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Journal of the Physical Society of Japan

Energy Transfer and Cooperative Optical Transitions in Rare-Earth Doped Inorganic Materials. III. Dominant Transfer Mechanism

Takashi Kushida

Published May 1, 1973• 43 citations
Publisher

Abstract

Estimations are made of the critical concentration of energy-acceptor ions for which the average efficiency of the excitation transfer from energy-donor ions is 1/2. This gives a measure of the activator concentration at which Inokuti and Hirayama's theory is no longer applicable. Study is also made of the dominant multipole interaction responsible for the energy transfer between rare earth ions in inorganic solids. Finally, importance of the J -selection rule in the determination of the dominant interaction term in the resonance transfer and cooperative processes is emphasized.

DOI
10.1143/jpsj.34.1334

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Energy transfer and cooperative optical transitions in rare-earth doped inorganic materials-1〜3-

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Journal of the Physical Society of Japan•May 1, 1973•1 citation
Estimations are made of the critical concentration of energy-acceptor ions for which the average efficiency of the excitation transfer from energy-donor ions is 1/2. This gives a measure of the activator concentration at which Inokuti and Hirayama's theory is no longer applicable. Study is also made of the dominant multipole interaction responsible for the energy transfer between rare earth ions in inorganic solids. Finally, importance of the J -selection rule in the determination of the dominant interaction term in the resonance transfer and cooperative processes is emphasized.
Calculations made of the rates for several processes involving interactions between rare earth ions in crystals, such as resonance energy transfer, cooperative excitation transfer and cooperative optical transitions. These processes are assumed to originate from the electric multipole interactions between the ions concerned. A tensor operator method is employed in order to take account of the individual characters of the energy levels involved in the transition. Evaluation of the typical transition probability is also made on the lowest-order parity-allowed processes in nearest neighbour ions. The rates for the resonance transfer and cooperative transfer processes thus estimated are much smaller than those obtained by Miyakawa and Dexter.
An analysis is made of the transfer of the excitation energy between trivalent rare earth ions in crystals. The multipole interaction mechanisms are considered and allowances made for the migration of the excitation energy between donor ions. The proposed model is used in estimating the probabilities of elementary energy transfer events, diffusion coefficients of excitations, and concentrations of quenching centers in the case of several rare earth ions in Y3Al5O12. A comparison is made of the experimental and calculated concentration and temperature dependences of the transfer of the excitation energy between trivalent rare earth ions in Y3Al5O12 crystals; the agreement between the calculations and the experiment is good.
Three-center energy transfer affords the basic mechanism for a variety of multiphoton processes identified within materials doped with rare earths. Addressing the theory using quantum electrodynamics, general results are obtained for systems in which the fundamental photophysics engages three ions. Distinct cooperative and accretive mechanistic pathways are identified and the theory is formulated to elicit their role and features in energy transfer phenomena of pooling upconversion, sensitization, and downconversion or quantum cutting. It is shown that although the two mechanisms play significant roles in pooling and cutting, only the accretive mechanism is responsible for sensitization processes. Both mechanisms are shown to invoke Raman selection rules, which govern transitions of the mediator ions in the accretive mechanisms and transitions of the acceptor ions in the cooperative mechanisms. The local, microscopic level results are used to gauge the lattice response, encompassing concentration and structural effects. Attention is drawn to a general implication of implementing a multipolar description for the optical properties of doped solid-state ionic materials.