A revisitation of the Förster energy transfer near a metallic spherical nanoparticle: (1) Efficiency enhancement or reduction? (2) The control of the Förster radius of the unbounded medium. (3) The impact of the local density of states

Abstract

The central motivation of this theoretical revisitation comes from the fact that some experimental works about Förster energy transfer report improvement of the Förster efficiency when the donor-acceptor molecular pair is in the vicinity of a metallic particle, while others found efficiency deterioration. In the presence of a nanoscale metallic sphere, we calculate contour plots of the Förster energy transfer rate KF and the Förster efficiency η as a function of the acceptor position rA for a fixed donor position. These contour plots clearly highlight the influence of the sphere on KF and η as the donor position, the orientations of donor and acceptor dipoles, and the particle size are varied; also the impact on KF(rA) and η due to the excitation of surface plasmons is easily noticeable from these contour plots. Moreover, we obtain the enhancement factor KF/KF0 (KF0 refers to the case without sphere) against the donor-surface separation for particular donor-acceptor spatial distributions, several particle sizes, and distinct molecular dipole orientations. Therefore, our calculations provide a systematic analysis of the Förster energy transfer in the presence of a metallic nanosphere. Based on these results, we formulate hypotheses for explaining the aforementioned contradictory experimental results about η. To complement our study, we examine the impact of the local density of states ρ on KF. KF is practically unperturbed by sphere when the intermolecular separation R is ≲ 3 nm, since the direct donor-acceptor electromagnetic interaction is dominant. On the contrary, when R ≳ 3 nm, the nanosphere perturbs KF and this perturbation is stronger if plasmonic resonances are excited. KF/KF0 can greatly be enhanced in certain regions, but these regions coincide with low-efficiency regions, compromising applications involving the Förster process. In the presence of the nanosphere, the high Förster efficiency region (η ≥ 0.5) has the same shape as that for the case without sphere, but its extension (Förster radius Ro) is reduced; this effect is a consequence of the large increase of the donor direct decay rate and Ro depends strongly on donor position. Consequently, the sphere controls Ro that is associated with the efficiency pattern that corresponds to the unbounded medium; this effect can be exploited in the measuring technique of nanoscale displacements of proteins that is based on the fluorescence resonant energy transfer. The functional form of KF(ρ) is determined by the intermolecular separation R, the spatial configuration and the dipole orientations of the molecular pair, and the donor proximity to the nanoparticle.

Enhanced upconversion quantum yield near spherical gold nanoparticles – a comprehensive simulation based analysis

“…In regard to Förster energy transfer, which is crucial for energy transfer upconversion (ETU) -the most significant upconversion process for lanthanide-doped upconverter materials -there is an ongoing discussion in the literature whether or not the rate of Förster energy transfer is influenced by the local density of photon states [40][41][42][43][44][45][46][47]. Following the argumentation by Dood et al [45] and the experimental findings by Rabouw et al [46], no modification of the energy transfer rate due to a locally modified density of photon states due to the presence of the metal nanoparticle was implemented into the model used for the investigations presented in this paper.…”

A theoretical investigation of the influence of gold nanosphere size on the decay and energy transfer rates and efficiencies of quantum emitters

“…There have been numerous experimental [67][68][69][70][71][72][73][74][75][76][77] and theoretical [78][79][80][81][82][83] studies of the ET process in donor-acceptor pairs. The studies reported increases in the ET rate, range, and efficiency for various NP materials, sizes, and geometries.…”

“…The energy transfer process has also been studied more recently in Ref. 83 for Ag spheres of 5 nm and 25 nm diameter. These are just some of the examples of studies reported in the literature.…”

“…The donor-acceptor energy transfer process in the presence of metallic NP has been investigated experimentally [67][68][69][70][71][72][73][74][75][76][77] and theoretically [78][79][80][81][82][83] with increases in the energy transfer rate, range, and efficiency reported for various NP materials, sizes, and geometries. The experimental studies of plasmon mediated energy transfer using nanospheres have included donor-acceptor molecules in proximity to 20 nm diameter Ag nanospheres 67,68 and 40 nm Au nanospheres 69 with 21-fold and 3.2-fold increases in the FRET rate, respectively.…”

Plasmonic Purcell factor and coupling efficiency to surface plasmons. Implications for addressing and controlling optical nanosources

“…Finally, since an emitter can be efficiently coupled to a surface plasmon, it has been proposed to use plasmon to couple two emitters for applications such as long range resonant energy transfer (above 10 nm) [93,94,95,96,97] or qubits entanglement [98,99]. In the following, we discuss the plasmonic Purcell factor for typical configurations.…”