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Enhancement of energy relaxation rates near metal-coated dielectric cylinders

G. D. Banyard, C. R. Bennett, M. Babiker

Published Jan 1, 2001• 11 citations
OpenAlex

Abstract

The electromagnetic modes and their field distributions are evaluated for a dielectric cylindrical structure embedded in another dielectric, with a thin metallic film at the cylinder/dielectric interface. These modes provide energy relaxation channels for excited dipole emitters located inside or outside the cylinder. Significantly, we find that the emission rate is sensitive to the magnitude of the electron density of the metallic film coating. For typical parameter values, we find large enhancements of the emission rate, which can be in excess of three orders of magnitude, relative to the case in the absence of the film, arising at specific ranges of electron density. The theory is shown to conform with known limits, including the high density (perfect conductor) limit and the large distance (unbounded bulk) limit. The implications of the predicted enhancement due to the metal coating for the purpose of guiding atoms within such microstructures are pointed out. PACS Numbers: 34.50.Dy, 32.80.-t, 41.20.Jb, 42.50.-p 1 There is at present much interest in small (micrometre to nanometre) scale spherical

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The electromagnetic modes and their field distributions are evaluated for a dielectric cylindrical structure embedded in another dielectric, with a thin metallic film at the cylinder/dielectric interface. These modes provide energy relaxation channels for excited dipole emitters located inside or outside the cylinder. Significantly, we find that the emission rate is sensitive to the magnitude of the electron density of the metallic film coating. For typical parameter values, we find large enhancements of the emission rate, which can be in excess of three orders of magnitude, relative to the case in the absence of the film, arising at specific ranges of electron density. The theory is shown to conform with known limits, including the high density (perfect conductor) limit and the large distance (unbounded bulk) limit. The implications of the predicted enhancement due to the metal coating for the purpose of guiding atoms within such microstructures are pointed out. PACS Numbers: 34.50.Dy, 32.80.-t, 41.20.Jb, 42.50.-p 1 There is at present much interest in small (micrometre to nanometre) scale spherical
We calculate the atomic energy-level shift and the modified dipolar radiation rate inside a hollow dielectric cylinder and outside a solid cylinder using a quantum-mechanical linear-response formalism in the dipole approximation. We first derive the electromagnetic fields scattered by the cylindrical surface for an oscillating dipole inside and outside the cylinder. When an atom is located on the axis of the cylindrical hollow, we obtain analytic expressions of the atomic level shifts in two limiting cases: when bbb (radius of hollow) is very small, the level shift is proportional to ${b}^{\ensuremath{-}2}$ which is associated with the kinetic-energy change of the atomic electron, whereas when bbb is very large, the shift is proportional to ${b}^{\ensuremath{-}4}$ which is identified as the retarded (Casimir-Polder) interaction energy. Moreover, we calculate the atomic potentials as a function of the position of atoms in the hollow region, which is important for the atom-guiding experiment. We also calculate the decay rates and find enhanced rates inside and outside the cylinder. In particular, we compare the radiative properties of an atom inside the hollow cylinder with those between two plates, and those near a cylinder with near a single surface.
We study the density of modes, and associated spontaneous emission properties, of cylindrical cavities exhibiting waveguiding. A model of a microstructure composed of a metallized cylinder with multiple internal dielectric layers (distributed Bragg reflectors) has been used to describe the Helmholtz modes and their quantization. A two-level excited atom is placed within the structure and interacts in the dipole approximation with the quantized vacuum modes. To describe this we have derived expressions for the density of modes which an interacting atom sees, and which determine the subsequent time evolution of the excited-state probability of the atom. This simple model allows the investigation of the two major influences on the density of modes, the waveguiding nature of a cylinder and the frequency selectivity of the distributed Bragg reflecting mirrors and shows that the interplay between these two factors can have significant design consequences for the smallest of practical structures. We determine the so-called “β factors” characterizing the coupling efficiency and threshold properties of the structure and show that values close to unity are expected. We also show that reversible spontaneous emission, or vacuum Rabi splitting, is expected, for some practically realizable structures.
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.
Summary form only given. Over the last three decades of the 20 th century many experiments have demonstrated that the rate of spontaneous emission for an emitter is determined by its electromagnetic surrounding. This phenomenon has been usually studied for atoms or molecules placed in the vicinity of mirrors or in optical resonators. Furthermore, it is also well-known that the fluorescence lifetime of an emitter changes after being embedded in dielectric media where aside from a change in the refractive index, it experiences the local fields in the dielectric. For a spherical medium larger than the order of a wavelength it is known that the coupling to Mie modes of this dielectric resonator has a large influence on the emission rate of an emitter inside. However, when the medium becomes comparable or smaller than a wavelength one can no longer speak of resonator modes. Here we report on an experiment where we have studied the variation of the spontaneous emission rate as the dielectric medium surrounding an emitter is made smaller and smaller down to a few nanometers.
A photonic crystal, defined as a periodic dielectric structure, can influence the radiation rate of an embedded dipolar emitter. A theory of this effect is developed and the efficiency of a dipolar photonic source is calculated for a realistic three-dimensional crystal. Taking as a starting point the photonic band structure and its associated eigenfields, it is shown that the emission rate is strongly correlated with the density of modes, but also that the density of modes alone cannot explain all features found in the emission spectrum. For an infinite crystal, the computation of the field propagator confirms that the emission rate falls to zero in the frequency range defined by the photonic band gap. The emitter lifetime changes with the dipole location and orientation, leading to a radiation rate enhancement or inhibition according to the direction of the emission. These results may open routes to photonic sources with very high quantum efficiency.
We show that the quantum interference between two spontaneous emission channels can be greatly enhanced when a three-level V-type atom is placed near plasmonic nanostructures such as metallic slabs, nanospheres, or periodic arrays of metal-coated spheres. The spontaneous emission rate is calculated by a rigorous first-principles electromagnetic Green's tensor technique. The enhancement of quantum interference is attributed to the strong dependence of the spontaneous emission rate on the orientation of an atomic dipole relative to the surface of the nanostructure at the excitation frequencies of surface plasmons.