טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentHochman Amit
SubjectComputational Methods for Analysis of Wave Interaction
with Plasmonic Nanowires
DepartmentDepartment of Electrical Engineering
Supervisor Professor Emeritus Yehuda Leviatan
Full Thesis textFull thesis text - English Version


Abstract

We have developed computational tools for efficient and rigorous analysis of Plasmonic Nanowires (PNs) in a number of configurations. Plasmonic Nanowires are made of metals which, at optical frequencies, are characterized by a plasma-like permittivity. Our research has been motivated, primarily, by the significant interest in the analysis of these structures. However, the difficulties encountered during the research were not always specific to PNs. As a result, the tools developed can be used to analyze PNs, but they are also of more general applicability.


The first of these tools is a solver for scattering from PNs in free-space. The solver is based, like the other computational tools developed, on the Source-Model Technique (SMT), which belongs to the method-of-moments (MoM) class of techniques. A method for automatic location of the sources for arbitrary smooth cross-sections is implemented, and used also in the other computational tools.


The second tool is a modal solver for PN waveguides. This tool is based on a formulation similar to that of the scattering solver, but it has a number of features which are unique to modal solvers. Among these, we propose a method for filtering spurious solutions, which occur in the SMT (and other MoM formulations). Also, we describe an adaptive sampling algorithm for finding the mode propagation constants, efficiently and reliably, even in cases of degenerate and nearly-degenerate modes.


When the PNs lie in free-space the Green's functions used in the solution are known analytically, and their evaluation is straightforward. In many cases, however, the PNs lie near layered media (a nearby substrate, or a prism, for example). Hence, a third tool was developed, to address the need to incorporate the layered media in the analysis. For this purpose, we devised an efficient and robust scheme for the evaluation of the Green's function of a dielectric half-space. The scheme generalizes the method of steepest-descent, hitherto used only for evaluation of the reflected fields, for the evaluation of the transmitted fields. Cases requiring special treatment, such as the critical angle case, the grazing angle case, and the quasi-static case, were addressed by use of specialized Gaussian integration rules.


Lastly, a rigorous modal analysis of periodic linear chains of PNs was undertaken. The effect of losses was included in the analysis by allowing the propagation constant to assume complex values. To avoid convergence problems that would occur in this case, a fast converging spectral representation of the periodic Green's function was employed.