TABLE OF CONTENTS The waveguide analyses described in Chapters 2 and 3 are restricted in applicability to the homogeneous-core (step-index) planar optical waveguides and optical fibers, except for the WKB (Wentzel Kramers Brillouin) method described in Section 3.7.2. However, inhomogeneous-core (graded-index) planar waveguides and fibers are utilized in many practical fields. Therefore, analysis techniques capable of solving the wave equations for inhomogeneous-core planar waveguides and fibers are quite important. As shown in Section 2.2.4, Ridge waveguides, which have a homogeneous core but complicated cross-sectional waveguide geometries, are often used for semiconductor optical devices, The finite element method (FEM) is suitable for the mode analysis of optical waveguides having arbitrary refractive-index profiles and complicated waveguide structures. Needless to say, FEM is also applicable to the stress analysis of optical waveguides. In this chapter, FEM mode analyses of slab waveguides, rectangular waveguides, and optical fibers are first presented. Then stress analysis of waveguides and the combination of stress analysis with mode analysis are explained.
In the variational method, the boundary-value problem (the problem given in the form of a differential equation in a certain domain, which should be solved under the given boundary conditions) is transformed into the equivalent variational problem and is solved by applying the variational principle [1 4]. In the finite element method, the domain of the problem is discretized into small elements. The solution of the problem is approximated in each element and it is connected at the nodal points to form the solution model in the entire analysis...
