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Journal of the Optical Society of America B

Effect of excited-state population density on nonradiative multiphonon relaxation rates of rare-earth ions

F. Pellé, Nicole Gardant, Francois E. Auzel

Published Feb 1, 1998• 24 citations
Publisher

Abstract

Multiphonon relaxation rate saturation is observed for rare-earth-doped glasses for high excited-state densities. This behavior is analyzed in a statistical approach; a theoretical model for the microscopic process is proposed. A phonon bottleneck effect on radiationless relaxation related to an accepting-modes saturation is suggested. At high excited-state density, ions in a phonon diffusion volume simultaneously fill the accepting modes. The critical distance below which excited ions share a common phonon bath is related to the phonon diffusion length in the host and deduced from our model. The results are in good agreement with the phonon mean free path independently deduced from sound velocity, thermal conductivity, and heat capacity.

DOI
10.1364/josab.15.000667

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Multiphonon relaxation rate saturation is observed for rare-earth-doped glasses for high excited-state densities. This behavior is analyzed in a statistical approach; a theoretical model for the microscopic process is proposed. A phonon bottleneck effect on radiationless relaxation related to an accepting-modes saturation is suggested. At high excited-state density, ions in a phonon diffusion volume simultaneously fill the accepting modes. The critical distance below which excited ions share a common phonon bath is related to the phonon diffusion length in the host and deduced from our model. The results are in good agreement with the phonon mean free path independently deduced from sound velocity, thermal conductivity, and heat capacity.
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The enhanced laser cooling performance of rare-earth-ion-doped nanocrystalline powders is predicted, compared to the bulk material, using Yb3+:Y2O3{\mathrm{Yb}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Yb3+:Y2​O3​ as the model material. This is achieved by enhancing the off-resonance, phonon-assisted absorption, which is proportional to the three factors considered in this paper: the dopant concentration, the pumping field energy, and the excitation coefficient. Using the energy transfer theory for concentration quenching, the optimum concentration corresponding to the maximum cooling power is found to be considerably larger than the currently used value, suggesting noticeable enhancement effects for laser cooling. The pumping field energy is enhanced in random nanopowders compared with bulk crystals under the same irradiation, due to the multiple scattering of photons. Photons are thus localized in the medium and do not propagate through, increasing the photon absorption of the pumping beam (and it is shown that the reabsorption of the fluorescence is negligible). Using molecular dynamics simulations, the phonon density of states (DOS) of the nanopowder is calculated, and found to have broadened modes, and extended small tails at low and high frequencies. The second-order electronic transition rate for the anti-Stokes luminescence is calculated using the Fermi golden rule, which includes the influence of this phonon DOS, and is shown to have enhancement effects on the laser cooling efficiency using nanopowders. It is finally concluded that these three enhancement mechanisms are essentially to increase the population of the three participating carriers (electron, photon, and phonon) in the interacting volume, and this also points out directions for enhancing laser cooling performance in bulk materials.
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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.
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