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Japanese Journal of Applied Physics

Spontaneous Emission in a Very Short Optical Cavity with Plane-Parallel Dielectric Mirrors

Kikuo Ujihara, Atsushi Nakamura, Osamu Manba Osamu Manba, Xiao-Ping Feng Xiao-Ping Feng

Published Dec 1, 1991• 35 citations
Publisher

Abstract

A detailed account of the calculation on the spontaneous emission rate in a very short optical cavity with plane-parallel dielectric mirrors is given. A cavity model consisting of a pair of plane dielectric slabs is used. Guided modes as well as outgoing modes are considered. The emission rate from a two-level atom is calculated under quantum-mechanical perturbation approximation. The enhancement factor for the rate is found to be of the order of unity except for extremely short cavities. The concept of quasimodes in a very short cavity and their effective area are discussed in relation to the enhancement factor. The coupling ratios into various quasimodes are derived.

DOI
10.1143/jjap.30.3388

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A detailed account of the calculation on the spontaneous emission rate in a very short optical cavity with plane-parallel dielectric mirrors is given. A cavity model consisting of a pair of plane dielectric slabs is used. Guided modes as well as outgoing modes are considered. The emission rate from a two-level atom is calculated under quantum-mechanical perturbation approximation. The enhancement factor for the rate is found to be of the order of unity except for extremely short cavities. The concept of quasimodes in a very short cavity and their effective area are discussed in relation to the enhancement factor. The coupling ratios into various quasimodes are derived.
A quantum theory of spontaneous emission from an initially excited two-level atom in a one-dimensional optical cavity with output coupling from both sides is developed. Orthonormal mode functions with a continuous spectrum are employed, which are derived by imposing a periodic boundary condition on the whole space with a period much larger than the cavity length. The delay differential equation of the atomic state of Cook and Milonni [Phys. Rev. A 35, 5081 (1987)] is re-derived in a strict manner, where the reflectivity of the cavity mirrors is included naturally in the mode functions. An approximate solution at a single-resonant-mode limit shows the results of ``vacuum'' Rabi oscillation in an underdamped cavity and enhanced spontaneous emission rate in an overdamped cavity. For the latter case, it is found that in the optical range the spontaneous emission rate is enhanced by a factor F (finesse of the 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.>
We consider spontaneous emission in dielectric microcavities with multiple resonances that may overlap in both position and frequency. By projecting the Green tensor onto a set of quasimodes associated with the resonances, we derive the reduced spontaneous emission rate. To demonstrate the accuracy and computational efficiency of our approach, we model spontaneous emission in a two-dimensional photonic crystal with two coupled defects. Employing a quantum mechanical interpretation, we show that the spontaneous emission involves both direct decay into the individual quasimodes and photon transfer between the quasimodes. The quantum path interference between these different emission channels can cause the spontaneous emission rate to differ dramatically from the rate obtained by the summation over resonant line shapes. We also show how our approach can be used to determine the emission into particular quasimodes of multiple-resonance microcavities.
The spontaneous electromagnetic decay of a two-level atom coupled to a narrow cavity resonance is investigated rigorously in terms of the (Hermitian) modes of the ``universe'' rather than the (dissipative) quasimodes of the cavity. Special attention is paid to the strong-coupling regime (atomic linewidth \ensuremath{\Gamma}\ensuremath{\gtrsim} cavity resonance width \ensuremath{\gamma}), in which there are significant corrections to the golden rule. In particular, spontaneous decay is most rapid for intermediate values of the quality factor Q of the cavity resonance. The photon line shape, the effect of several cavity resonances, and the competition of several transitions are also investigated. The additivity of partial rates does not hold, and in some circumstances, the addition of an extra decay channel may reduce the total decay rate. These results are relevant to optical processes observed in dielectric microspheres, and also to usual laser cavities.
The spontaneous emission of photons by an atom placed near the dielectric slab is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (traveling) and the modes trapped to a waveguide formed by the slab (trapped). To describe angular properties of spontaneous emission a parametrization of the traveling modes by the outgoing waves has been proposed. Angular characteristics of the traveling photon emission, distributions of the trapped photon emission, as well as global decay rates have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error in an earlier paper by Khosravi and Loudon [Proc. R. Soc. London Ser. A 436, 373 (1992)] affecting thin slabs and results near waveguide-mode thresholds has been improved.