Plasmon-Coupled Resonance Energy Transfer II: Exploring the Peaks and Dips in the Electromagnetic Coupling Factor

We study resonance energy transfer between a donor-acceptor pair located on opposite sides of a spherical silver nanoparticle and explore the dependence of energy-transfer rate on nanoparticle size using a quantum electrodynamics theory we developed previously. This theory indicates that the rate is determined by the product of donor emission spectra, acceptor absorption spectra, and an electronic coupling factor (CF) that is determined by electrodynamics associated with the donor as a dipole emitter near the nanoparticle. We find that the CF spectra show peaks that are associated with localized surface plasmon resonances, but the locations of the most significant peaks are less correlated to the size of the nanoparticle than is found for extinction spectra for the same particle. For small nanoparticles (≲30 nm), where dipole plasmon excitation dominates, a quasi-static analysis leads to an analytical formula, in which the CF peaks and dips involve interference between donor electric field and the scattered dipolar field of the nanoparticle. For larger nanoparticles (60-210 nm), the CF maximizes at a wavelength near 355 nm independent of particle size that is determined by the highest multipole plasmon that contributes significantly to the extinction spectrum, with only small contributions arising from lower multipole plasmons, such as the dipole plasmon. Also, for wavelengths near 325 nm where the bulk plasmon resonance of silver can be excited, surface plasmons cannot be excited, so excitation from the donor cannot be transmitted by surface plasmons to the acceptor, leading to a pronounced dip in the CF. This work provides new concepts concerning plasmon-mediated energy transfer that are quite different from conventional (Förster) theory, but which should dominate energy-transfer behavior when donor and acceptor are sufficiently separated.