A comparison of Lanczos electric field propagation methods

The authors analyze the losses of a strongly guiding semiconductor rib waveguide Y-junction with the aid of various propagation algorithms based on Lanczos reduction. Although for the example Lanczos procedures adequately describe electric field propagation in the Fresnel approximation, the Helmholtz implementation converges unacceptably slowly. They therefore propose a finite-difference wide-angle approach which employs a power-series expansion of the forward propagation operator. The computational efficiency of the method is comparable to that of the Fresnel formalism with little or no reduction in accuracy from the Helmholtz technique