There is considerable interest in the study of strong nonlinear effects in integrated optics for use in optical switching. Nonlinear thin films have already been studied extensively by both analytical and numerical techniques. Only in more complex nonlinear waveguides, however, can one obtain very high power density for moderate input power through two-dimensional field confinement in a tiny cross-section.

This book provides researchers at the forefront of nonlinear optical technologies with robust procedures and software for the systematic investigation of the fundamental phenomena in nonlinear optical waveguide structures. A full vectorial electromagnetic formulation is adopted and the conditions under which simplification to a scalar formulation is possible are clearly indicated. The need to model the dielectric saturation properly is identified, and improved algorithms are presented for obtaining the complete power dispersion curve of structures exhibiting bistability. As the stability analysis of nonlinear modes is crucial to the development of nonlinear model methods, an effective procedure to investigate the propagation of the scalar nonlinear waves in 3D is another important feature of the book. All of the procedures described, as well as an automatic mesh generator for the finite element method, are incorporated into a software package which is included with this book.

Dielectric optical waveguides have been investigated for more than two decades. In the last ten years they have had the unique position of being simultaneously the backbone of a very practical and fully developed technology, as well as an extremely exciting area of basic, forefront research. Existing waveguides can be divided into two sets: one consisting of waveguides which are already in practical use, and the second of those which are still at the laboratory stage of their evolution. This book is divided into two separate parts: the first dealing with anisotropic waveguides, and the second with nonlinear behaviour. Nonlinear behaviour in optical waveguides is a topic of current research interest, an effect eagerly being sought in waveguides. The relative importance of nonlinearity versus anisotropy in theoretical papers changes enormously from problem to problem. Many theories can be quite useful and enlightening even though they neglect entirely one of the two aspects. Scientists may find their research work leading them in the near future to deal simultaneously with anisotropy and nonlinearity in order to pursue their own investigations. This book will be of interest to researchers who first need to understand the individual topics, suitably chosen from the two parts of this work, thus providing them with the necessary ingredients to pursue their explorations.

Recent advances in the field of guided-wave optics, such as fiber optics and integrated optics, have included the introduction of arbitrarily-shaped optical waveguides which, in many cases, also happened to be arbitrarily inhomogeneous, dissipative, anisotropic, and/or nonlinear. Most of such cases of waveguide arbitrariness do not lend themselves to analytical so lutions; hence, computational tools for modeling and simulation are es sential for successful design, optimization, and realization of the optical waveguides. For this purpose, various numerical techniques have been de veloped. In particular, the finite element method (FEM) is a powerful and efficient tool for the most general (i. e. , arbitrarily-shaped, inhomogeneous, dissipative, anisotropic, and nonlinear) optical waveguide problem. Its use in industry and research is extensive, and indeed it could be said that with out it many optical waveguide problems would be incapable of solution. This book is intended for students, engineers, designers, and techni cal managers interested in a detailed description of the FEM for optical waveguide analysis. Starting from a brief review of electromagnetic theory, the first chapter provides the concepts of the FEM and its fundamentals. In addition to conventional elements, i. e. , line elements, triangular elements, tetrahedral elements, ring elements, and triangular ring elements which are utilized for one-dimensional, two-dimensional, three-dimensional, axisymmetric two dimensional, and axisymmetric three-dimensional problems, respectively, special-purpose elements, such as isoparametric elements, edge elements, infinite elements, and boundary elements, are also introduced.