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Spectroscopy Letters

Macroscopic Models for the Radiative Relaxation Lifetime of Luminescent Centers Embedded in Surrounding Media

Chang‐Kui Duan, Michael F. Reid

Published Mar 1, 2007• 19 citations
Publisher

Abstract

Two macroscopic models for the dependence of the spontaneous emission rate of luminescent ions or nanoparticles embedded in dielectric media of various optical refractive indexes are presented. The available experimental results on the spontaneous emission rate (lifetime) are examined using the two models. A simple criterion for how to choose the proper model for a given system is summarized.

DOI
10.1080/00387010701247340

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Two macroscopic models for the dependence of the spontaneous emission rate of luminescent ions or nanoparticles embedded in dielectric media of various optical refractive indexes are presented. The available experimental results on the spontaneous emission rate (lifetime) are examined using the two models. A simple criterion for how to choose the proper model for a given system is summarized.
Spontaneous emission rate is not only affected by the properties of the material itself, but also depends on the dielectric properties of the surrounding media. Recently, some work has been carried out to study the dependence of spontaneous emission rates of the luminescent-ion-containing nanometer particles on the refractive index of the media. Based on the free distribution of nanometer particles in media, the pro-bability density of luminescent lifetime is analyzed. Since nanometer particles distribute freely in media, the number of nanometer particles in a given volume surrounding the luminescent center obeys the Poission distribution. The local relative refractive index nr, which is the ratio of media effective refractive index to particle refractive index, is affected by the particle number of nanoparticles within a sphere of radius half of the radiative wavelength. The probability density function of nr can be obtained according to the dependence of nr on the particle number. Based on the relation between nr and luminescence lifetime, the analytical form of probability density function of lifetime is obtained. A calculation has been done based on the parameters given in Meltzer's experiment (Eu3+ doped Y2O3 in methanol). The result shows that the relative fluctuation of luminescence lifetime is too small to be observed. However, with increasing size of nanometer particles or density of nanometer particles, the relative fluctuation of lifetime increases greatly and could be observed.
In order to discriminate between the two macroscopic models for the dependence of the spontaneous emission rates of emitters on the refractive indices of the surrounding optical dielectric media, i.e., the local-field effect, Eu3+ activated glass samples with a range of different refractive indices were prepared for the measurements of photoluminescence emission spectrum, luminescent decay rate and refractive index. Detail analyses indicate that the local-field effect on the spontaneous emission rates follows the virtual-cavity model derived by assuming the doped luminescent ions do not disturb the optical dielectric media.
The radiative lifetime of an emitter (such as a luminescent ion) is affected not only by the properties of the emitter itself but also by the dielectric properties of the surrounding media. The fluctuation of the local electrical field caused by random distribution of polarized luminescent-ion-containing nanoparticles in media leads to the fluctuation of radiative lifetime of luminescent ions. Lifetime fluctuation has been calculated analytically by considering this effect. The results show that the fluctuation of radiative lifetime is not negligible and can be shown and observed in future experiments.
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.
An analytical expression is proposed for the rate of radiative decay of excitations of optical centers in an ellipsoidal nanoparticle that is considerably smaller than the light wavelength ( a, b, c ≪ λ ) and is embedded in the surrounding medium. This expression is compared with the corresponding expression for a bulk crystal. The time of radiative decay in nanoparticles spherical in shape and identical in size (2 R ≪ λ ) is derived as a function of the dielectric characteristics of a nanocomposite and the nanoparticle volume fraction C in suspensions and aerosols. The expressions describing the emission and absorption cross sections in spherical nanoparticles are obtained. The experimentally measured and theoretically calculated decay times of metastable levels of rare-earth impurity ions in YAG and Y 2 O 3 crystalline nanoparticles are compared with those for bulk crystals with the same structure.