Analysis of lossy dielectric optical waveguides

Abstract

An efficient vector finite element method with the hybrid edge/nodal triangular element is described in this thesis for the analysis of dielectric optical waveguides with an emphasis to the analysis of loss. The hybrid type element (a combination of linear edge elements and quadratic nodal elements) are used in' the work. The edge element models the transverse fields and nodal element model axial component of field variable. Thus, in the approach a true hybrid mode analysis is ensured. The undesired spurious (non-physical) solutions do not appear anywhere and the approach provides a direct solution for the propagation constant. Since the eigenvalue corresponds to propagation constant rather than frequency, the method can be easily applied to the analysis of lossy waveguides. However in this work, an indirect approach based on perturbation technique is employed for the calculation of loss in optical waveguides. Here, lossless field solutions obtained from the finite element method are used in the perturbation equation to calculate loss in optical rib waveguides and r.ectangular dielectric waveguides. Furthermore, the method is very flexible and can handle a wide variety of problems having sharp metal and/or dielectric edges. The most important is that the sparsity and the bandedness of the matrices are maintained, so high speed computation with large sparse generalized complex eigenvalue problem is possible. But in the work, the need for solving complex eigenvalue problem is eliminated by using the perturbation formula. Finally, the accuracy of this approach is checked by comparing the propagation characteristics of step index dielectric optical waveguides with and without loss.