Nonlinear propagation of light in structured media: generalized unidirectional pulse propagation equations

Unidirectional pulse propagation equations [UPPE, Phys. Rev. E 70, 036604 (2004)] have provided a theoretical underpinning for computer-aided investigations into dynamics of high-power ultrashort laser pulses and have been successfully utilized for almost a decade. Unfortunately, they are restricted to applications in bulk media or, with additional approximations, to simple waveguide geometries in which only a few guided modes can approximate the propagating waveform. The purpose of this work is to generalize the directional pulse propagation equations to structures characterized by strong refractive index differences and material interfaces. We also outline a numerical solution framework that draws on the combination of the bulk-media UPPE method with single-frequency beam-propagation techniques.