Spatio-temporal initial conditions for multi-mode nonlinear optics

We investigate pumping nonlinear interactions in multi-mode waveguides with focused laser pulses that contain space-time correlations. This allows for the different modes of the waveguide to be excited with different temporal envelopes. Established nonlinear processes in standard multi-mode graded-index fibers, such as beam self-cleaning or supercontinuum generation, could be significantly affected or even controlled by such novel initial conditions. We will introduce precisely how to introduce such initial conditions and show numerical results of parameter scans of different space-time couplings and relate them to more standard cases. We will also discuss implications for experiments, and analouges in other waveguide platforms, such as vortex fibers or integrated photonic waveguides.