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Conference on Lasers and Electro-Optics

Trapped mode contribution to spontaneous emission in a planar Fabry-Perot microcavity

Bryan J. Dalton, F. Babiker, P. L. Knight

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given. We present the results of a full quantum treatment of the contribution of trapped modes to the total spontaneous emission rate. For the case of a high Q Fabry Perot microcavity of the simple type treated by Dutra and Knight, we find that for both normal and parallel orientations of the atomic dipole matrix element, the trapped mode contribution is negligible for all atomic positions in the microcavity, so that almost all the energy radiated goes into the traveling modes.

DOI
10.1109/iqec.1998.680273

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Summary form only given. We present the results of a full quantum treatment of the contribution of trapped modes to the total spontaneous emission rate. For the case of a high Q Fabry Perot microcavity of the simple type treated by Dutra and Knight, we find that for both normal and parallel orientations of the atomic dipole matrix element, the trapped mode contribution is negligible for all atomic positions in the microcavity, so that almost all the energy radiated goes into the traveling modes.
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.
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.
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Using a continuous basis set of optical modes, the spontaneous emission into the lowest-order resonant quasimode of a planar cavity is analyzed for the case of a laterally distributed multiemitter system. We show that for a spatially distributed, randomly phased multiemitter system, the spontaneous rate into the lowest-order cavity quasimode contains a Purcell effect, increases with increasing mode quality factor Q, and saturates when the mode loss becomes less than the dipole dephasing rate. Cooperative effects leading to superradiance for a properly phased multiemitter system are also considered, for which the change in the cavity-confined total spontaneous emission rate can be sizable. \textcopyright{} 1996 The American Physical Society.
In the present and the accompanying paper a justification of the standard model of cavity quantum electrodynamics is given in terms of a quasi-mode theory of macroscopic canonical quantization. The coupling of the cavity quasi-mode to external quasi-modes is treated for the representative case of the three-dimensional Fabry-Perot cavity. The general form of the travelling and trapped mode functions for this cavity are derived in this paper and the mode-mode coupling constants are calculated in the accompanying paper. The slow dependence of the coupling constants with the mode frequency difference demonstrates that the conditions for Markovian damping of the cavity quasimode are satisfied. As also discussed in the accompanying paper, the interaction of radiative atoms with cavity quasi-modes is associated with reversible energy exchanges between atom and cavity and represented by Rabi coupling constants. The interaction of radiative atoms located within the cavity with sideways travelling external quasi-modes involves slowly varying coupling constants and is associated with irreversible spontaneous emission dampling. The basic processes represented in the standard cavity quantum electrodynamics model and the associated coupling constant and decay rates thereby follow from the quasi-mode theory.
We discuss the frequency dependence of the spontaneous-emission rate (power) in a Fabry-Perot microcavity containing a Lorentz dielectric, with emphasis on modifications of the spectrum under the circumstances of the strong medium-cavity coupling. With the standard-cavity tuning, the total spontaneous-emission power spectrum consists of a multiwave version of the familiar low-frequency vacuum Rabi split peak and a broad structure on the high-frequency side coming from the enhanced spontaneous emission into the continuum of the obliquely propagating waves. This form of the spectrum derives from the properties of the (single-wave) radiation-intensity spectrum of the molecule. Depending on the observation direction, the radiation-intensity spectrum exhibits either a double-peak structure characteristic of the vacuum Rabi splitting, as observed in light transmisssion and reflection experiments, or a single-peak structure describing the enhanced spontaneous emission at the corresponding cavity resonant frequency.