The alternating-direction implicit method proposed by McKee-Mitchell is applied to full-vectorial paraxial wave equations. The high computational efficiency of the present method is demonstrated in comparison with an iterative solver. Novel finite-difference formulas that take into account discontinuities of the fields are proposed and employed to ensure second-order accuracy. Calculations regarding the effective index of rib waveguides show that the present results remarkably agree with values obtained from the modal transverse resonance method.
Junji Yamauchi, Gen Takahashi, and Hisamatsu Nakano, "Full-Vectorial Beam-Propagation Method Based on the McKee-Mitchell Scheme with Improved Finite-Difference Formulas," J. Lightwave Technol. 16, 2458- (1998)