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.