Beam-propagation method based on matrix diagonalization

A novel beam-propagation method, based on diagonalization of the Hermitian operator that generates the solution to the Helmholtz equation in media with real refractive indices, is described. This method solves some of the problems of the conventional split-step beam-propagation method, namely, the difficulty of handling large index steps and large spatial frequencies, at the expense of higher computational requirements in structures with a refractive-index distribution that varies in the direction of propagation.