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.
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