  Optical nanoantennas can affect the decay rates of nearby emitters by
modifying the local density of photonic states around them. In the
weak-coupling limit, and according to the Fermi's Golden Rule, the emission
spectrum of a dye is given by the energy of all the possible radiative
transitions weighted by the probability of each of them to occur. By
engineering the resonance of a nanoantenna, one can selectively enhance
specific vibronic transitions of a dye molecule, thus shaping its emission
spectrum. Since interactions between emitters and nanoantennas are known to be
position dependent, we make here use of DNA origami to precisely place an
individual dye at different positions around a gold nanorod. We show how this
relative position between the nanorod and the emitter affects the emission
spectrum of the latter. In particular, we observe the appearance of a second
fluorescence peak whose wavelength and intensity are correlated with the
fundamental plasmonic resonance of the nanorod, which we extract from its
photoluminescence spectrum. This second peak results from the selective
enhancement of transitions to different vibrational levels of the excitonic
ground state, whose energies are in resonance with the plasmonic one.
Furthermore, we argue that the drastic alteration of the fluorescence spectrum
in some of our samples cannot be accounted for with Kasha's rule, which
indicates that radiative and vibrational relaxation dye lifetimes can become
comparable through the coupling to the gold nanorods.
