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An efficient 3-D semivectorial horizontally wide-angle beam-propagation method (WA-BPM) based on the alternating direction implicit (ADI) scheme is proposed, where only the paraxial term in the vertical direction is considered. The present formulation reduces the splitting error to the second order and shows good compatibility with previously developed WA-BPMs. A block matrix decomposition process and a simulation window-cutting scheme are utilized to further improve the efficiency of the WA-BPM. Then, by applying Padé approximation to the resulting operator, an efficient ADI scheme that can be solved by the Thomas algorithm is constructed. Alternatively, the resulting operator can be approximated by the Denman–Beavers iterative scheme, leading to an ADI scheme with faster convergence rate and reasonable efficiency. Results from several numerical examples show the effectiveness of the present WA-BPM. [ABSTRACT FROM PUBLISHER]

Abstract: A full-vectorial (FV) analysis of optical dielectric waveguide bends by using finite difference (FD) method in terms of magnetic field components is developed in a local cylindrical coordinate system. The perfectly matched layer absorbing boundary conditions via the complex coordinate stretching technique are incorporated into the FV wave equations for effectively demonstrating the leaky nature of waveguide bends, and a six-point FD scheme is constructed to approximate the cross-coupling terms for improving the convergent behavior. The leaky modes of a typical rib waveguide bend are calculated and the complex propagation constants and the field patterns for TE- and TM-like modes are obtained. Solutions are good agreement with those from the film mode matching method, which shows the validity and utility of the established method. [Copyright &y& Elsevier]