Resonance energy transfer: The unified theory via vector spherical harmonics

Abstract

A general formula for the rate of resonant transfer of energy between two electric multipole moments of arbitrary order using molecular quantum electrodynamics J. Chem. Phys. In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in terms of vector spherical harmonics while Hankel functions are used to define the radial component. This approach alleviates the problem of having to select physically correct solution from non-physical solutions, which seems to be inherent in plane wave derivations. The spherical coordinate system allows one to easily decompose the photon's fields into longitudinal and transverse components and offers a natural way to analyse near-, intermediate-, and far-zone RET within the context of the relative orientation of the transition dipole moments for the two molecules. Published by AIP Publishing. [http://dx

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Interpreting angular momentum transfer between electromagnetic multipoles using vector spherical harmonics

“…In the region between the emitter and the absorber the out-going field generated by the emitter interacts with the in-coming field of the absorber, also expressed by Eq. 3, but with a Hankel function of second kind [25,26]. In adherence to the principle of timereversal invariance, when both fields are expressed in a single coordinate system, their interaction, and hence the probability of photon transfer, is proportional to the Hermitian scalar product of the two fields, E JlM…”

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“…The long-standing semiclassical treatment encapsulated in the well-known Förster theory is based on a nonretarded description of electromagnetic fields [141], which was shown to strictly fail to conform to the demands of causality [142,143]. By correctly describing the interaction between the transition moments of the donor and acceptor in terms of virtual photon propagation, it emerges from QED analysis that the short-and long-range mechanisms previously considered radiationless and radiative, respectively, are simply two asymptotic limits of a unified theory of energy transfer, fully accommodating both retardation and quantum uncertainty effects [123,124,[144][145][146][147][148]. Inter alia, the QED analysis also showed that the two supposedly different mechanisms can never compete in determining the distance-dependent dynamics of energy transfer.…”