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Physical Review A

Spontaneous emission in the presence of a dielectric cylinder

Władysław Żakowicz, Maciej Janowicz

Published Jun 16, 2000• 47 citations
Publisher

Abstract

Spontaneous emission of photons by an atom placed near a dielectric cylindrical waveguide at an arbitrary position is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (travelling) and the modes trapped to a waveguide (waveguided). To describe angular properties of the spontaneous emission, a parametrization of the travelling modes by the outgoing waves has been proposed. Angular characteristics of the travelling photon emission, distributions of the trapped photon emission, as well as the global decay rates have been calculated using the quantum approach and the standard perturbation theory. Difficulties due to the presence of sharp resonances (whispering gallery modes) among the travelling photons are pointed out.

DOI
10.1103/physreva.62.013820

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Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences•Feb 8, 1992•77 citations
Spontaneous emission of photons by an atom placed near a dielectric cylindrical waveguide at an arbitrary position is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (travelling) and the modes trapped to a waveguide (waveguided). To describe angular properties of the spontaneous emission, a parametrization of the travelling modes by the outgoing waves has been proposed. Angular characteristics of the travelling photon emission, distributions of the trapped photon emission, as well as the global decay rates have been calculated using the quantum approach and the standard perturbation theory. Difficulties due to the presence of sharp resonances (whispering gallery modes) among the travelling photons are pointed out.
Spontaneous emission of photons by an atom placed near the dielectric waveguide is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the waveguide boundaries 1. These modes include modes extended over the whole space (travelling) and modes trapped to the waveguide. To describe angular properties of the spontaneous emission, a parameterization of the travelling modes by the outgoing waves has been proposed. Otherwise, using a more common parameterization of these modes by the incoming waves, one has to take into account the interference of different reflected and transmitted waves accompanying photons incoming from both sides of the waveguide 2, what was overlooked in 3. Angular characteristics of the travelling photon emission (a), distributions of the trapped photon emission (b), as well as global decay rates (c), have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error, in the treatment of the density of trapped states, in an earlier paper by Khosravi and Loudon 4, affecting emission rates for thin waveguides, has been corrected.
The spontaneous emission of photons by an atom placed near the dielectric slab is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (traveling) and the modes trapped to a waveguide formed by the slab (trapped). To describe angular properties of spontaneous emission a parametrization of the traveling modes by the outgoing waves has been proposed. Angular characteristics of the traveling photon emission, distributions of the trapped photon emission, as well as global decay rates have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error in an earlier paper by Khosravi and Loudon [Proc. R. Soc. London Ser. A 436, 373 (1992)] affecting thin slabs and results near waveguide-mode thresholds has been improved.
This thesis is concerned with the theory of spontaneous emission in the context of cavity QED and the guiding of atoms by laser light in confined geometries. We focus on three different geometrical shapes of waveguide, namely the parallel plate guide and two kinds of cylindrical waveguide: one with a rectangular cross section and another with a circular cross section. These waveguides are assumed to be characterised by two distinct properties. Firstly, all three types of guide have perfect conductor boundary conditions, which means that the guide walls are infinitely conducting and, consequently, lossless. Secondly, the guides are assumed to have subwavelength dimensions (less than the atom electric dipole transition wavelength #lambda#). The first consequence of this is that the spontaneous emission process is possible only via a few cavity modes. For each type of structure, we examine the confinement of electromagnetic fields within it and proceed to quantise these fields by following the standard procedure, incorporating the boundary conditions at the guide walls. This allows the position-dependent spontaneous emission rate to be evaluated for an electric dipole located at an arbitrary point within the guide. Asymptotic limits of the spontaneous emission rate are then derived which serve as useful checks of the calculations. For the rectangular guide, we are able to recover the results appropriate for the parallel-plate case when side a of the rectangular cross section becomes large, while side b is kept fixed. For the circular guide, we are able to recover the results appropriate for the free space case when the radius of the guide becomes large. The second part of the thesis deals with the theory of the motion of atoms in the spatially varying light fields inside the three different shapes of waveguide. In each structure we examine the forces that act on the atom and solve the equation of motion leading to the atom dynamics when an electric dipole within the guide is subject to an excited p-polarised cavity mode. The characteristics of the atomic motion in the guide in the presence of a cavity mode are then explored. We show that under these conditions the atom becomes subject to a transverse dipole potential and a dissipative force, both of which vary across the guide and are also functions of the atom velocity along the mode propagation direction. The dipole potential is responsible for the transverse trapping (and hence the channelling) of atoms at specific regions of the cross section, while the dissipative force controls the longitudinal motion of the channelled atoms. The conditions facilitating atom guiding are explored using typical parameters for sodium atoms in guides of subwavelength dimensions. The roles of the van der Waals and Casimir-Polder potentials on the atomic motion in waveguides is clarified theoretically in the context of the parallel-plate guide and we show that such potentials are effective only at relatively short distances from the guide walls. Finally, we show that atomic motion in a hollow circular guide is subject to a quantised torque arising from the orbital angular momentum effects associated with any excited waveguide mode of order l > 0. We find that an appropriately detuned atom immersed in such a mode may be trapped radially in a vibrational state and be made to exhibit novel rotational effects associated with the light torque, including a rotational frequency shift. (author)
We study the spontaneous emission of an atom embedded in a one-dimensional photonic crystal or superlattice using a classical electrodynamic theory of radiation. The rate of emission is a function of the frequency of the emitted photon, the dipole's position and orientation, as well as the geometric and material parameters of the superlattice. The emission spectrum shows an oscillatory behavior which follows the photonic band structure. For TE modes, there are frequency regions where radiative emission is completely prohibited due to the absence of modes with k//>omega/c; the radiation is then TM polarized. In addition to the radiative modes, there are always evanescent modes with k//>omega/c which are waveguided by the dielectric layers. The evanescent contribution to the spontaneous emission is dominant if a dielectric layer is in the near field region of the dipole. For TM modes, emission rates greatly vary for parallel and perpendicular dipole moments. In a photonic crystal with a high filling fraction of the dielectric and perpendicular dipoles located in the low-index layer, the decay rate can be as much as 76 times the free space value for a single atom and 50 times for a gas of atoms. We also find that the rate of emission presents a strong dependence on the atom's position.
The motion of atoms inside a long hollow cylindrical waveguide with a circular cross section is investigated. The guide is assumed to have subwavelength dimensions, in which case the spontaneous decay process is effected only by emission of a few possible cavity modes. The characteristics of the atomic motion in the guide are explored in the presence of an excited waveguide mode. We show that the atomic motion in this case is determined by an axial channelling force and a trapping dipole force, plus a quantized light torque associated with the orbital angular momentum property of excited waveguide modes of order l>0.\mathcal{l}>0.l>0. It is predicted that in addition to its axial motion, an atom subject to such a mode should be trapped radially in a vibrational state and should exhibit interesting rotational features due to the light torque, including a rotational frequency shift.
Abstract The electromagnetic field is quantized on the basis of the complete set of spatial modes of a plane dielectric slab of arbitrary thickness and refractive index but infinite transverse dimensions, located in otherwise empty three-dimensional space. The vacuum field fluctuations and spontaneous emission rates are evaluated as functions of position both inside and outside the slab. The source-field operator is derived for emission by atoms inside the slab, in the direction perpendicular to its surfaces. Particular attention is given to the possibility of suppressing spontaneous emission by placing atoms in, or close to, a dielectric slab.