Vectorial Integrated Finite-Difference Analysis of Dielectric Waveguides

AbstracfAn 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 positive eigenvalues and the corresponding eigenvectors are calculated by the Arnoldi method @awl on the modified Gram-Schmidt) coupled with multiple detlation by computing a suitable small size matrix. The Arnddi process is followed by an inverse power method combined with an iterative solver. The nonphysical modes have been exeluded by applying the divergence relation V . H = 0. Three numerical examples are calculated for verifying the reliability and emciency of this technique, the first two of them are used for the cOmpIrjsOn with the results obtained by other methods, and last one is a quantum well single mode optical waveguide. Tbe technique in this paper could be used for any shape of dielectric waveguides with any profile of refractive index in the cmss section plane with proper Taylor expansion of the index.