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Physical Review A

Spontaneous emission from stratified dielectrics

Geert L. J. A. Rikken

Published Jun 1, 1995• 30 citations
Publisher

Abstract

We have measured the radiative transition rate of ${\mathrm{Eu}}^{3+}$ complexes in polystyrene films on various dielectric substrates. Both inhibition and enhancement of the transition rate are observed, depending on the refractive index of the substrate and thickness of the film. This is explained in terms of local photon mode amplitudes.

DOI
10.1103/physreva.51.4906

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We have measured the radiative transition rate of Eu3+{\mathrm{Eu}}^{3+}Eu3+ complexes in polystyrene films on various dielectric substrates. Both inhibition and enhancement of the transition rate are observed, depending on the refractive index of the substrate and thickness of the film. This is explained in terms of local photon mode amplitudes.
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 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 d0{d}_{0}d0​ 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 nj{n}_{j}nj​ of media j=0,1,and2j=0, 1, \mathrm{and} 2j=0,1,and2 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 Eu3+{\mathrm{Eu}}^{3+}Eu3+ ions in varying optical environments, which yielded the quantum efficiency of the emitting state.
The effect of the dielectric medium upon the spontaneous emission rate was investigated using lead borate glass of various compositions lightly doped with the Eu3+{}^{3+}3+ lanthanide ion. A dual approach used the variation of (i) electric dipole/magnetic dipole (ED/MD) emission rates from spectral integrations and (ii) absolute ED emission rates from lifetime measurements for comparison with the variation of the refractive index of the glass medium. Contrary to a previous study [Phys. Rev. Lett. 91, 203903 (2003)], the results show the relevance of the virtual-cavity model in this case. The MD emission rates were taken to follow the n3{n}^{3}n3 increase in density of photon states in the medium. The justifications for employing Eu3+{}^{3+}3+ for identifying the appropriate model are given.
We observed the change in fluorescence lifetime from a molecular dye embedded in a colloidal suspension of polystyrene spheres when the mean separation between spheres remains less than the wavelength of emission. At high densities of colloidal particles the spontaneous emission is inhibited, while as the density of colloidal particles is lowered the spontaneous emission is enhanced. This phenomenon is interpreted in terms of coherent interference from the electric field radiated by the molecular dipole and the reradiated field from the dielectric spheres.