Physical review. B, Condensed matter

Concentration dependence of the fluorescent energy transfer

Moshe Fibich, David L. Huber

Published Dec 15, 1979• 8 citations

Abstract

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 $c$ and present results for the ${c}^{2}$ term.

DOI: 10.1103/physrevb.20.5369

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Physical review. B, Condensed matter

Concentration dependence of the fluorescent energy transfer

Moshe Fibich, David L. Huber

Published Dec 15, 1979• 8 citations

Publisher

Abstract

c

and present results for the

{c}^{2}

term.

DOI: 10.1103/physrevb.20.5369

Related papers

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Fluorescence-line-narrowing and time-resolved studies have been conducted in ruby crystals and powders, in concentrations varying from 0.025 to 0.9 at.%. The resonance fluorescence component of the ${R}_{1}$ line at low temperatures is observed to increase dramatically as the laser is tuned from line center toward the low-energy wing of the inhomogeneously broadened absorption. This is presumed to indicate the presence of weakly coupled pairs in the wings of the line. Intraline and interline (${R}_{1}\ensuremath{\rightarrow}{N}_{1,2}$) energy transfer have also been studied, and an elaboration of earlier work is given. Time-resolved selective-excitation scans have revealed numerous channels in the vicinity of the $R$ lines by which the different pairs can be directly excited. These are assumed to be Cr ions near enough to a pair to be in a highly perturbed environment. Various experimental results are shown to be consistent with a model of rapid transfer between resonant Cr ions which feeds the pairs via a weak, nonresonant coupling to these perturbed ions. Macroscopic strain broadening is also shown to be favored over microscopic broadening, and the implications for Anderson localization in ruby are discussed.Fluorescence-line-narrowing and time-resolved studies have been conducted in ruby crystals and powders, in concentrations varying from 0.025 to 0.9 at.%. The resonance fluorescence component of the ${R}_{1}$ line at low temperatures is observed to increase dramatically as the laser is tuned from line center toward the low-energy wing of the inhomogeneously broadened absorption. This is presumed to indicate the presence of weakly coupled pairs in the wings of the line. Intraline and interline (${R}_{1}\ensuremath{\rightarrow}{N}_{1,2}$) energy transfer have also been studied, and an elaboration of earlier work is given. Time-resolved selective-excitation scans have revealed numerous channels in the vicinity of the $R$ lines by which the different pairs can be directly excited. These are assumed to be Cr ions near enough to a pair to be in a highly perturbed environment. Various experimental results are shown to be consistent with a model of rapid transfer between resonant Cr ions which feeds the pairs via a weak, nonresonant coupling to these perturbed ions. Macroscopic strain broadening is also shown to be favored over microscopic broadening, and the implications for Anderson localization in ruby are discussed.

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The time development of the spectral transfer of optical excitations in inhomogeneously broadened systems is investigated as a function of transfer range, concentration of optically active ions and the dimensionality of the system. The equation of motion method is employed to calculate the spin-wave density of states for the equivalent ferromagnet and this is transformed to obtain the time dependence of the narrow band fluorescence. It is found that neighbours out to the fifth shell in a simple cubic lattice are significant for dipole-dipole interactions. Reducing the effective dimensionality of the model leads to a considerably slower spectral redistribution of the fluorescence.The time development of the spectral transfer of optical excitations in inhomogeneously broadened systems is investigated as a function of transfer range, concentration of optically active ions and the dimensionality of the system. The equation of motion method is employed to calculate the spin-wave density of states for the equivalent ferromagnet and this is transformed to obtain the time dependence of the narrow band fluorescence. It is found that neighbours out to the fifth shell in a simple cubic lattice are significant for dipole-dipole interactions. Reducing the effective dimensionality of the model leads to a considerably slower spectral redistribution of the fluorescence.

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c

and present results for the

{c}^{2}

term.

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.

Fluorescence-line-narrowing and time-resolved studies have been conducted in ruby crystals and powders, in concentrations varying from 0.025 to 0.9 at.%. The resonance fluorescence component of the

{R}_{1}

line at low temperatures is observed to increase dramatically as the laser is tuned from line center toward the low-energy wing of the inhomogeneously broadened absorption. This is presumed to indicate the presence of weakly coupled pairs in the wings of the line. Intraline and interline (${R}_{1}\ensuremath{\rightarrow}{N}_{1,2}$) energy transfer have also been studied, and an elaboration of earlier work is given. Time-resolved selective-excitation scans have revealed numerous channels in the vicinity of the

R

lines by which the different pairs can be directly excited. These are assumed to be Cr ions near enough to a pair to be in a highly perturbed environment. Various experimental results are shown to be consistent with a model of rapid transfer between resonant Cr ions which feeds the pairs via a weak, nonresonant coupling to these perturbed ions. Macroscopic strain broadening is also shown to be favored over microscopic broadening, and the implications for Anderson localization in ruby are discussed.