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Physical Review A

Systematic study of spontaneous emission in a two-dimensional arbitrary inhomogeneous environment

Peng-fei Qiao, Wei E. I. Sha, Wallace C. H. Choy, Weng Cho Chew

Published Apr 20, 2011• 34 citations
Publisher

Abstract

The spontaneous emission (SE) of the excited atoms in a two-dimensional (2D) arbitrary inhomogeneous environment has been systematically studied. The local density of states, which determines the radiation dynamics of a point source (for 3D) or a line source (for 2D), in particular, the SE rate, is represented by the electric dyadic Green's function. The numerical solution of the electric Green's tensor has been accurately obtained with the finite-difference frequency-domain method with the proper approximations of the monopole and dipole sources. The SE of atoms in photonic crystal and plasmonic metal plates has been comprehensively and comparatively investigated. For both the photonic crystal and plasmonic plates systems, the SEs depend on their respective dispersion relations and could be modified by the finite-structure or finite-size effects. This work is important for SE engineering and the optimized design of optoelectronic devices.

DOI
10.1103/physreva.83.043824

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The spontaneous emission (SE) of the excited atoms in a two-dimensional (2D) arbitrary inhomogeneous environment has been systematically studied. The local density of states, which determines the radiation dynamics of a point source (for 3D) or a line source (for 2D), in particular, the SE rate, is represented by the electric dyadic Green's function. The numerical solution of the electric Green's tensor has been accurately obtained with the finite-difference frequency-domain method with the proper approximations of the monopole and dipole sources. The SE of atoms in photonic crystal and plasmonic metal plates has been comprehensively and comparatively investigated. For both the photonic crystal and plasmonic plates systems, the SEs depend on their respective dispersion relations and could be modified by the finite-structure or finite-size effects. This work is important for SE engineering and the optimized design of optoelectronic devices.
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 lifetime distribution functions of the spontaneous emission (SE) of the excited atoms embedded in two-dimensional (2D) photonic crystals (PCs) with square lattice, consisting of square air rods in dielectric medium with different filling factors, are calculated by using the plane wave expansion method. The numerical results show that the SE in the 2D PCs cannot be prohibited completely but it can be inhibited intensively by the pseudo-PBG of the PCs. In the pseudoband edges, the SE is accelerated obviously. The reduced average lifetime of the excited atoms and the extension of the reduced lifetime distribution in the 2D PCs both are the same as those in the 3D PCs in the order of magnitude. Our results provide an available way to control the behavior of the SE by changing the structures of the 2D PCs.
Defining a quantum mechanical wavefunction for photons is one of the remaining open problems in quantum physics. Thus quantum states of light are usually treated within the realm of second quantization. Consequently, spontaneous emission (SE) in arbitrary photonic media is often described by Fock space Hamiltonians. Here, we present a real space formulation of the SE process that can capture the physics of the problem accurately under different coupling conditions. Starting from first principles, we map the unitary evolution of a dressed two-level quantum emitter onto the problem of electromagnetic radiation from a self-interacting complex harmonic oscillator. Our formalism naturally leads to an efficient computational scheme of SE dynamics using finite difference time domain method without the need for calculating the photonic eigenmodes of the surrounding environment. In contrast to earlier investigations, our computational framework provides a unified numerical treatment for both weak and strong coupling regimes alike. We illustrate the versatility of our scheme by considering several different examples.
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.
Starting from a quantum Maxwell equation for the vector potential operator, we study the spontaneous emission properties of a two-level atom interacting with the electromagnetic field in a lossless and inhomogeneous dielectric structure and express the spontaneous emission rate, the external quantum efficiency, and the spontaneous emission factor in terms of the classical Green function of the dielectric structure. Comparing these results with the corresponding classical results, we show that the above quantities can be calculated from the radiation field of a classical dipole. Based on this correspondence, a numerical algorithm is developed to calculate the modification of spontaneous emission in microcavities. The line shape of the emission spectrum of the light source and the decay of the cavity resonant modes are automatically taken into account in this algorithm. The approximate expressions for the spontaneous emission rate and the spontaneous emission factor are discussed.
In applications like quantum cryptography and quantum computation, it is desirable to obtain single photon sources which can produce a train of single photons on demand at a high repetition rate, especially at or near room temperature. Such single-photon sources can be realized by tailoring the photonic environment of the quantum emitter. The photonic environment determines the local density of states, into which the photon can be emitted. A number of structures such as interfaces, cavities and waveguides have already been used to modify the spontaneous emission (SE) rate; nevertheless there is still room for improving the overall efficiency of the single-photon sources, e.g., by inventing new ways of enhancing light-matter interaction.