Resonance Energy Transfer in Arbitrary Media: Beyond the Point Dipole Approximation

In this work, we present a comprehensive theoretical and computational study of donor/acceptor resonance energy transfer (RET) beyond the dipole approximation, in arbitrary inhomogeneous and dispersive media. The theoretical method extends Förster theory for RET between particles (molecules or nanoparticles) to the case where higher multipole transitions in the donor and/or acceptor play a significant role in the energy transfer process. In our new formulation, the energy transfer matrix element is determined by a fully quantum electrodynamic expression, but its evaluation requires only classical electrodynamics calculations. By means of a time domain electrodynamical approach (TED), the matrix element evaluation involves the electric and magnetic fields generated by the donor and evaluated at the position of the acceptor, including fields associated with transition electric dipoles, electric quadrupoles, and magnetic dipoles in the donor, and the acceptor response to the electric and magnetic fields and to the electric field gradient. As an illustration of the benefits of the new formalism, we tested our method with a 512 atom lead sulfide (PbS) quantum dot as the donor/acceptor in vacuum, and with spherical nanoparticles (toy model) possessing designed transition multipoles. This includes an analysis of the effects of interferences between multipoles in the energy transfer rate. The results show important deviations from the conventional Förster dipole theory that are important even in vacuum but that can be amplified by interaction with a plasmonic nanoparticle.