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Abstract-For the analysis of a -variant optical waveguide with high-index contrast by the beam-propagation method (BPM), the error often grows up during the propagation process. In this paper, the formulation of the BPM is revisited, taking into account the effects of the longitudinal field component. The improvement in accuracy is demonstrated through the analysis of a vertically tapered rib waveguide. The power expression based on the Poynting vector is also employed to improve the power conservation property. As an application, the present technique is applied to the design of a spot-size converter composed of a multicore structure. It is numerically demonstrated that the use of a curvilinearly tapered core leads to a conversion length of 570 m, which is 42% less than the length of a linearly tapered core, with a coupling efficiency of 97% being maintained at a wavelength of 1.55 m.Index Terms-Beam-propagation method (BPM), power conservation, spot-size converter (SSC).

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