Modified finite-difference beam-propagation method based on the Douglas scheme

A modified finite-difference beam-propagation method (FD-BPM) based on the Douglas scheme is presented. The truncation error in the modified FD-BPM is reduced to o(Deltax)(4) in the transverse direction, whereas the error in the conventional FD-BPM is typically o(Deltax)(2). With trivial programming changes, the accuracy can be improved without the introduction of additional computation time. Numerical results obtained for a slab optical waveguide and a directional coupler illustrate the advantage of this method.