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IET Optoelectronics

Spontaneous emission in microcavities

R. Loudon, M.J. Adams

Published Dec 10, 2007• 1 citation
Publisher

Abstract

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.

DOI
10.1049/iet-opt:20070043

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Cambridge University Press eBooks•Sep 6, 2014•0 citations
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.
For pt.IV see J. Phys. Soc. Japan, vol.47, p.217-224 (1982). Spontaneous emission in a lossy one-dimensional cavity is analyzed under the perturbation approximation and the Wigner-Weisskopf approximation. The cavity loss due to output coupling is treated quantum mechanically by the use of a set of continuously distributed radiation modes. The enhancement and reduction factors in the spontaneous emission probability due to the presence of the cavity structure are derived. Interesting transients in spontaneous emission during a time of the order of the cavity decay time are predicted, which leads to an interpretation of the enhancement or the reduction in spontaneous emission in terms of feedback and self-interference effects. The detection of the emitted photon by a detector atom outside the cavity is also discussed.>
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 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.
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 formula describing the intensity of spontaneous emission outside a planar microcavity is derived quantum mechanically. It reflects the quantum mechanical interference of the atom and the emitted photon via multiple reflections in the cavity. The expression derived for the power spectrum reproduces the results of the classical theory by Huang et al.. [Appl. Phys. Lett. 61 (1992) 2961]. The quantum mechanical expression for the electric field amplitude for a single emission event is given together with its evolution equation.
Introduction Most of the lightwave transmission systems operating today benefit fully from extensive deployment of optical amplifiers (OA). These components perform the amplification of optical intensity directly in the optical domain, without resorting to any electrical-domain regeneration. Optical amplifiers increase the average number of output photons per unit time by several orders of magnitude compared with the incoming signal intensity. However, as with every amplifying process, optical amplification cannot be achieved without paying back for the unavoidable noise power added to the signal intensity. As we will see in detail in Chapter 6, the optical amplification process comes with optical noise generated by spontaneous emission inside the active medium. The intensity of the optical signal is represented by the flux of the signal photon population. Conversely, the photons generated by the spontaneous emission process inside the optical cavity represent the noise photon population. The fundamental phenomenon supporting optical amplification is stimulated emission. The basic property of stimulated emission, making the great difference from spontaneous emission and enabling optical amplification, is the coherent nature of the photon generation process. Accordingly, both signal and noise photons go through the same multiplication process by means of stimulated emission. Unless the optical cavity where the stimulated emission takes place (the active cavity) presents selective features for enhancing the signal photon population relative to the spontaneous one, there is no way to avoid noise photons going through stimulated emission, filling most of the cavity population. As a consequence, both photon populations increase, leading respectively to amplified signal intensity and to amplified spontaneous emission intensity. It should be apparent that every noise photon can create a new identical noise photon as a result of stimulated emission, effectively increasing the noise intensity in the active optical cavity. This is the well-known mechanism of amplified spontaneous emission (ASE) noise in optical amplification. Any improvement in the optical amplifier structure devoted to increasing stimulated over spontaneous emission will probably increase the optical signal-to-noise ratio (OSNR) at the cavity output. The spectrum of gain characteristic of the optical active medium is usually wide enough to support an efficient amplification of the broadband spontaneous emission spectrum, leading to the broadband ASE noise power spectral density.