Wide-Angle Alternating-Direction Implicit Finite-Difference Beam Propagation Method

An alternating direction implicit (ADI), scheme for the wide-angle finite-difference beam propagation method (FD-BPM) based on the wide angled Pade multistep method is presented. The scheme incorporates an iterative technique for correction of the operator splitting error. The resulting equations are efficiently solved by the Thomas algorithm for tri-diagonal band matrices. The dispersion characteristics, accuracy and stability of the scheme is verified analytically and numerically for the cases of a plane wave propagating at fixed angle to the assumed propagation direction of the algorithm and the three dimensional angled propagation of a Gaussian beam. The computational requirements of the method are assessed against a standard wide-angle Pade multistep method that uses direct and iterative sparse matrix solvers.