An integrated finite difference approach is formulated for the full vector solution using transverse magnetic field components for dielectric waveguides, which is particularly suitable for nonuniform mesh and internal flux boundary conditions. This approach creates a sparse banded asymmetric matrix. Only few largest possible eigenvalues and the corresponding eigenvectors are calculated by the Arnoldi method (based on the modified Gram-Schmidt) coupled with multiple deflation by computing a suitable small size matrix. The Arnoldi process is followed by an inverse power method combined with an iterative solver. The nonphysical modes have been excluded by applying the divergence relation ▽H = 0. Three numerical examples are calculated for verifying the reliability and efficiency of this technique, the first two of them are used for the comparison with the results obtained by other methods, and last one is a quantum well single mode optical waveguide. The technique in this paper can be used for any shape of dielectric waveguides with any profile of refractive index in the cross section plane with proper Taylor expansion of the index.
Bibliographical noteFunding Information:
Manuscript received December 4, 1992; revised March 25, 1993. This work was supported in part by DARPA Contract under AF/F19628-91-K-W. The Minnesota Supercomputing Institute (MSI) provided the Cray computing time. H. Dong and A. Gopinath are with the Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455. A. Chronopoulos is with the Department of Computer Sciences, University of Minnesota, Minneapolis, MN 55455. J. Zou is with Cray Research Incorporation, Chippewa Falls, WI 54729. IEEE Log Number 9210189.