© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

The Journal of Chemical Physics

A quantum electrodynamical theory of three-center energy transfer for upconversion and downconversion in rare earth doped materials

Davıd L. Andrews, Robert D. Jenkins

Published Jan 15, 2001• 56 citations

Abstract

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.

DOI: 10.1063/1.1323958

Related papers

Mechanisms for three-centre energy pooling in lanthanide doped crystals

Robert D. Jenkins, Davıd L. Andrews

Summary form only given. The migration of excitation energy within dielectric crystals doped with lanthanide ions is a rich area for the study of mechanisms involving both conventional pairwise resonance energy transfer and more complex many-body effects. Within the framework of molecular quantum electrodynamics, we present a delineation of systems undergoing simultaneous transfer from two pre-excited donor ions to a single ground-state acceptor, termed three-centre energy pooling. Calculations lead to the identification of two competing mechanisms of transfer co-existing in each system-one cooperative pathway where the excitation is transferred directly to the acceptor from both donors, alongside an accretive mechanism where the excitation energy of one donor is accrued by a second, with net transfer to the acceptor ensuing.

Conference on Lasers and Electro-Optics•Aug 29, 2005•0 citations

Perspectives of a Four Center Cooperative Process in Rare Earth Doped Crystals

K. C. Mishra, John Collins

We have investigated the possibility of realizing a 4-center energy transfer among trivalent rare Earth ions in suitable hosts. A 4-center energy transfer process was originally proposed in the context of photo-physics of dendrimer molecular systems using molecular quantum electrodynamics methods. Later, a similar theoretical construct was proposed for rare Earth ions in crystalline solids. Here, we search for rare Earth ions suitable for 4-center energy transfer based on observed energy levels of 4f n multiplet structures in suitable hosts. A search for this 4-center cooperative energy transfer process experimentally will open a novel area of research in luminescence.

ECS Journal of Solid State Science and Technology•Mar 1, 2026•0 citations

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

Takashi Kushida

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.

Journal of the Physical Society of Japan•May 1, 1973•43 citations

Four-center resonance energy transfer in rare earth doped crystals

Candu, C., Victor Ciobu, Enachi, V.N. +1 more

The four-center resonance energy transfer in the framework of multipolar Hamiltonian formalism of interaction of the ions with the local transverse compound of the electromagnetic field has been investigated. The structure of the transfer amplitude points to distinct transfer mechanisms. The particular case of rare-earth ions was considered when calculating the transition dipoles matrix elements.

•Apr 1, 2005•0 citations

[Infrared multiphoton quantum cutting phenomena of rare earth materials].

Xiaobo Chen, Guojian Yang, Yun-Zhi Zhang +9 more

Infrared quantum cutting of rare earth ion is an international hot research field. It is significant for the enhancement of solar cell efficiency and for the reduction of solar cell price. The present paper summarizes the research significance of infrared quantum cutting of rare earth ion. Based on the summarization of general principle and loss mechanism of solar cell, the possible method to enhance the solar cell efficiency by infrared quantum cutting is analyzed. Meanwhile, the present paper summarizes the infrared quantum cutting phenomena of Er3+ ion single-doped material. There is intense 4I13/2 --> 4I15/2 infrared quantum cutting luminescence of Er3+ ion when the 2H11/2 energy level is excited. The intense {2H11/2 --> 4I9/2, 4I15/2 --> 4I13/2} cross energy transfer is the main reason for the result in the high quantum cutting efficiency when the 2H11/2 energy level is excited.

•Oct 1, 2012•0 citations

Energy Transfer and Cooperative Optical Transitions in Rare-Earth Doped Inorganic Materials. I. Transition Probability Calculation

Takashi Kushida

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.

Journal of the Physical Society of Japan•May 1, 1973•288 citations

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.

Summary form only given. The migration of excitation energy within dielectric crystals doped with lanthanide ions is a rich area for the study of mechanisms involving both conventional pairwise resonance energy transfer and more complex many-body effects. Within the framework of molecular quantum electrodynamics, we present a delineation of systems undergoing simultaneous transfer from two pre-excited donor ions to a single ground-state acceptor, termed three-centre energy pooling. Calculations lead to the identification of two competing mechanisms of transfer co-existing in each system-one cooperative pathway where the excitation is transferred directly to the acceptor from both donors, alongside an accretive mechanism where the excitation energy of one donor is accrued by a second, with net transfer to the acceptor ensuing.

We have investigated the possibility of realizing a 4-center energy transfer among trivalent rare Earth ions in suitable hosts. A 4-center energy transfer process was originally proposed in the context of photo-physics of dendrimer molecular systems using molecular quantum electrodynamics methods. Later, a similar theoretical construct was proposed for rare Earth ions in crystalline solids. Here, we search for rare Earth ions suitable for 4-center energy transfer based on observed energy levels of 4f n multiplet structures in suitable hosts. A search for this 4-center cooperative energy transfer process experimentally will open a novel area of research in luminescence.

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.

Infrared quantum cutting of rare earth ion is an international hot research field. It is significant for the enhancement of solar cell efficiency and for the reduction of solar cell price. The present paper summarizes the research significance of infrared quantum cutting of rare earth ion. Based on the summarization of general principle and loss mechanism of solar cell, the possible method to enhance the solar cell efficiency by infrared quantum cutting is analyzed. Meanwhile, the present paper summarizes the infrared quantum cutting phenomena of Er3+ ion single-doped material. There is intense 4I13/2 --> 4I15/2 infrared quantum cutting luminescence of Er3+ ion when the 2H11/2 energy level is excited. The intense {2H11/2 --> 4I9/2, 4I15/2 --> 4I13/2} cross energy transfer is the main reason for the result in the high quantum cutting efficiency when the 2H11/2 energy level is excited.

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.