Electrodynamics of Noble Metal Nanoparticles and Nanoparticle Clusters

In this paper we examine the electrodynamics of silver nanoparticles and of clusters of nanoparticles, with an emphasis on extinction spectra and of electric fields near the particle surfaces that are important in determining surface-enhanced Raman (SER) intensities. The particles and clusters are chosen to be representative of what has been studied in recent work on colloids and with lithographically prepared particles. These include spheres, spheroids, truncated tetrahedrons, and clusters of two or three of these particles, with sizes that are too large to be described with simple electrostatic approximations but small compared to the wavelength of light. The electrodynamics calculations are mostly based on the discrete dipole approximation (DDA), which is a coupled-finite element approach which produces exact or nearly exact results for particles of arbitrary size and shape if fully converged. Mie theory results are used to study the validity of the DDA for spherical particles, and we also study the validity of the modified long wavelength approximation (MLWA), which is based on perturbative corrections to the electrostatic limit, and of the single dipole per particle approximation (SDA). The results show how the dipole plasmon resonance properties and the electric field contours around the particle vary with particle shape and size for isolated particles. For clusters of particles, we study the effect of interparticle spacing on plasmon resonance characteristics. We also show that the quadrupole resonance is much less sensitive to particle shape and interparticle interactions than the dipole plasmon resonance. These results provide benchmarks that will be used in future comparisons with experiment.