Waveguides Analysis and Numerical Methods
- Speaker:
- Nick Karanikas, Master Student of Gerard Sleijpen
- Date/time:
- Friday 6 July 2007, 11:00
- Location:
- M.I. room K8b
Abstract
Waveguides structures play a fundamental role in many fields of technology like optical communication and integrated optics and they demand advanced analysis methods for an accurate modeling.
The main objective of this thesis is to describe the behavior of the electromagnetic field in a waveguide, which turns out to be an eigenvalue problem. We study two numerical methods that can be used for solving this eigenproblem.
Specifically, the electromagnetic field in the waveguide is described by Maxwell's equations. Our interest will be focused on waveguides that are uniform in one direction. The problem leads to a solution of a partial differential equation(eigenvalue problem). We will use the finite difference method in order to discretize the p.d.e. and we will use two numerical methods in order to solve the eigenvalue problem: the Jacobi-Davidson method(Sleijpen-Van de Vorst,1996) and a nonlinear iterative method(NLI), originally developed by Hewson-Browne in geomagnetism(1981). A priori, the second method seems attractive because it requires less memory than the first one. Both methods will be tested and compared for two kinds of waveguides: the buired rectangular and the rib waveguide.