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Physical Review A

Theory of spontaneous emission in an optical cavity

Ichiro Takahashi, Kikuo Ujihara

Published Sep 1, 1997• 13 citations
Publisher

Abstract

Spontaneous emission in a one-dimensional Fabry-P\'erot-type optical cavity is analyzed quantum mechanically. Via a monolayer dielectric cavity model, expressions describing the atomic-location dependence of the emission intensities and the spectra observed on both sides of the cavity are obtained. The probability amplitude for the upper atomic state is analyzed and its time-evolution equation is given. The probability amplitude is shown to be proportional to ``the electric field amplitude for a single emission event'' introduced classically by Huang et al. [Appl. Phys. Lett. 61, 2961 (1992)]. An expression for the emission spectrum applicable to a general one-dimensional cavity structure is obtained.

DOI
10.1103/physreva.56.2299

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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.
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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.>
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 formalism for studying spontaneous decay of an excited two-level atom in the presence of dispersing and absorbing dielectric bodies is developed. An integral equation, which is suitable for numerical solution, is derived for the atomic upper-state-probability amplitude. The emission pattern and the power spectrum of the emitted light are expressed in terms of the Green tensor of the dielectric-matter formation, including absorption and dispersion. The theory is applied to the spontaneous decay of an excited atom at the center of a three-layered spherical cavity, with the cavity wall being modeled by a band-gap dielectric of Lorentz type. Both weak and strong coupling are studied, the latter with a special emphasis on cases where the atomic transition is (i) in the normal-dispersion zone near the medium resonance, and (ii) in the anomalous-dispersion zone associated with the band gap. In a single-resonance approximation, conditions of the appearance of Rabi oscillations and closed solutions to the evolution of the atomic state population are derived, which are in good agreement with the exact numerical results.