic mode overlap of the emitters. We present a unified formalism capturing how these cooperative effects change from one dimension to the next. Cooperative light scattering between emitters underpins collective effects such as super- and sub-radiance, and we numerically investigate how our previous results give rise to the key experimental signatures that can be used to identify those phenomena. Specifically, we study how the superadiant decay rate scales with the size of a $2$-dimensional atomic cloud, and how cooperative effects between a small number of emitters alter the emission spectrum of strongly driven resonance fluorescence.

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Matter coupled to light can emit photons. In the absence of an external field this process is known as spontaneous emission. The radiation properties depends in detail the nature of the emitter. In this thesis we consider a two level point-source emitter, and examine how the emission is affected by engineering the local environment. We begin by studying analytically how embedding an emitter in a multi-layer cylindrical structure with radius much smaller than the emission wavelength alters the intensity of the emitted light. We find that for carefully chosen metal-dielectric interfaces, the emission can be strongly enhanced by the plasmonic effect. With this intuition, we experimentally study an InGaN semiconductor quantum dot-in-wire structure as our two level emitter, and manipulate the local field environment by coupling to a lossy plasmonic cavity. We find that the strong enhancement of the field around the quantum dot due to the metal more than compensates for the non-radiative losses, leading to order-of-magnitude increases in the radiative spontaneous emission rate, as well as overall brightness. We then examine how the emission of light can be affected by other nearby emitters. The cooperative effects are strongly dependent on the dimension of the system which controls the electromagnetic mode overlap of the emitters. We present a unified formalism capturing how these cooperative effects change from one dimension to the next. Cooperative light scattering between emitters underpins collective effects such as super- and sub-radiance, and we numerically investigate how our previous results give rise to the key experimental signatures that can be used to identify those phenomena. Specifically, we study how the superadiant decay rate scales with the size of a 222-dimensional atomic cloud, and how cooperative effects between a small number of emitters alter the emission spectrum of strongly driven resonance fluorescence.
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.
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.
Surface plasmon polaritons are charge density waves of electrons in a metal, which are coupled to an electromagnetic field at a metal-dielectric interface. The electro- magnetic field associated with surface plasmons is confined, resulting in increased field intensities near the interface. Optical emitters placed near a metal film interact strongly with the surface plasmon modes present, not only modifying the radiation rates, but also the radiation profile. These emitters may be used to store and process information, and understanding their behaviour in the presence of a lossy metal film is important in determining the advantages and limitations of using surface plasmons. In this thesis, we wish to understand how we can optically control atoms by exploring two physical phenomena: first, the influence of surface plasmons on collective effects in an ensemble of emitters. Secondly, the single photon excitation of an emitter near a metal film. In the first case, we analyze the collective radiative behaviour of multiple classical emitters near a metal film that radiatively couple to the far-field through surface plasmon modes. We demonstrate that the contributions of dipolar image charges within the metal film significantly affect the cooperative emission of nearby sources, generating sub- and super-radiant emission that can be controlled with a suitably detuned external driving field. In the second case, we determine the excitation probability of an atom near a metal film by a single photon pulse that is time reversed. Using a quantum electro- dynamic description of absorbing dielectrics, we show that non-radiative decay will limit the excitation probability to about half of the maximum that could be achieved in the absence of losses.
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.
Control of spontaneously emitted light lies at the heart of quantum optics. It is essential for diverse applications ranging from lasers, light-emitting diodes, solar cells, and quantum information. According to the quantum electrodynamics theory, the spontaneous emission (SE) of an atom can be a weak-coupling radiation process due to the vacuum fluctuations of electromagnetic field. A suitable modification of inhomogeneous environment is required so that the vacuum fluctuations controlling the SE can be manipulated. Inhibiting unwanted SE and boosting desired ones will promote the novel optoelectronic designs tailored to industrial standard. The local density of states (LDOS) counts the number of electromagnetic modes where photons can be emitted at the specific location of the emitter, and can be interpreted as the density of vacuum fluctuations. The inhibition or enhancement of SE boils down to how the LDOS of photons is controlled. In this work, the SE of the excited atoms in 2D arbitrary inhomogeneous environment has been systematically studied. The LDOS determines the radiation dynamics of a point source (for 3D) or a line source (for 2D). In particular, it also determines the SE rate, and the LDOS is represented by the electric dyadic Green’s function. The numerical solution of the electric Green’s tensor has been accurately obtained by the finite-difference frequency-domain method with the proper approximations of the monopole and dipole sources. The SE of the atoms in the photonic crystal and plasmonic metal plates has been comprehensively and comparatively investigated. For both systems, the SE strongly depends on their respective dispersion relations and could be modified or tuned by the finite-structure or finite-size effects. This work is important for the SE engineering and optimized design of optoelectronic devices.
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.