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.
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.
A new quantum electrodynamical (QED) method is presented, based in the Schrödinger representation, for the calculation of the rate of energy transfer between identical molecules. In contrast to existing methods in this representation, the new treatment gives explicitly causal and energy-conserving results. By returning to perturbation theory the correct, complex form for the electric dipole–electric dipole interaction tensor is obtained, without recourse to the physical, ‘‘outgoing wave’’ arguments of quantum scattering theory necessary if the Fermi rule is used. This method also allows a new interpretation for the role of the time-ordered diagrams involved, which may be useful in the rigorous treatment of higher order cooperative processes. The QED treatment uses virtual photon coupling, and incorporates both the Coulombic, R−6 dependence, and the R−2 dependence characteristic of two-step radiative transfer.
A pair of nonidentical two-level atoms, separated by a fixed distance R, interact through photon exchange. The system is described by a state vector which is assumed to be a superposition of four "essential states": (1) the first atom is excited, the second one is in the ground state, and no photon is present, (2) the first atom is in its ground state, the second one is excited, and no photon is present, (3) both atoms are in their ground states and a photon is present, and (4) both atoms are excited and a photon is also present. The system is initially in state (1). The probabilities of each atom being excited are calculated for both the minimally-coupled interaction and the multipolar interaction in the electric dipole approximation. For the minimally-coupled interaction Hamiltonian, the second atom has a probability of being instantaneously excited, so the interaction is not retarded. For the multipolar interaction Hamiltonian, the second atom is not excited before the retardation time, which agrees with special relativity. For the minimally-coupled interaction the nonphysical result occurs because the unperturbed Hamiltonian is not the energy operator in the Coulomb gauge. For the multipolar Hamiltonian in the electric dipole approximation the unperturbed Hamiltonian is the energy operator. An active view of unitary transformations in nonrelativistic quantum electrodynamics is used to derive transformation laws for the potentials of the electromagnetic field and the static Coulomb potential. For a specific choice of unitary transformation the transformation laws for the potentials are used in the minimally-coupled second-quantized Hamiltonian to obtain the multipolar Hamiltonian, which is expressed in terms of the quantized electric and magnetic fields.
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.
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.
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.
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.