Physical review. B, Condensed matter

Theory of donor fluorescence in the diffusion limit

Koushik Ghosh, John Hegarty, David L. Huber

Published Sep 15, 1980• 16 citations

Abstract

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 $t$-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 ${\mathrm{Pr}}_{0.95}$${\mathrm{F}}_{3}$: ${\mathrm{Nd}}_{0.05}^{3+}$ and also with the results of the diffusion model of Yokota and Tanimoto.

DOI: 10.1103/physrevb.22.2837

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Physical review. B, Condensed matter

Theory of donor fluorescence in the diffusion limit

Koushik Ghosh, John Hegarty, David L. Huber

Published Sep 15, 1980• 16 citations

Publisher

Abstract

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

t

-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

{\mathrm{Pr}}_{0.95}$${\mathrm{F}}_{3}

{\mathrm{Nd}}_{0.05}^{3+}

and also with the results of the diffusion model of Yokota and Tanimoto.

DOI: 10.1103/physrevb.22.2837

Related papers

Time-dependent effects in fluorescent line narrowing

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

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.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.

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Temperature Dependence of Fluorescence Linewidths in Pr F3 : A Comment on "Excited-State Exchange Broadening of Optical Transitions in Pr Cl3 "

J. W. Allen

Data are reported which show that the temperature dependence of fluorescence linewidths in Pr ${\mathrm{F}}_{3}$ are qualitatively like those in La ${\mathrm{F}}_{3}$ : ${\mathrm{Pr}}^{3+}$ . This result is interpreted as supporting the explanation of German and Kiel for the anomalous temperature dependence of fluorescence linewidths in Pr ${\mathrm{Cl}}_{3}$ .Data are reported which show that the temperature dependence of fluorescence linewidths in Pr${\mathrm{F}}_{3}$ are qualitatively like those in La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$. This result is interpreted as supporting the explanation of German and Kiel for the anomalous temperature dependence of fluorescence linewidths in Pr${\mathrm{Cl}}_{3}$.

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Trapping of optical excitation by two types of acceptors in La0.72 Pr0.25 Nd0.03 F3

Thomas J. Glynn, I. Laulicht, Liren Lou +2 more

We have investigated the process of quenching of fluorescence from the $^{3}P_{0}$ state of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{La}}_{0.72}$ ${\mathrm{Pr}}_{0.25}$ ${\mathrm{Nd}}_{0.03}$ ${\mathrm{F}}_{3}$ due to cross relaxation to Pr and Nd ions. The fluorescence decay of the ensemble of Pr ions after pulsed excitation is measured as a function of temperature in the (2-70)-K region. Cross relaxation occurs either directly or through a donor-donor transfer within the inhom-geneous line. Knowledge of the dynamics occurring within the inhomogeneous line derived from previous fluorescence line-narrowing experiments is used to analyze the cross-relaxation process from a microscopic viewpoint according to models for fluorescence decay in the presence of traps. In general the decay is consistent with an electric dipole-dipole transfer mechanism. At 2 K the decay can be well described by a direct transfer to Pr and Nd traps without donor-donor transfer. The temperature dependence of the decay at long times can be described for $35<T<70$ K by the hopping model. The agreement with theory is much better if the cross relaxation to Nd ions is assumed to occur mainly via the lowest Stark level of the $^{4}I_{\frac{9}{2}}$ manifold.We have investigated the process of quenching of fluorescence from the $^{3}P_{0}$ state of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{La}}_{0.72}$${\mathrm{Pr}}_{0.25}$${\mathrm{Nd}}_{0.03}$${\mathrm{F}}_{3}$ due to cross relaxation to Pr and Nd ions. The fluorescence decay of the ensemble of Pr ions after pulsed excitation is measured as a function of temperature in the (2-70)-K region. Cross relaxation occurs either directly or through a donor-donor transfer within the inhom-geneous line. Knowledge of the dynamics occurring within the inhomogeneous line derived from previous fluorescence line-narrowing experiments is used to analyze the cross-relaxation process from a microscopic viewpoint according to models for fluorescence decay in the presence of traps. In general the decay is consistent with an electric dipole-dipole transfer mechanism. At 2 K the decay can be well described by a direct transfer to Pr and Nd traps without donor-donor transfer. The temperature dependence of the decay at long times can be described for $35<T<70$ K by the hopping model. The agreement with theory is much better if the cross relaxation to Nd ions is assumed to occur mainly via the lowest Stark level of the $^{4}I_{\frac{9}{2}}$ manifold.

Physical review. B, Condensed matterMay 1, 19849 citations

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

t

-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

{\mathrm{Pr}}_{0.95}$${\mathrm{F}}_{3}

{\mathrm{Nd}}_{0.05}^{3+}

and also with the results of the diffusion model of Yokota and Tanimoto.

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.

\frac{2}{3x}

and

3x

, where $x=\frac{(\ensuremath{\gamma}+{\ensuremath{\gamma}}_{c})}{(\ensuremath{\gamma}+2{\ensuremath{\gamma}}_{c})}$. The envelope of the intensity correlations is found to decay at the rate $\frac{(3\ensuremath{\gamma}+{\ensuremath{\gamma}}_{c})}{2}$.

The dynamics of trapping of optical excitation in a disordered system of ions in a solid is studied using time-resolved fluorescence measurements. In the system Pr

{\mathrm{F}}_{3}

doped with Nd, the randomly distributed Nd ions act as sinks for the Pr excitation. The transfer to the Nd traps can occur in conjunction with transfer among the Pr ions. In this system the Pr-Pr transfer is strongly temperature dependent while the Pr-Nd transfer is temperature independent at low temperatures. By changing the temperature we can span the range from no Pr-Pr transfer to very (infinitely) fast Pr-Pr transfer in one single system. We have identified these limits. In addition we have placed boundaries on the applicability of the diffusion and hopping models in describing trapping in the intermediate temperature regime where the Pr-Pr and Pr-Nd transfer rates are comparable.

Data are reported which show that the temperature dependence of fluorescence linewidths in Pr

{\mathrm{F}}_{3}

are qualitatively like those in La

{\mathrm{F}}_{3}

{\mathrm{Pr}}^{3+}

. This result is interpreted as supporting the explanation of German and Kiel for the anomalous temperature dependence of fluorescence linewidths in Pr

{\mathrm{Cl}}_{3}

We have investigated the process of quenching of fluorescence from the

^{3}P_{0}

state of

{\mathrm{Pr}}^{3+}

{\mathrm{La}}_{0.72}

{\mathrm{Pr}}_{0.25}

{\mathrm{Nd}}_{0.03}

{\mathrm{F}}_{3}

due to cross relaxation to Pr and Nd ions. The fluorescence decay of the ensemble of Pr ions after pulsed excitation is measured as a function of temperature in the (2-70)-K region. Cross relaxation occurs either directly or through a donor-donor transfer within the inhom-geneous line. Knowledge of the dynamics occurring within the inhomogeneous line derived from previous fluorescence line-narrowing experiments is used to analyze the cross-relaxation process from a microscopic viewpoint according to models for fluorescence decay in the presence of traps. In general the decay is consistent with an electric dipole-dipole transfer mechanism. At 2 K the decay can be well described by a direct transfer to Pr and Nd traps without donor-donor transfer. The temperature dependence of the decay at long times can be described for

35<T<70

K by the hopping model. The agreement with theory is much better if the cross relaxation to Nd ions is assumed to occur mainly via the lowest Stark level of the

^{4}I_{\frac{9}{2}}

manifold.