While the optical properties of a metal nanoparticle are determined by its surface plasmon resonance, there is dramatic change in these properties when nanoparticles come into close proximity.27,92-98 This is due to the coupling of the plasmon oscillations of the interacting particles. The plasmon oscillation generates an enhanced electric field localized on the nanoparticle surface, decaying with distance away from the nanoparticle. The near-field of particles present in close proximity can interact with each other strongly. Thus the electric field E' felt by each particle is the sum of the incident light
field E and the perturbation due to the presence of the electric dipole present on the neighboring particle:99 3 0 '
4
d
E
E
mε
πε
µ
ξ
+
=
(21)where µ is the dipole moment due to the particle plasmon and ξ is an orientation factor. Because of the near-field coupling of the plasmons, there is a change in the frequency of the surface plasmon oscillation of the coupled nanoparticle system with respect to the isolated particle. For example, the assembly or aggregation of spherical Au nanoparticles into a close packed structure results in a red shift of the SPR wavelength from the isolated nanosphere SPR wavelength at ~520 nm to longer wavelengths.93 The extent of the coupling-induced red shift increases with decreasing inter-particle distance and increasing number of particles in the assembly.93,100 The shift in the surface plasmon resonance wavelength maximum resulting from the electromagnetic coupling between
the nanoparticles allows the use of far-field absorption or scattering-based measurements to probe the near-field coupling.
The coupling-induced plasmonic shift shows a polarization-dependence as governed by the orientation factor ξ in eq 21. Experimentally measured plasmon resonances of pairs of 150 nm Au nanodiscs fabricated by electron-beam lithography showed that when the light polarization direction is parallel to the inter-particle axis, the plasmon resonance of the nanodisc pair is red-shifted with respect to the single particle case.101 Conversely, when the light is polarized orthogonal to the inter-particle axis, the plasmon spectrum is relatively blue shifted with respect to the single-particle case. In the parallel polarization case, the interparticle interaction is strongly attractive (ξ is positive), resulting in the plasmon red-shift; the blue-shift in the perpendicular polarization case is due to a repulsive interaction between the electronic dipoles of the particle pair partners (ξ is negative). It must be noted that the situation is much more complex when the particle size becomes large enough to have severe retardation effects, such that the driving fields do not maintain the same phase across the nanoparticle.102
The attractive plasmon coupling between metal nanoparticles assembled in pairs or 1-D chains has been shown, mainly through simulations, to result in a huge enhancement in the electric field at the junction between the nanoparticles, especially at small gaps.27,97,103 The field enhancement at the junction is further enhanced in the case of coupling between sharp tips (with highly concentrated fields), as found for nanotriangles interacting tip-to-tip (bowties)27,104,105 and nanorods interacting end-to- end.94
The distance dependence of near-field coupling has also been studied experimentally on lithographically fabricated arrays of ellipsoidal gold nanodisc pairs with systematically varying inter-particle separations, supported by electrodynamic simulations.95 In this study, Su et al. found that the plasmon resonance of the nanodisc
pair red-shifts exponentially with the decrease in the inter-particle gap.95 They further showed that when the inter-particle gap is normalized by the particle size, this near- exponential trend becomes independent of the particle size. The plasmon shift decays to zero over a separation of 2.5 diameters. A similar observation was made by Gunnarsson et al. in lithographically fabricated silver nanodisc pair arrays.96 They also showed that
discs that are in metallic contact, show completely new plasmon modes that have extremely large (almost abrupt) shifts relative to the single-particle resonances. In addition, higher-order modes are also seen to emerge at lower wavelengths.99,106
It has been found from the studies of Lamprecht et al.107 and Haynes et al.108 on periodic 2-D lithographic arrays, that in addition to the near-field coupling between the particles in close proximity, there is a far-field radiative coupling between the particles in a periodic array. This coupling, which is diffractive in nature, is maximum when the grating constant of the array is equal to the wavelength of the light in the medium, manifested by a plasmon band that is considerably narrower and red-shifted. As we move away from this grating constant towards smaller inter-particle separations, a blue-shift and broadening of the plasmon resonance is observed until the separations become small enough such that near-field coupling becomes important. Both far-field interactions and near-field interactions have been studied in bowtie nano-antennas.109 Far-field coupling
wavelength) along with electromagnetic retardation effects, whereas smaller inter-particle separations are dominated by near-field coupling, which decays as 1/d3 in the dipolar- coupling limit.109
The effect of inter-particle interactions in noble metal nanoparticle assemblies on non-radiative properties has also been observed.69 Feldstein et al.69 studied the hot electron lifetimes in thin films aggregates of 12-nm gold nanoparticles as a function of the film thickness, which was a measure of the degree of aggregation. It was found that the hot-electron lifetimes decreased with greater aggregation. The faster relaxation of the electrons in the films with greater degree of aggregation was attributed to the mobility or conduction of the electrons between the closely interacting (although not touching) nanoparticles in the aggregate.
Silver nanocrystals self-organized in face-centered cubic supracrystals show a shift of their coherent Raman-active lattice vibration frequency to lower values, attributed to the near-field coupling between the nanoparticles.110 Similarly, the surface plasmon coupling between silver nanocolumns fabricated in an oriented assembly has been found to affect the Raman-active phonon vibration frequency of the nanostructure.111