Theoretical study of nonlinear and non-hermitian electrodynamics in chains of plasmonic nanoparticles

Abstract

In view of the recent advancement in the development of techniques for fabrication of metal nanoparticles, plasmonic chains of nanoparticle, has been widely studied theoretically and experimentally in recent years. In this thesis, we focus on the nonlinear and non-Hermitian electrodynamics in chains of plasmonic nanoparticles. Two special configurations, namely, the plasmonic resonator and the diatomic plasmonic chain were studied and presented. The ideology of a plasmonic resonator, which presumes metal nanoparticles in a one-dimensional array as mechanical resonators, can greatly simplify the mathematics behind. A proper design of the one-dimensional plasmonic chain was outlined, in which the respective linear and nonlinear behaviour were studied by the method of linearization, eigenvalue problem and Runge-Kutta iterations. With the data sets obtained by the Runge-Kutta method, Fourier analysis and mode energy analysis could be exploited which led to various phenomena in the classical FPU model, such as the equipartition and the spatial energy localization. In the meanwhile, the diatomic plasmonic chain also performs various astonishing features due to its distinctive spatial configuration to open up band gap in the dispersion relation. A finite one-dimensional diatomic chain having coated metal nanoparticles with alternatively changing separations was investigated. The coupled dipole equation together with quasistatic polarizability having radiation corrections suggested the existence of edge state localized at the two edges of the finite chain, which was then further verified by setting up a compatible simulation in Lumerical FDTD. Upon implementing balanced gain/loss into the system, the diatomic plasmonic chain could be PT-symmetric by nature, which would eventually induce the disappearance of the extinction of the edge state supported by the chain. The aforesaid effect was examined through a precise formulation of the coupled dipole equation, and by simulations conducted in FDTD together with an analytic calculation using the multiple scattering theory (MST). Both results suggested that the zero extinction property was given by the perfect cancelation of the scattering and absorbing behaviour within the diatomic chain at the edge state frequency.