A simple beam-propagation method for solving the scalar TE nonparaxial or Helmoltz equation is presented. This versatile algorithm, based on a two-step finite-difference scheme for solving the propagation coordinate, is amenable to be easily extended to solve vector wave equations, which could take into account nonlinear effects. In addition, a general procedure to check its stability is given in detail. The applicability of the present method and its distinction from paraxial or Fresnel solutions are demonstrated through several examples, including very strongly guided structures of variable transverse section. © 1994 IEEE