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Physical Review A

Three-dimensional nonperturbative analysis of spontaneous emission in a Fabry-Perot microcavity

Ho Trung Dung, Kikuo Ujihara

Published Nov 1, 1999• 20 citations

Abstract

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.

DOI: 10.1103/physreva.60.4067

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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.

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The decay rate of an excited molecule (atom) embedded in a dispersive and absorbing planar cavity is derived by using a recently obtained compact form of the Green's function for a multilayer. As a by-product, a hint is provided for a straightforward extension of the results obtained for lossless cavities of other shapes to the corresponding absorbing cavities. The decay rate in an absorbing cavity consists of the spontaneous emission rate and of the nonradiative rates caused by the near-field interaction of the molecule with the cavity medium and, for nearby molecules, with the cavity mirrors. Only the spontaneous emission rate is satisfactorily described in the macroscopic approach adopted. The theory is applied to an analysis of the effects of the weak cavity absorption on the decay rate in a dielectric microcavity formed by two metallic mirrors. As expected, dissipation in the cavity medium spoils the conditions for controlled spontaneuos emission and strongly suppresses the intensity of spontaneous emission. However, its effect on the spontaneous emission rate is much less pronounced.

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.