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Physical Review A

Spontaneous emission in a planar Fabry-Pérot microcavity

S. M. Dutra, P. L. Knight

Published May 1, 1996• 54 citations
Publisher

Abstract

We study the spontaneous-emission of a single atom located between two parallel infinite plates where one of the plates is partially reflective and the plate separation is of the order of the wavelength of the atomic transition. We pay particular attention to the nature of the field modes in such a finite finesse cavity, including the full three-dimensional nature of the field. We then compute the decay rate of an excited atom placed inside such a cavity. The angular distributions of the spontaneous-emission and of the cavity field vacuum fluctuation variances are investigated. Finally, we examine the output field from an atom inside a finite finesse microcavity. We show that the radiation transmitted outside such microcavity forms a nondiffracting Bessel beam. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.3587

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We study the spontaneous-emission of a single atom located between two parallel infinite plates where one of the plates is partially reflective and the plate separation is of the order of the wavelength of the atomic transition. We pay particular attention to the nature of the field modes in such a finite finesse cavity, including the full three-dimensional nature of the field. We then compute the decay rate of an excited atom placed inside such a cavity. The angular distributions of the spontaneous-emission and of the cavity field vacuum fluctuation variances are investigated. Finally, we examine the output field from an atom inside a finite finesse microcavity. We show that the radiation transmitted outside such microcavity forms a nondiffracting Bessel beam. \textcopyright{} 1996 The American Physical Society.
A three-dimensional quantum nonperturbative theory of spontaneous emission in a planar microcavity is developed on the basis of a complete set of orthogonal standing-wave mode functions. Earlier results on the spontaneous decay rate and far-field emission pattern which have been obtained in a perturbative fashion are shown to be contained in our theory. Time evolution of the initially excited atomic state is considered and comparison with perturbative results is given. It is found that though the Fabry-Perot cavity is of an open type, vacuum-field Rabi oscillations are still possible. Conditions that are favorable for this strong coupling regime are discussed. The near-field spontaneous-emission pattern and the transition from the near field to the far field are investigated. For moderate mirror reflectivities, the spread in the near-field emission pattern is found to be in good agreement with the effective mode radius concept. When the mirror reflectivity increases, however, one has a strong coupling regime and together with it, multiple reabsorptions and reemissions of the photon may occur, leading to a better localization of the photon around the atomic position. These considerations may be useful in designing microlasers of the planar type.
We study the transient regime of spontaneous emission by an atom excited in a planar high-Q microcavity. The variation of the spatial distribution of the radiation outside the cavity is determined as a function of the increasing number of internal reflections for transition dipole moments parallel and perpendicular to the mirrors and for mirror separations equal to $\ensuremath{\lambda}/2$ and $\ensuremath{\lambda}/4.$ Particular attention is given to the parallel dipole in the $\ensuremath{\lambda}/2$ cavity, where the number of reflections is closely proportional to the elapsed time. It is shown that the transient regime extends over times of the order of the cavity decay time, in contrast to the effectively one-dimensional cavities previously studied, where the steady state is achieved after the cavity round-trip time. The field distribution inside the cavity tends to a steady-state form whose dimension parallel to the mirrors is of the order of the transverse coherence length. Despite this transverse localization of the field excitation, it is shown that the conditions for the achievement of strong atom-field coupling and the observation of Rabi oscillations cannot be met in the planar microcavity.
A complete set of cavity modes in planar dielectric microcavities is presented which naturally includes guided modes. We show that most of these orthonormal fields can be derived from a coherent superposition of plane waves incoming on the stack from the air and from the substrate. Spontaneous emission of a dipole located inside the microcavity is analyzed, in terms of cavity modes. Derivation of the radiation pattern in the air and in the substrate is presented. The power emitted into the guided modes is also determined. Finally, a numerical analysis of the radiative properties of an erbium atom located in a Fabry-P\'erot multilayer dielectric microcavity is investigated. We show that a large amount of light is emitted into the guided modes of the structure, in spite of the Fabry-P\'erot resonance, which increases the spontaneous emission rate in a normal direction. \textcopyright{} 1996 The American Physical Society.
Summary form only given. We have reported on an analysis of the spontaneous emission by two identical two-level atoms a distance R apart, both of which are initially in the upper state. In this paper we apply this analysis to the two-atom spontaneous emission in a planar microcavity. The two atoms are located on the x-axis on the center plane of a symmetric cavity of length l and are separated by a distance R. The atomic dipoles are oriented in the y-direction parallel to the mirrors. We examine the motion of the probability amplitude of the initial state where both atoms are in the upper state.
The transverse distributions of intensity inside and outside an optical cavity produced by spontaneous emission from atoms inside the cavity are reviewed. The mode properties inside a closed passive one-dimensional cavity are summarised and the spatial distributions of emitted light for a passive cavity with partially transmitting mirrors are discussed. A qualitative theory describes the effects of an amplifying medium inside the cavity, covering the regimes both below and above the lasing threshold. Expressions are derived for the angular spread of the output light in the presence of gain. A theory based on rigorous general relations between gain and noise provides more complete results for the spontaneous emission noise from an amplifying slab within an optical cavity.