Plasmon Hybridization in Nanoparticle Dimers

We apply the recently developed plasmon hybridization method to nanoparticle dimers, providing a simple and intuitive description of how the energy and excitation cross sections of dimer plasmons depend on nanoparticle separation. We show that the dimer plasmons can be viewed as bonding and antibonding combinations, i.e., hybridization of the individual nanoparticle plasmons. The calculated plasmon energies are compared with results from FDTD simulations. The optical properties of metallic nanoparticles are a subject of considerable experimental and theoretical interest.1-7 Much of this attention is stimulated by the possibilities of using the large electromagnetic field enhancements associated with the excitations of nanoparticle plasmons to increase the cross section for spectroscopies such as Raman spectroscopy.8 Recent experiments have shown enhancements as large as 10-14 orders of magnitude, enabling spectroscopic detections of a single molecule.9-11 Nanoparticle dimers are of considerable importance in this context because of the large electromagnetic field enhancements that can occur at their junctions when the surface plasmons are excited.12 While nanoparticle dimers may not be the optimal structure for electromagnetic field enhancements, they serve as a simple prototypical model system for the study of the important physical factors underlying the electromagnetic field enhancements. The two major factors are believed to be the interaction of localized plasmons and the interference of the electromagnetic fields generated by these plasmons. The plasmonic properties of nanoparticle dimers have recently been investigated using a variety of methods.13-19 Despite these studies, there is a lack of physical consensus of how the dimer plasmon modes depend on interparticle separation. For instance, in the case of high aspect ratio dimers, one study finds that the energy shifts of the dimer dipolar plasmon energies can be accounted for by a simple dipolar interaction,16 while another study finds shifts that depend exponentially on the interparticle spacing.17 In this paper we apply the plasmon hybridization method to investigate the nature of the plasmons of nanoparticle dimers.2,20 We show that the dimer plasmons can be viewed as bonding and antibonding combinations, i.e., hybridization of the individual nanoparticle plasmons. For large D, the shifts of the dipolar dimer plasmons essentially follow the interaction energy between two classical dipoles (1/D3). As D becomes smaller, the shifts of the dipolar dimer plasmons become much stronger and vary much faster, with D due to the interaction and mixing with higher multipole oscillations. In a recent paper, we have shown that calculating the energies of plasmon resonances of complex metallic nanoparticles is equivalent to calculating the electromagnetic interactions between plasmons of nanostructures of simpler geometry.2 The plasmons of a complex nanoparticle result from hybridization of the plasmons of the individual nanoparticles. The strength of the hybridization depends on the geometry of the composite particle. In the plasmon hybridization method, the conduction electrons are modeled as a charged, incompressible liquid sitting on top of a rigid, positive charge representing the ion cores. The ion cores are treated within the jellium approximation, so the positive charge n0 is uniformly distributed within the particle’s boundaries. This hydrodynamic limit is NANO LETTERS 2004 Vol. 4, No. 5 899-903 10.1021/nl049681c CCC: $27.50 © 2004 American Chemical Society Published on Web 04/14/2004 justified by the fact that ab initio and classical calculations lead to the same plasmon energies for metallic nanoparticles larger than a few nanometers.21 The plasmon modes are selfsustained deformations of the electron liquid. Because the liquid is incompressible, the only effect of such deformations is the appearance of a surface charge. For a single solid metallic sphere, the surface charge can be expressed as where Ylm(Ω) is a spherical harmonic of the solid angle Ω. The deformation amplitudes Slm represent the new degrees of freedom. R is the radius of the sphere. The dynamics of the deformations is described by the following Lagrangian: