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A novel Yee-mesh-based finite-difference full-vectorial beam-propagation method is proposed with the aid of an implicit scheme. The efficient algorithm is developed by splitting the propagation axis into two steps. The eigenmode analysis of a rib waveguide is performed using the imaginary-distance procedure. The results show that the present method offers reduction in computational time and memory, while maintaining the same accuracy as the conventional explicit Yee-mesh-based imaginary-distance beam-propagation method. It is demonstrated by the analysis of a polarization converter that the present method can be used for not only the eigenmode analysis but also the propagating beam analysis.