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Annual Meeting Optical Society of America

Experimental studies of refractive-index dependence of exciton spontaneous decay rates

Seng‐Tiong Ho, S. L. McCall, Richard E. Slusher

Published Jan 1, 1990• 0 citations
Publisher

Abstract

The spontaneous decay rates of atoms can be altered by embedding them in a bulk dielectric medium. The alteration of the decay rates depends on three physical factors: a photon density of state factor, a local-field correction factor, and a field normalization factor. There are conflicting expressions in the literature for the local-field correction and field normalization factors. However, it is expected that for a thin slab a change in the total decay rate for an embedded atom or exciton should change when the slab thickness is approximately ( λ )/2πn. We are fabricating dielectric slabs with dimensions in this range that will allow us to demonstrate both the dependence of decay rate on the slab thickness and the index of the surrounding medium. Our experiment involves a technique for embedding thin GaAs/AlGaAs quantum well structures in different dielectric media with n ranging 1.5–3.5 and measuring the spontaneous decay rates.

DOI
10.1364/oam.1990.wq3

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The spontaneous decay rates of atoms can be altered by embedding them in a bulk dielectric medium. The alteration of the decay rates depends on three physical factors: a photon density of state factor, a local-field correction factor, and a field normalization factor. There are conflicting expressions in the literature for the local-field correction and field normalization factors. However, it is expected that for a thin slab a change in the total decay rate for an embedded atom or exciton should change when the slab thickness is approximately ( λ )/2πn. We are fabricating dielectric slabs with dimensions in this range that will allow us to demonstrate both the dependence of decay rate on the slab thickness and the index of the surrounding medium. Our experiment involves a technique for embedding thin GaAs/AlGaAs quantum well structures in different dielectric media with n ranging 1.5–3.5 and measuring the spontaneous decay rates.
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 calculations of the rates of decay of an excited atom embedded in an absorbing dielectric. Decay can occur by spontaneous emission into transverse radiative modes of the electromagnetic field and by Joule heating via longitudinal coupling of the atom to the dielectric. The spontaneous emission (transverse) decay rate is modified in a dielectric, being the free-space rate multiplied by the real part of the refractive index at the transition frequency of the atom. There is a further modification due to the difference between the macroscopic dielectric field and the local field at the position of the atom. In addition there is a longitudinal decay rate which is proportional to the imaginary part of the dielectric constant and therefore vanishes in non-absorbing media. We derive expressions for each of these rates of decay and discuss the physical mechanisms leading to them.
We have calculated the effect of material absorption on the rate of spontaneous emission by an embedded atom using a macroscopic Green-function approach and a microscopic Hamiltonian method that includes reservoir damping. When local field effects are neglected, the free-space emission rate is modified by the real part of the refractive index at the transition frequency of the embedded atom. Local field effects are introduced via a local field correction factor. This modification of the spontaneous emission rate generalizes a well-known result for transparent media and is of crucial importance in assessing the degree of inhibition of spontaneous emission for frequencies close to the resonances of the dielectric.
Recently, there has been great experimental interest in studying the behavior of active atoms embedded in a dielectric medium because of the possibility of manipulating the spontaneous decay rate of these atoms.1 More important, the decay rate of such atoms warrants special study as it is affected by additional physical factors not present in cavity QED. We show that the usual value given for one of these additional factors is incorrect, and the correct value can be related to a basic property of the standard QED Hamiltonian.