Optical Waveguide Theory by the Finite Element Method

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.