Ab initio simulations of light propagation in silver cluster nanostructures

Abstract

We present a theoretical approach for the simulation of the optical response and light propagation in aggregates and in ordered arrays of small noble-metal clusters with discrete electronic structure. We construct the Hamiltonian for the aggregate system based on the time-dependent density functional theory electronic states of the individual subunits and describe the interaction between them using the dipole approximation. The time evolution of the aggregate under the influence of the external electric field is obtained from the numerical solution of the time-dependent Schrödinger equation with the coupled excitonic Hamiltonian. For each subunit, the time-dependent dipole moment is calculated using the reduced density matrix formalism. Such quantum- mechanically determined dipole moments are used to simulate the spatiotemporal distribution of the electric field produced by the array. Additionally, we introduce an approximate self-consistent iterative approach to treat arrays consisting of many subunits which are of interest in the context of nanoplasmonics, nano-optical applications, and development of light-harvesting materials. The developed methodology is illustrated first on the example of Ag2 and Ag8 cluster pairs. Subsequently, light propagation in a triangular- shaped array consisting of six Ag8 clusters is simulated.