Elsevier

Journal of Luminescence

Volumes 94–95, December 2001, Pages 293-297
Journal of Luminescence

The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity

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Abstract

The purpose of this work is to present a simple quantitative theoretical study of the self-quenching process for resonant transitions when radiative self-trapping occurs both in samples of given concentration and shape, and in a planar cavity of known reflectivity and loss. Comparing with experimental results from literature for Cr3+ and Yb3+ for T⩾77 k, we show that self-trapping may increase the self-quenching process by reducing the active ion critical concentration.

Considering that studies of effects of micro-cavities on optical transitions have generally dealt with resonant transitions, we think that another important outcome of this study is to show that, without having to rely on density of states coupling effects, a cavity of given Q may both increase or reduce the measured spontaneous lifetime of a resonant transition.

Section snippets

Theoretical aspects of self-quenching in resonant transitions

The usual picture for self-quenching is that to an increase of the active ion concentration corresponds a correlative increase of the diffusion towards non-radiative sinks. In resonant transitions, such sinks are not the usual intrinsic cross-relaxation step between two active ions but are rather the extrinsic sinks constituted by a non-radiative species or “poisonous center” [1].

The first case is typically the case of Nd3+ in many materials [2], the second case is usually the one for

Theoretical aspects of the self-quenching process with self-trapping

Because Holstein's theory for trapping [10] applies to cases with very strong absorption (α) such that α−1l, l being the sample dimension, as already noted by Nelson and Sturge in their qualitative study [9], it cannot be applied to the ruby case. In the following we shall follow Milne's approach for gas [11] and assume its applicability to solids. The diffusion equation for trapped photons proposed by Milne is the following:2x2n2n2t=4σ2N2τn2twith n=n1−(g1/g2)n2 where n1 and g1 are,

Comparison with experiments

We shall first look back at the results found in literature at 77–80 K and which had been recognized as exempt of self-trapping [3]. Only one set of results is available [4]. The more recent ones which can be derived from the induced grating experiments of Liao et al. [12], which by the very method of the experiment is unaffected by trapping [13] are unfortunately at 10 K at which temperature our assumptions on thermal equilibrium are no longer valid. The experimental points of Tolstoi and Liu [4]

Simulation of the role of a cavity

Now considering the cavity case, Eq. (11) applies and for parameters typical of a resonant transition for ions in solids, the result of Fig. 3 is obtained.

It shows that for concentrations above 0.1N0 (in the ruby case, it corresponds to about 2×1018 cm −3), the observed lifetime can be lower or higher than the radiative lifetime according to the value of the cavity Q-factor without having to consider any quantum electrodynamics effects taking place under strong confinement before the photon

Acknowledgments

One of the author (F.A.) would like to thank L. Laversenne for kindly sending her Yb3+ measurements before publication and to acknowledge an ENEA grant allowing him to start this work.

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