An Efficient 3-D Semivectorial Horizontally Wide-Angle Beam-Propagation Method

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.