Application of effective medium modeling to plasmonic nanosphere waveguides

A proposed visible spectrum nanoscale imaging method requires material with permittivity values much larger than those available in real world materials to shrink the visible wavelength to attain the desired resolution. It has been proposed that the extraordinarily slow propagation experienced by light guided along plasmon resonant structures is a viable approach to obtaining these short wavelengths. To assess the feasibility of such a system, an effective medium model of a chain of Noble metal plasmonic nanospheres is developed, leading to a straightforward calculation of the waveguiding properties. Evaluation of other models for such structures that have appeared in the literature, including an eigenvalue problem nearest neighbor approximation, a multi- neighbor approximation with retardation, and a method-of-moments method for a finite chain, show conflicting expectations of such a structure. In particular, recent publications suggest the possibility of regions of invalidity for eigenvalue problem solutions that are considered far below the onset of guidance, and for solutions that assume the loss is low enough to justify perturbation approximations. Even the published method-of-moments approach suffers from an unjustified assumption in the original interpretation, leading to overly optimistic estimations of the attenuation of the plasmon guided wave. In this work it is shown that the method of moments approach solution was dominated by the radiation from the source dipole, and not the waveguiding behavior claimed. If this dipolar radiation is removed the remaining fields ought to contain the desired guided wave information. Using a Prony's-method-based algorithm the dispersion properties of the chain of spheres are assessed at two frequencies, and shown to be dramatically different from the optimistic expectations in much of the literature. A reliable alternative to these models is to replace the chain of spheres with an effective medium model, thus mapping the chain problem into the well-known problem of the dielectric rod. The solution of the Green function problem for excitation of the symmetric longitudinal mode (TM01) is performed by numerical integration. Using this method the frequency ranges over which the rod guides and the associated attenuation are clearly seen. The effective medium model readily allows for variation of the sphere size and separation, and can be taken to the limit where instead of a chain of spheres we have a solid Noble metal rod. This latter case turns out to be the optimal for minimizing the attenuation of the guided wave. Future work is proposed to simulate the chain of photonic nanospheres and the nanowire using finite-difference time-domain to verify observed guided behavior in the Green's function method devised in this thesis and to simulate the proposed nanosensing devices.