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.
