VECTORIAL INTEGRATED FINITE-DIFFERENCE ANALYSIS OF DIELECTRIC WAVE-GUIDES

An integrated finite difference approach is formulated for the full ve ctor solution using transverse magnetic field components for dielectri c waveguides, which is particularly suitable for nonuniform mesh and i nternal flux boundary conditions. This approach creates a sparse bande d asymmetric matrix. Only few largest positive eigenvalues and the cor responding eigenvectors are calculated by the Arnoldi method (based on the modified Gram-Schmidt) coupled with multiple deflation by computi ng a suitable small size matrix. The Arnoldi process is followed by an inverse power method combined with an iterative solver. The nonphysic al modes have been excluded by applying the divergence relation del.H = 0. Three numerical examples are calculated for verifying the reliabi lity and efficiency of this technique, the first two of them are used for the comparison with the results obtained by other methods, and las t one is a quantum well single mode optical waveguide. The technique i n this paper could be used for any shape of dielectric waveguides with any profile of refractive index in the cross section plane with prope r Taylor expansion of the index.