Path-integral formulation of optical beam propagation

Propagation of optical beams described by the Schr\uf6dinger-type equations can be expressed in terms of the propagator obtained in the framework of the Feynman path-integral formulation of quantum mechanics, which can also be obtained from a standard representation of the propagator by an exact integration. A numerical scheme is developed to evaluate the path-integral propagator by the fast Fourier transform method. The resulting procedure is convenient, efficient, versatile, and accurate, comparing favorably with other methods. Numerical operations required are about half of those in a commonly used method employing fast Fourier transforms. Further, a transformation is shown to eliminate inconvenience associated with a beam of rapidly varying radius. The scheme is illustrated with several examples, including the soliton propagation and the converging beams in a self-focusing medium together with the impact of plasma it generates.Peer reviewed: YesNRC publication: Ye