Vectorial integrated finite-difference analysis of dielectric waveguides

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 positive 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 Δ×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 the last one is a quantum well single mode optical waveguide. The technique presented could 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