A three dimensions of semivectorial finite difference beam propagation method (FD-BPM) in cylindrical coordinates is investigated in order to analyze the optical wave propagation in the bent waveguides with the strong lateral confinement which will keep low radiation loss. The three-dimensional (3-D) semivectorial wave propagation equation is programmed in the quick and unconditionally stable procedure by using the alternating-direction implicit method. This version of FD-BPM could well express the polarization characteristics of modal field near the dielectric interfaces and accurately simulate the wave propagation in bent waveguides even at a very small radius (<100\;\mum). Moreover, it is pointed out that the numerical precision of the algorithm is intensively affected by the propagation loss of bent waveguides along with the propagation step length of beam propagation method.
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