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Physical Review B

Local-field effect on the spontaneous radiative emission rate

Chang‐Kui Duan, Hongli Wen, Peter A. Tanner

Published Jun 24, 2011• 23 citations
Publisher

Abstract

The effect of the dielectric medium upon the spontaneous emission rate was investigated using lead borate glass of various compositions lightly doped with the Eu${}^{3+}$ 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 ${n}^{3}$ increase in density of photon states in the medium. The justifications for employing Eu${}^{3+}$ for identifying the appropriate model are given.

DOI
10.1103/physrevb.83.245123

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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.
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.
We report the first measurements, to our knowledge, of the modification of spontaneous emission rates of Eu3+ ions in the visible region owing to an absorbing medium. Precise levels of the absorption coefficient are introduced by codoping with different amounts of Nd3+. We use a binary glass system PbO-B2O3 as the host, the compositional variation of which leads to a change in the real part of the refractive index. Measured lifetimes are found to follow the real cavity model, and the data are analyzed by the model proposed by Scheel et al. [Phys. Rev. A 60, 4094 (1999)]. We give estimates of the parameter that is related to the radius of the cavity around Eu3+.
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.
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.
We present a simple theory on the effect of optical dephasing on the spontaneous emission (SE) rate in a microcavity containing (absorbing) dispersive dielectric media based on a photon Green's-function formalism in which the reservoir damping of medium polarizations is included in a phenomenological way. The theory yields the well-known result that the SE rate in free space is modified by the real part of the refractive index at the transition frequency of an atom in a bulk dielectric. On the other hand, it turns out that the degree of the alteration of the SE rate in a high-Q microcavity with dispersive media is affected not only by the real part of the refractive index but also by the imaginary part of the refractive index that is associated with the dephasing of the photon field due to the reservoir damping, i.e., the destruction of self-interference of the photon field.