Finite-difference beam propagation method based on the generalized Douglas scheme for a nonuniform grid

The finite-difference beam propagation method based on the Douglas scheme is extended to a nonuniform grid. The truncation error is reduced to O(/spl Delta/x)/sup 4/, provided the grid growth factor is r=1+O(/spl Delta/x), while maintaining a tridiagonal matrix. The numerical results show that the accuracy is improved as compared with that obtained from the conventional nonuniform Crank-Nicholson scheme.