Correction to the analysis of dielectric guides by transverse magnetic field finite element penalty function method with extensions

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 (see M. Silveira and A Gopinath, "Analysis of dielectric guides by tranverse magnetic field finite element penalty method," ibid., vol. 13, pp. 442-1446, Mar. 1995). We have determine that the results were obtained using an eigenvalue solver that did not account for the asymmetry in the final eigenvalue matrix. Here, 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. 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.