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Optics and Spectroscopy

Spontaneous emission of broadened molecules on the surface of a microdroplet

Y. Xia, Guang‐Can Guo, P. T. Leung

Published Sep 1, 2005• 0 citations
Publisher

Abstract

The spontaneous emission of a broadened molecule on the surface of a microsphere is studied. Through detailed analysis, we show that only weak coupling between a broadened atom (molecule) and the electromagnetic fields exists in a spherical dielectric cavity whether the sphere is small or large. From these results, we find an explicit expression for the spontaneous emission decay rate for a broadened surfactant molecule on the surface of a microdroplet with radius a , in which only 1/ a and 1/ a 2 components are exhibited. Then we apply this expression to a real experiment and obtain a consistent result with the experiment.

DOI
10.1134/1.2055948

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The spontaneous emission of a broadened molecule on the surface of a microsphere is studied. Through detailed analysis, we show that only weak coupling between a broadened atom (molecule) and the electromagnetic fields exists in a spherical dielectric cavity whether the sphere is small or large. From these results, we find an explicit expression for the spontaneous emission decay rate for a broadened surfactant molecule on the surface of a microdroplet with radius a , in which only 1/ a and 1/ a 2 components are exhibited. Then we apply this expression to a real experiment and obtain a consistent result with the experiment.
We consider the spontaneous emission of a broadening molecule on the surface of a micro-sphere in this paper. The density of states for the micro-cavity is derived from quasi-normal models(QNM's) expansion of the correlation functions of electromagnetic fields. Through detailed analysis we show that only weak coupling between a broadening atom(molecule) and the electromagnetic fields exists in a dielectric sphere cavity whether the sphere is small or big. From these results we find the explicit expression of the spontaneous emission decay rate for a surfactant broadening molecule on the surface of a micro-droplet with radius aaa, in which only 1/a1/a1/a and 1/a21/a^{2}1/a2 components exhibit. Then we apply this expression to a real experiment and obtain a consistent result with the experiment. We also show that the real-cavity model of local field correction is accurate, and reveal that the local-field correction factor can be measured precisely and easily by fluorescence experiments of surfactant molecules. Moreover, the spontaneous decay of a surfactant molecular on droplet's surface is sensitive to the atomic broadening, so that the fluorescence experiment in a micro-sphere cavity can be used to estimate the radiative broadening.
Summary form only given. Over the last three decades of the 20 th century many experiments have demonstrated that the rate of spontaneous emission for an emitter is determined by its electromagnetic surrounding. This phenomenon has been usually studied for atoms or molecules placed in the vicinity of mirrors or in optical resonators. Furthermore, it is also well-known that the fluorescence lifetime of an emitter changes after being embedded in dielectric media where aside from a change in the refractive index, it experiences the local fields in the dielectric. For a spherical medium larger than the order of a wavelength it is known that the coupling to Mie modes of this dielectric resonator has a large influence on the emission rate of an emitter inside. However, when the medium becomes comparable or smaller than a wavelength one can no longer speak of resonator modes. Here we report on an experiment where we have studied the variation of the spontaneous emission rate as the dielectric medium surrounding an emitter is made smaller and smaller down to a few nanometers.
Spontaneous decay of an excited atom near a dispersing and absorbing microsphere of given complex permittivity that satisfies the Kramers-Kronig relations is studied, with special emphasis on a Drude-Lorentz permittivity. Both the whispering gallery field resonances below the band gap (for a dielectric sphere) and the surface-guided field resonances inside the gap (for a dielectric or a metallic sphere) are considered. Since the decay rate mimics the spectral density of the sphere-assisted ground-state fluctuation of the radiation field, the strengths and widths of the field resonances essentially determine the feasible enhancement of spontaneous decay. In particular, strong enhancement can be observed for transition frequencies within the interval in which the surface-guided field resonances strongly overlap. When material absorption becomes significant, then the highly structured emission pattern that can be observed when radiative losses dominate, reduces to that of a strongly absorbing mirror. Accordingly, nonradiative decay becomes dominant. In particular, if the distance between the atom and the surface of the microsphere is small enough, the decay becomes purely nonradiative.
We have investigated the use of micron-sized liquid droplets as sample medium to detect single fluorescent molecules in solution. The use of microdroplets (5 - 15 micrometers diameter) offers several powerful advantages over single-molecule detection schemes involving measurements on bulk liquids where the probe volume is defined by the laser beam. In addition, cavity-quantum electrodynamical (QED) effects have been observed which influence both spontaneous emission rates and fluorescence yields of dye molecules in these microspheres.
Fluorescence decay kinetics of Rhodamine 6-G molecules in levitated glycerol microdroplets (4--20 microns in diameter) have been investigated to determine the effects of spherical cavity resonances on spontaneous emission rates. For droplet diameters greater than 10 microns, the fluorescence lifetime is essentially the same as in bulk glycerol. As the droplet diameter is decreased below 10 microns, bi-exponential decay behavior is observed with a slow component whose rate is similar to bulk glycerol, and a fast component whose rate is as much as a factor of 10 larger than the bulk decay rate. This fast component is attributed to cavity enhancement of the spontaneous emission rate and, within the weak coupling approximation, a value for the homogeneous linewidth at room temperature can be estimated from the fluorescence lifetime data.
The rates of spontaneous emission and stimulated emission and absorption for a two-level atom in a dielectric microsphere are calculated for weak E1 coupling. The A coefficient for spontaneous emission is proportional to the zero-point fluctuation of the electric field ℰij evaluated in the previous paper [ J. Opt. Soc. Am. B4, 1995 ( 1987)], which shows sharp resonances in frequency (Q > 104). It is verified that the ratio of the A and B coefficients is determined by the spectral density of thermal radiation. The level shift tends to repel the transition line away from the cavity resonance.