Computation of light waves in linear and nonlinear wave-guiding structures

Abstract

In this thesis, a number of novel and e±cient numerical techniques are de- veloped for numerical simulation of light propagating in 2-dimensional optical waveguides with or without nonlinear e®ects taken into account. The ¯nite di®erence in time domain (FDTD) method, various modal meth- ods and the bidirectional beam propagation methods are the most popular methods used in the design and analysis of optical waveguides. The FDTD method is generally applicable, but it appears to be less e±cient, especially when the medium is dispersive. The modal methods depend on solving of the eigenmodes, and they require a large computation e®ort when the perfectly matched layer (PML) technique is used or when media with complex dielectric functions are considered. The BiBPMs rely on rational approximations of a square root operator and its exponential (i.e. the one-way propagator). But the rational approximations cannot easily model both of the propagating and evanescent modes accurately. Besides, the modal methods and BiBPMs are only applicable to piecewise uniform waveguides. For piecewise uniform wave- guiding structures, a new numerical method based on Dirichlet-to-Neumann (DtN) maps is developed in this thesis. The DtN map method is more accu- rate than the existing BiBPMs, while the required computation e®ort does not increase. For periodic piecewise uniform wave-guiding structures, a recursive doubling process is given to speed up the DtN map method, so that the com- putation e®ort is proportional to log2N, where N is the number of periods. For optical waveguides with an array of holes, a novel numerical method based on Robin-to-Dirichlet (RtD) maps is also developed. Existing simulation methods for second-harmonic generations in optical waveguides are generalizations of numerical methods for linear models. In this thesis, the new DtN map method is extended to study second-harmonic gen- erations in piecewise uniform wave-guiding structures and on metal surfaces. This method rigorously solves the inhomogeneous Helmholtz equation of the second-harmonic wave without any analytic approximations. It is more accu- rate than existing methods extended from the modal expansion methods and the BiBPMs.

Date of Award	2 Oct 2007
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Ya Yan LU (Supervisor)