Coupling to multi-mode waveguides with space-time shaped free-space pulses

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 sophistication in parallel with technological improvements and advancing 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.