Recently a method to obtain the propagation constants of lossless dielectric waveguides using the Helmholtz equation with the finite element method and penalty function method was presented . The advantage of using this approach is that only one final eigenvalue matrix needs to be solved for only two components of the H-fields. We have determine that the results in  were obtained using an eigenvalue solver that did not account for the asymmetry in the final eigenvalue matrix. In this paper, we present the results of the same cases simulated using the correct eigenvalue solver, and the results obtained are in good agreement with previously published ones  and . We also show by simulation of appropriate cases, a high penalty factor is correlated to highly coupled modes, while weakly coupled modes may be correlated to small penalty factors. Finally, we have extended the penalty function method to include the complex case without the use of the perturbation method. The gain results obtained for a channel waveguide are in good agreement with previously published ones  and .
Bibliographical noteFunding Information:
Manuscript received April 4, 1996; August 2, 1996. This work was supported in part by Fundacao de Amparo a Pesquisa do Estado de Sao Paulo-FAPESP, under Contract 9213142-2, in part by the University of Minnesota, Minneapolis and Duluth campus, and the Minnesota Supercomputer Institute. P. Cheung is with the Department of Electrical and Computer Engineering, University of Minnesota, Duluth, MN 55812 USA. M. Silveira is with the Universidade Federal de Sao Carlos, Sao Carlos, SP 13560, Brazil. A. Gopinath is with the Department of Electric1 Engineering, University of Minnesota, Minneapolis, MN 55455 USA. Publisher Item Identifier S 0733-8724(96)08914-1.