  Guided wave optics, including most prominently fiber optics and integrated
photonics, very often considers only one or very few spatial modes of the
waveguides. Despite being known and utilized for decades, multi-mode guided
wave optics is currently rapidly increasing in parallel with technological
improvements and better simulation tools. The physics of multi-mode
interactions are usually driven by some initial energy distribution in a number
of spatial modes. In this work we introduce how, with free-space input beams
having space-time couplings, the different modes can be excited with different
complex frequency or time profiles. We cover fundamentals, the coupling with a
few simple space-time aberrations, different waveguides, and a number of
technical nuances. This concept of space-time initial conditions in multi-mode
waveguides will provide yet another tool to study the rich nonlinear
interactions in such systems.
