  Many key functionalities of optical frequency combs such as self-referencing
and broad spectral access rely on coherent supercontinuum generation (SCG).
While nanophotonic waveguides have emerged as a compact and power-efficient
platform for SCG, their geometric degrees of freedom have not been fully
utilized due to the underlying nonlinear and stochastic physics. Here, we
introduce inverse design to unlock free-form waveguides for coherent SCG. The
efficacy of our design is numerically and experimentally demonstrated on Si3N4
waveguides, producing flat and coherent spectra from visible to mid-infrared
wavelengths. Our work has direct applications in developing chip-based
broadband light sources for spectroscopy, metrology, and sensing across
multiple spectral regimes.
