15 Cooperative Effects in Plasmonics
545
efficient only for relatively short distances ∪10 nm between a donor and an acceptor
[37], the plasmon-mediated energy transfer channels provided by NPs [29, 62–66],
metal films and waveguides [31, 65] or doped monolayer graphene [67] can lead to
a significant increase of FRET efficiency and range.
The efficiency of plasmon-mediated FRET between a donor and an acceptor
situated near a metal nanostructures is determined in a competition between the
plasmonic enhancement and the losses due to radiation and dissipation in metal.
Close to the metal surface, the dissipation largely prevails and only a fraction of
donor’s energy is transferred to the acceptor, while for intermediate distances the
transfer efficiency significantly exceeds Förster’s one [29, 62–66]. In a closely related
phenomenon of plasmon-enhanced fluorescence, quantum efficiency of a fluorophore
near a plasmonic nanostructure is determined by its distance to the metal surface,
d, and the measured fluorescence [20–23] shows that, with decreasing d, plasmonic
enhancement is replaced by quenching due to energy transfer to the metal [24, 25].
In a FRET configuration, an acceptor placed nearby will absorb some fraction of
excited donor fluorophore energy via three main channels: Förster channel due to
direct Coulomb interaction, non-radiative plasmon-mediated channel, and plasmonenhanced radiative channel, the latter being dominant for intermediate distances [66].
Note, however, that the enhancement of individual donor’s fluorescence will now
contribute to the losses in FRET which is thus determined by an intimate interplay
between transfer, radiation and dissipation channels [66].
Here we describe a highly efficient cooperative mechanism of energy transfer
from an ensemble of donors to acceptors near a plasmonic nanostructure that takes
advantage of the subtle balance between energy flow channels in the system. In a typical experimental setup, the energy transfer takes place from a large number of donors,
e.g., deposited on top of silica shell around gold or silver core, to acceptors attached
to NP surface via linker molecules. If the distance separating excited donors from
metal is not too small, so that dissipation is not the dominant channel, then donors’
coupling through NP plasmons gives rise to new system eigenstates—plasmonic
superradiant and subradiant states, which, in the presence of a NP, are considerably
more robust due to a strong plasmonic enhancement of radiative coupling [12, 13].
In this case, the energy transfer takes place from these collective states rather than
from many individual donors coupled to the NP. Although the energy stored in a
superradiant state is only a small fraction of the entire system energy, its large matrix
element with external electric fields, e.g., leads to a huge decay rate that scales with
the system size. In fact, in a similar manner, the large coupling of superradiant states
with the electric field of an acceptor spatially separated from donor layer ensures, as
we below demonstrate, a much more efficient plasmon-assisted FRET than from the
same number of individual donors.
On the other hand, the multitude of subradiant states which carry almost the
entire system energy are characterized by a much lower decay rate (radiative and
nonradiative) than individual donors coupled to a NP [12, 13]. This gives rise to
yet another plasmon-assisted FRET scenario that relies on the reduction of radiative
and dissipative losses that naturally occurs in cooperative regime. Indeed, as show
below, the FRET from plasmonic subradiant states is considerably larger than from
545
efficient only for relatively short distances ∪10 nm between a donor and an acceptor
[37], the plasmon-mediated energy transfer channels provided by NPs [29, 62–66],
metal films and waveguides [31, 65] or doped monolayer graphene [67] can lead to
a significant increase of FRET efficiency and range.
The efficiency of plasmon-mediated FRET between a donor and an acceptor
situated near a metal nanostructures is determined in a competition between the
plasmonic enhancement and the losses due to radiation and dissipation in metal.
Close to the metal surface, the dissipation largely prevails and only a fraction of
donor’s energy is transferred to the acceptor, while for intermediate distances the
transfer efficiency significantly exceeds Förster’s one [29, 62–66]. In a closely related
phenomenon of plasmon-enhanced fluorescence, quantum efficiency of a fluorophore
near a plasmonic nanostructure is determined by its distance to the metal surface,
d, and the measured fluorescence [20–23] shows that, with decreasing d, plasmonic
enhancement is replaced by quenching due to energy transfer to the metal [24, 25].
In a FRET configuration, an acceptor placed nearby will absorb some fraction of
excited donor fluorophore energy via three main channels: Förster channel due to
direct Coulomb interaction, non-radiative plasmon-mediated channel, and plasmonenhanced radiative channel, the latter being dominant for intermediate distances [66].
Note, however, that the enhancement of individual donor’s fluorescence will now
contribute to the losses in FRET which is thus determined by an intimate interplay
between transfer, radiation and dissipation channels [66].
Here we describe a highly efficient cooperative mechanism of energy transfer
from an ensemble of donors to acceptors near a plasmonic nanostructure that takes
advantage of the subtle balance between energy flow channels in the system. In a typical experimental setup, the energy transfer takes place from a large number of donors,
e.g., deposited on top of silica shell around gold or silver core, to acceptors attached
to NP surface via linker molecules. If the distance separating excited donors from
metal is not too small, so that dissipation is not the dominant channel, then donors’
coupling through NP plasmons gives rise to new system eigenstates—plasmonic
superradiant and subradiant states, which, in the presence of a NP, are considerably
more robust due to a strong plasmonic enhancement of radiative coupling [12, 13].
In this case, the energy transfer takes place from these collective states rather than
from many individual donors coupled to the NP. Although the energy stored in a
superradiant state is only a small fraction of the entire system energy, its large matrix
element with external electric fields, e.g., leads to a huge decay rate that scales with
the system size. In fact, in a similar manner, the large coupling of superradiant states
with the electric field of an acceptor spatially separated from donor layer ensures, as
we below demonstrate, a much more efficient plasmon-assisted FRET than from the
same number of individual donors.
On the other hand, the multitude of subradiant states which carry almost the
entire system energy are characterized by a much lower decay rate (radiative and
nonradiative) than individual donors coupled to a NP [12, 13]. This gives rise to
yet another plasmon-assisted FRET scenario that relies on the reduction of radiative
and dissipative losses that naturally occurs in cooperative regime. Indeed, as show
below, the FRET from plasmonic subradiant states is considerably larger than from