Modified finite-difference beam propagation method based on thegeneralized Douglas scheme for variable coefficients

The accuracy of the implicit finite-difference beam propagation method (FD-BPM), in which the phase term is not split, is improved using the generalized Douglas scheme. The propagation error of the fundamental mode in two- and three-dimensional waveguides is evaluated by the mode-mismatch loss calculation. It Is demonstrated that the truncation error is reduced to O(Δx)⁴ in the transverse direction, even when the parabolic wave equation contains variable coefficients, The computational time is almost identical to the conventional FD-BPM based on the Crank-Nicholson scheme