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Chinese Journal of Luminescence

Probability Distribution of Luminescence Lifetime of Nanometer Particles Containing Luminescent Ions Embedded in Media

Chang‐Kui Duan

Published Jan 1, 2007• 0 citations

Abstract

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.

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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.

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.

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.

Summary form only given. Over more than three decades many experiments have shown that the rate of spontaneous emission from an emitter can be strongly modified due to its electromagnetic surrounding. It is also well-known that the fluorescence lifetime of an emitter changes when embedded in dielectric media where aside from a change in the density of states, it is influenced by the local fields in the dielectric. The goal of our work has been to study the transition between the regime of an emitter in vacuum to that of a bulk dielectric medium, emphasizing the domain where the emitter's environment has a subwavelength extent. In our experiment we have investigated the dependence of the spontaneous emission rate of Eu/sup 3+/ ions in polymer nanospheres of different diameters, ranging from 20nm to 2000nm. In order to perform well-defined control experiments, we have combined atomic force microscopy and fluorescence confocal microscopy to make measurements only on isolated single spheres lying on a glass substrate.

The spontaneous-emission rates of emitters embedded in a thin layer 0 of a loss-free dielectric depend on their optical environment, i.e., on the optical properties of the two media 1 and 2 adjoining layer 0. For electric- and magnetic-dipole transitions the spontaneous-emission rates, normalized with respect to those in an infinite medium 0, are expressed in terms of the Fresnel reflection coefficients for plane and evanescent waves incident from medium 0 on the interfaces to the planar-stratified or homogeneous media 1 and 2, respectively. From this result which is valid for arbitrary layer thicknesses

{d}_{0}

we derive an approximation for extremely thin layers of optical thickness ${n}_{0}{d}_{0}\ensuremath{\ll}\frac{\ensuremath{\lambda}}{8}$ (where $\ensuremath{\lambda}$ is the emission wavelength) between two homogeneous loss-free dielectric media 1 and 2. For the normalized spontaneous-emission rates as functions of the refractive indices

{n}_{j}

of media

j=0, 1, \mathrm{and} 2

analytical expressions are obtained. We have used these expressions previously without proof [Phys. Rev. B 21, 4814 (1980)] to analyze experimentally observed changes in the fluorescence lifetime of

{\mathrm{Eu}}^{3+}

ions in varying optical environments, which yielded the quantum efficiency of the emitting state.