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Spontaneous emission in the optical microscopic cavity

F. De Martini, Michele Marrocco, R. Loudon

Published May 21, 1990• 0 citations
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Abstract

The quantum theory of the spontaneous emission (SpE) in the optical microscopic cavity (microcavity) is reported we believe for the first time.1,2 The forms of the modes propagating orthogonally to the mirrors and previously studied by Ley and Loudon3 are here generalized to cover all spatial directions. Microcavity field quantization leads to the expressions of the SpE probabilities Γ||, Γ⊥ for dipoles parallel and orthogonal to the mirrors, respectively. These are computer calculated for some experimentally significant cases involving both metal and dielectric multilayer-mirror coatings.

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Physical Review A•Sep 1, 1996•91 citations
The quantum theory of the spontaneous emission (SpE) in the optical microscopic cavity (microcavity) is reported we believe for the first time.1,2 The forms of the modes propagating orthogonally to the mirrors and previously studied by Ley and Loudon3 are here generalized to cover all spatial directions. Microcavity field quantization leads to the expressions of the SpE probabilities Γ||, Γ⊥ for dipoles parallel and orthogonal to the mirrors, respectively. These are computer calculated for some experimentally significant cases involving both metal and dielectric multilayer-mirror coatings.
The quantum theory of the spontaneous emission (SpE) from an active microscopic cavity (microcavity) is given with emphasis on mirror separations of the order of the optical wavelength. The theory is based on a complete set of orthonormal-mode functions that include both transverse polarizations and span the infinite three dimensional space that pervades and surrounds the microcavity. SpE rates for different active-dipole orientations and cavity configurations are calculated. The SpE pulse shape detected outside the cavity is shown to be generally nonexponential. A detailed computer simulation of the process is presented on the basis of the given theory in the perspective of our experiment, for a cavity terminated by mirrors bearing either metal- or semiconductor-multilayered coatings. We then report an extensive experimental verification of the theory by adopting an Eu-dibenzoylmethane complex as active medium with SpE from the 5^{5}5${\mathit{D}}_{0\mathrm{\ensuremath{-}}}^{7}$F2{\mathit{F}}_{2}F2​ line at \ensuremath{\lambda}=6111 \AA{}, under coherent uv excitation at ${\ensuremath{\lambda}}_{\mathit{p}}$=3547 \AA{}. The results show evidence of ``SpE inhibition'' and ``enhancement,'' of nonexponential decay of SpE signals, and of competition with superradiance and stimulated emission. Finally we report the results of an experimental test of the algorithm adopted in all computer calculations of the optical parameters of the multilayered structures used for cavity confinement.
The process of the spontaneous emission (SpE) from an active microscopic cavity (microcavity) is shown with emphasis on mirror separation of the order of the optical wavelength. The relevant effects of SpE enhancement and inhibition, non-exponential decay, and emission anisotropy are outlined for a cavity terminated by mirrors bearing either metal -- or semiconductor -- multilayered coatings. Finally, an experiment regarding the possibility of detecting the field distribution within the cavity of the emission wavelength is shown.
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.
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.