Key points are not available for this paper at this time.
A new beam-propagation method is presented whereby the exact scalar Helmholtz propagation operator is replaced by any one of a sequence of higher-order (n, n) Padé approximant operators. The resulting differential equation may then be discretized to obtain (in two dimensions) a matrix equation of bandwidth 2n + 1 that is solvable by using Standard implicit solution techniques. The final algorithm allows (for n = 2) accurate propagation at angles of greater than 55 deg from the propagation axis as well as propagation through materials with widely differing indices of refraction.
G. Ronald Hadley (1992) studied this question.