Characterization of spatiotemporal chaos in arrays of nonlinear plasmonic nanoparticles

Abstract

We investigate spatiotemporal chaos dynamics in a finite nanoparticles array with Kerr-type nonlinear response, excited by an incident plane wave of varying intensity and tunable frequency close to the localized plasmon resonance of a single particle. Considering dipole-dipole coupling between the nanoparticles described by their polarizability, we compute the temporal evolution of the dipoles and numerically extract the Lyapunov spectra, allowing us to characterize different dynamical behaviors. Furthermore, we estimate the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. We show that time-modulated solutions which are generated at the onset of modulational instability experience secondary instabilities leading to a complex nonlinear dynamic. It is also shown that in the highly nonlinear regime, the spatiotemporal chaos is robust and exists in a large range of parameters that we have determined numerically.