  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.
