Optical Waveguide Theory by the Finite Element Method

Recent progress in research on the finite element method (FEM) for optical waveguide design and analysis is reviewed, focusing on the author's works. After briefly reviewing fundamentals of FEM such as a theoretical framework, a conventional nodal element, a newly developed edge element to eliminate nonphysical, spurious solutions, and a perfectly matched layer to avoid undesirable reflections from computational window edges, various FEM techniques for a guided-mode analysis, a beam propagation analysis, and a waveguide discontinuity analysis are described. Some design examples are introduced, including current research activities on multi-core fibers.