An efficient Krylov-subspace-based algorithm to solve the dielectric-waveguide problem

An efficient scheme based on the bi-lanczos algorithm has been developed fo r analysis of the dielectric-waveguide problem. A two-dimensional finite-di fference scheme in the frequency domain is used to discretize the waveguide cross section. The resulting sparse eigenvalue problem is solved efficient ly using the bi-lanczos algorithm. Apart from solving the modes of the diel ectric waveguide, a scheme to solve for the Fields in the presence of a loc alized source is also described. Numerical results are also included to con firm the validity of the method.