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Physical Review A

Quantum theory of microcavity-modified fluorescence decay rate under a strong coupling condition

Ying Wu

Published Feb 11, 2000• 48 citations
Publisher

Abstract

In this article, we propose a simple approach to deal with the fluorescence of a quasi-three-level system in $\ensuremath{\Lambda}$ configuration in which one of the ``levels'' is actually a band with possibly a large width. By solving this quasi-three-level molecule model, we obtain an analytical expression for the microcavity-modified fluorescence decay rate suitable for arbitrary cavities with any geometrical shape under a strong coupling condition. Applying the general result to a microsphere, we express explicitly the fluorescence decay rate's dependence on the cavity radius, emission linewidth, and the quantities characterizing the involved cavity modes, and find it in remarkable agreement with the recent fluorescence experiment by Barnes et al. [Phys. Rev. Lett. 76, 3931 (1996)]. In addition we briefly discuss the suitability of the approach for other microcavity-modified optical processes such as lasing and Raman scattering.

DOI
10.1103/physreva.61.033803

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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.

Physical Review A•Nov 1, 1997•47 citations
In this article, we propose a simple approach to deal with the fluorescence of a quasi-three-level system in \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration in which one of the ``levels'' is actually a band with possibly a large width. By solving this quasi-three-level molecule model, we obtain an analytical expression for the microcavity-modified fluorescence decay rate suitable for arbitrary cavities with any geometrical shape under a strong coupling condition. Applying the general result to a microsphere, we express explicitly the fluorescence decay rate's dependence on the cavity radius, emission linewidth, and the quantities characterizing the involved cavity modes, and find it in remarkable agreement with the recent fluorescence experiment by Barnes et al. [Phys. Rev. Lett. 76, 3931 (1996)]. In addition we briefly discuss the suitability of the approach for other microcavity-modified optical processes such as lasing and Raman scattering.
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.
Fluorescence decay rate modification has been observed for molecules in liquid microspheres (3.5 to 25 \ensuremath{\mu}m in diameter) where the molecular position and transition moment orientation are well defined. For small sizes ( <6<6<6 \ensuremath{\mu}m), the decay rates scale roughly as ${r}^{\ensuremath{-}1}$ and agree quantitatively with semiclassical calculations. For larger sizes ( >15>15>15 \ensuremath{\mu}m) where the cavity storage time and fluorescence lifetime are roughly equal, an anomalous decrease in the decay rate of $\ensuremath{\approx}30%$ is observed which is interpreted as a consequence of intermediate molecule-cavity coupling.
We use standard quantum laser theory to examine the linewidth of lasers with a four-level atomic gain medium as a function of the spontaneous emission rate into the lasing mode and the decay rates from the upper and lower lasing levels. We find that the laser linewidth ceases to exhibit the customary decrease with increased photon number when a critical photon number, proportional to the ratio of the decay rate from the lower lasing level to the rate of spontaneous emission into the lasing mode, is reached. This critical photon number would decrease as the size of the optical cavity is decreased. In addition we show that, in general, the laser linewidth depends critically on the ratio of the overall decay rates from the upper and lower lasing levels.
We consider a system consisting of a particle in the harmonic approximation, having frequency ωˉ\barωωˉ, coupled to a scalar field inside a spherical reflecting cavity of diameter LLL. By introducing {\it dressed} coordinates we define {\it dressed} states which allow a non-perturbative unified description of the radiation process, for weak and strong coupling regimes. We perform a study of the energy distribution in a small cavity, with the initial condition that the particle is in the first excited state. In the {\it weak} coupling regime, we conclude for the quasi-stability of the excited particle. For instance, for a frequency ωˉ\barωωˉ of the order ωˉ∼4.00×1014/s\barω\sim 4.00\times 10^{14}/sωˉ∼4.00×1014/s (in the visible red), starting from the initial condition that the particle is in the first excited level, we find that for a cavity with diameter L∼1.0×10−6mL\sim 1.0\times 10^{-6}mL∼1.0×10−6m, the probability that the particle be at any time still in the first excited level, will be of the order of 97%. For appropriate cavity dimensions, which are of the same order of those ensuring stability for weak coupling, we ensure for strong coupling the complete decay of the particle to the ground state in a small ellapsed time. Also we consider briefly the effects of a quartic interaction up to first order in the interaction parameter λλλ. We obtain for a large cavity an explicit λλλ-dependent expression for the particle radiation process. This formula is obtained in terms of the corresponding exact expression for the linear case and we conclude for the enhancement of the particle decay induced by the quartic interaction.
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.