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Physical review. B, Solid state

Time-dependent effects in fluorescent line narrowing

David L. Huber, D. S. Hamilton, Baruch Barnett

Published Nov 15, 1977• 200 citations
Publisher

Abstract

A study is made of time-dependent effects in fluorescent line narrowing. We analyze the ratio $R(t)=\frac{{I}_{N}(t)}{[{I}_{N}(t)+{I}_{B}(t)]}$ where ${I}_{N}(t)$ is the intensity of the narrow component and ${I}_{B}(t)$ is the intensity of the background. We formulate a theory for $R(t)$ based on coupled rate equations, which is applicable when $\mathrm{kT}$ is much greater than the inhomogeneous linewidth. $R(t)$ is calculated exactly for an ordered array of optically active ions. In the case of dilute systems the short-time behavior is determined for all values of the concentration. Backtransfer effects are treated in a variety of approximations. Comparison is made with experimental data from ${\mathrm{Pr}}_{0.2}$${\mathrm{La}}_{0.8}$${\mathrm{F}}_{3}$, and suggestions are given for further development of the theory.

DOI
10.1103/physrevb.16.4642

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A study is made of time-dependent effects in fluorescent line narrowing. We analyze the ratio R(t)=IN(t)[IN(t)+IB(t)]R(t)=\frac{{I}_{N}(t)}{[{I}_{N}(t)+{I}_{B}(t)]}R(t)=[IN​(t)+IB​(t)]IN​(t)​ where IN(t){I}_{N}(t)IN​(t) is the intensity of the narrow component and IB(t){I}_{B}(t)IB​(t) is the intensity of the background. We formulate a theory for R(t)R(t)R(t) based on coupled rate equations, which is applicable when kT\mathrm{kT}kT is much greater than the inhomogeneous linewidth. R(t)R(t)R(t) is calculated exactly for an ordered array of optically active ions. In the case of dilute systems the short-time behavior is determined for all values of the concentration. Backtransfer effects are treated in a variety of approximations. Comparison is made with experimental data from {\mathrm{Pr}}_{0.2}$${\mathrm{La}}_{0.8}$${\mathrm{F}}_{3}, and suggestions are given for further development of the theory.
We analyze the time development of the sharp-line fluorescence in a time-resolved fluorescent-line-narrowing experiment. The optically active ions are distributed at random on a lattice. Symmetric transfer rates are assumed which are independent of the energy mismatch between ions. We discuss a systematic expansion of fluorescent intensity in powers of the concentration ccc and present results for the c2{c}^{2}c2 term.
We outline the results of an analysis of fluorescence line narrowing1 in dilute systems. We assume that a fraction, p, of the sites on a d-dimensional lattice are occupied at random by optically active ions and that the transfer of optical excitation can only take place between ions occupying nearest-neighbor sites. The normalized intensity of the sharp line fluorescence following excitation of an inhomogeneously broadened line by a monochromatic source is equal to exp [−γRt]<P(t)>, where γR is the radiative decay rate and <P(t)> is the probability that an ion excited at t=0 is also excited at time t.2
Time dependence of fluorescence from donors is studied in the diffusion limit when there is a large number of donors in the sphere of influence of an acceptor. The average ttt-matrix approximation is used to derive the Laplace transform of the normalized intensity in this limit. The time dependence of the decay of the fluorescence is compared with experimental data on Pr0.95{\mathrm{Pr}}_{0.95}Pr0.95​F3{\mathrm{F}}_{3}F3​: Nd0.053+{\mathrm{Nd}}_{0.05}^{3+}Nd0.053+​ and also with the results of the diffusion model of Yokota and Tanimoto.
The temporal dependence of the fluorescence line shape of Pr ion diluted in LaF3{\mathrm{F}}_{3}F3​ has been studied in detail. The line-shape study is based on the assumption that the cross relaxation between Pr ions dominates the nonradiative process. The ion-ion interaction has been directly probed by the two-ion cooperative absorption process under which a 3P0^{3}P_{0}3P0​ level lifetime dilation has been observed. The dilation effect can be suppressed when the spectral energy transfer is switched on by raising the temperature of the host crystal. The temporal behavior of the fluorescence line shape of the 1D2^{1}D_{2}1D2​ level has been systematically investigated. The "inhomogeneous" linewidth is found to be composed of a main central peak and a series of ion-pair satellites. The shorter decay lifetime of the ion-pair states results in the narrowing of the emission line shape at later times. The energy positions of the ion-pair states have been measured from the 1D2^{1}D_{2}1D2​ ion pairs up-conversion fluorescence process. The lifetime of the ion-pair states is determined by the coupling strength of the cross relaxation from an excited ion to its partner ion and hence varies according to the ion-pair separation. The decay under the inhomogeneous width is nonexponential in general. Based on the number of the distinguished ion pair levels, a concept of the sphere of influence is introduced. Following this model, an approach has been developed which allows us to study the decay characteristics. Systematical trends emerge from such analysis. The cross-relaxation coupling constants for ion pairs have been extracted from the decay curves and profiles of the ion-pairs line shape have been mapped out. Their peak positions agree with those obtained from 1D2^{1}D_{2}1D2​ ion-pair up-conversion fluorescence measurements.
We analyze the early-time development of the spectral transfer of optical excitation in inhomogeneously broadened systems. Previous models for the decay of the narrow-band fluorescence are generalized to include systems with asymmetric energy-dependent transfer rates. It is assumed that the energy splittings of the ions are uncorrelated. An analogous model for the early-time development of the background fluorescence is outlined. Detailed results are presented for spectral transfer over a Gaussian line shape assuming a dipole-dipole mechanism with rates that are inversely proportional to the square of the energy mismatch. Comparison is made with the treatment of Holstein et al.