Semivectorial Helmholtz beam propagation by Lanczos reduction

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Abstract
By using the finite-difference method to perform Lanczos reduction, a semivectorial Helmholtz beam propagation algorithm is demonstrated. The applicability of this algorithm is no longer limited to paraxial beams and scalar fields. Mode indices of rib waveguides are calculated and compared to previously published data. Losses of Y -branch for two orthogonal polarizations are also presented. This algorithm is more efficient than the conventional beam propagation method in determining the mode index. To calculate the radiation loss however, it requires much more computational effort. More than 30 Krylov vectors are needed to avoid numerical dissipation