Journal of the Optical Society of America B

Probability density function of the rate of energy transfer from luminescent ions to a random distribution of traps in the static limit

Jean‐François Bisson

Published Apr 8, 2015• 1 citation

Abstract

The transfer of excitation of luminescent ions to a random distribution of traps is revisited in the static limit, with the emphasis on the probability density function (PDF) of the decay rate. Knowledge of the PDF is advantageous for situations when the time evolution of an individual ion’s excited state differs from an exponential decay or when no closed-form solution for the ensemble average exists, because it allows one to reconstruct an ensemble average from the knowledge of the behavior of a single class of ions. A model with dipole-dipole interactions with no minimum distance leads, in the continuum limit, to an inverse gamma (IG) PDF with shape parameter α=1/2, which has infinite moments. With a minimum nearest trap distance, closed-form solutions of the moments of the actual PDF are well matched with those of a smoothly truncated IG distribution.

DOI: 10.1364/josab.32.000757

Related papers

Editors' Choice—A Quantum Electrodynamics Formulation of Energy Transfer between Two Optically Active Ions

K. C. Mishra, John Collins

We have visited the nonradiative electron transfer process between optically active ions in luminescent materials. In contrast to the earlier formulations using multipolar expansion of instantaneous coulomb interaction between electrons, we have utilized a quantum electrodynamics (QED) approach to study the process of energy transfer from an excited ion to another. Such energy transfers occur in both sensitized luminescence and cross relaxations in the excited state. We have here investigated the nonradiative energy transfer processes specifically mediated by electric dipole moment-magnetic dipole moment and magnetic electric dipole moment-magnetic dipole moment interactions using a Feynman diagrammatic method. We have shown how experimentally relevant transfer rates could be obtained using a QED formulation involving discrete energy levels and spectral line shape function for emission and absorption profiles of interactive ions. Additional features of the dependence of the energy transfer rates on the interionic distance arising from retarded interaction potential have been pointed out.

ECS Journal of Solid State Science and TechnologyJan 1, 20186 citations

Energy transfer by diffusion and the dipole-dipole interaction: A new perturbation expansion

Paolo Sibani, Jørgen Boiden Pedersen

The transfer of electronic energy by diffusion and by the dipole-dipole interaction in solids and liquids is modeled by a diffusion equation with an ${r}^{\ensuremath{-}6}$ sink term plus a boundary condition at the distance of closest approach. The boundary condition is either absorptive, giving rise to diffusive transfer, or reflective, in which case the transfer is direct but modulated by diffusion. We solve the equation by a perturbation expansion in which the expansion parameter is inverse time, i.e., the $t\ensuremath{\rightarrow}\ensuremath{\infty}$ limit (the steady-state value) is reproduced exactly. The perturbation method gives accurate results for physically relevant values of the characteristic parameters and simple closed-form expressions for the time-dependent rate coefficient and the survival probability of an isolated pair are obtained for the first time when the diffusional transfer is larger than the direct transfer.

Physical Review AMar 1, 19849 citations

Fluorescence Line Narrowing in Dilute Systems with Nearest-Neighbor Transfer

David L. Huber

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

International Conference on Luminescence - 1984Jan 1, 19840 citations

Spontaneous emission of an excited atom in a random absorbing medium

Wei Guo

The problem of spontaneous emission of an excited atom inside a random medium formed by randomly distributed dipoles is theoretically discussed by explicitly calculating the decay rate of the atom. After averaging over all the density fluctuations of the medium, we obtain an analytical expression of the decay rate in the low-density limit, which shows that inside a random medium the relaxation of an excited state is enhanced due to the density-fluctuation correlations of the random medium.

Physical Review AApr 1, 200410 citations

Kinetics of luminescence of isoelectronic rare-earth ions in III-V semiconductors

H. J. Łożykowski

In this work we have developed a kinetics model of energy transfer from the host lattice to the localized core excited states of rare-earth isoelectronic structured traps (REI traps). The presence of low-lying empty core orbitals in rare-earth impurities introduces new excitation and recombination phenomena. To adequately describe the energy transfer to a REI trap, the buildup and decay kinetics of rare-earth luminescence, we consider six separate states of the REI impurity (unoccupied, electron occupied, electron occupied excited, exciton occupied, excited electron occupied, and excited exciton occupied). The energy-transfer processes occur through an Auger mechanism where the recombination energy of the bound electron with a free hole is transferred nonradiatively to the core states, or energy can be transferred from the bound exciton on a REI trap to the core states. If the initial and final states are not resonant (in both mechanisms), the energy mismatch must be accommodated by emission or absorption of phonons. Furthermore we discuss details of several quenching processes, which are incorporated into the kinetics equations. We derive two sets of differential equations for semi-insulating and n-type semiconductors governing the kinetics of rare-earth luminescence. Equations have been solved by a numerical method to derive the time dependence of the rise and decay kinetics as a function of excitation intensity. The numerically simulated luminescence rise and decay times show a good overall quantitative agreement with experimental data obtained for InP:Yb, over a wide range of generation rates.

Physical review. B, Condensed matterDec 15, 1993105 citations

Depolarization of Resonance Fluorescence from Interacting Atoms

Lue‐Yung Chow Chiu

The polarization of the resonance fluorescence of interacting atoms and the transfer of coherence, due to the exchange of excitation, are studied theoretically. The treatment is for the general case where both the excited and the ground states can have arbitrary angular momenta, except that they can be connected to each other by an allowed transition. Electrostatic dipole–dipole interaction and electromagnetic radiative interaction are considered simultaneously as the perturbations on the system. Heitler and Ma's generalized time-dependent perturbation method is used. The system is quantized with respect to the space-fixed z axis and a static magnetic field along the z axis may be present, so that the magnetic sublevels (m, m′, etc., for the excited state J, and α, β, etc., for the ground state J′) are not necessarily degenerate. The intensity of the scattered light of a given polarization, in a given direction, is expressed as a function of kR (where ℏck is the energy of excitation and R is the internuclear distance), and of the orientation of R with respect to z axis. The matrix elements (ℏ / 2)γmβ,αm′ and Vmβ,αm′, which cause resonant transfer of excitation between two atoms through radiative and electrostatic interaction, respectively, are also expressed as a function of kR, and of the orientation of R. For randomly oriented atoms, the polarization after being averaged over the random orientation of R becomes a function of kR. Numerical calculations have been carried out for S01 → 1P1 transition. The coherence is shown to be conserved upon resonant transfer of excitation when R is parallel to the quantization axis.

The Journal of Chemical PhysicsJan 1, 19704 citations