Spontaneous emission of homogeneous broadening molecules on a micro-droplet's surface and local-field correction

Abstract

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 $a$, in which only $1/a$ and $1/a^{2}$ 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.