High-accuracy finite-difference beam-propagation method for cylindrical geometry

A high-accuracy finite-difference beam-propagation method (HAFD- BPM) based on high-accuracy divided-difference formulas is presented. The truncation error in this HAFD- BPM is reduced to o (Delta r)(4)in the transverse direction, whereas the error in a conventional FD-BPM is typically o (Delta r)(2). Gaussian beam propagation in vacuum and nonlinear medium is simulated by this new method and conventional one. The comparison between them in computing time and accuracy reveals the advantage of this new method. As an example, this method is applied to the simulation of blow-up in self-focusing of a Gaussian beam.