  The advent of dispersion-engineered and highly nonlinear nanophotonics is
expected to open up an all-optical path towards the strong-interaction regime
of quantum optics by combining high transverse field confinement with
ultra-short-pulse operation. Obtaining a full understanding of photon dynamics
in such broadband devices, however, poses major challenges in the modeling and
simulation of multimode non-Gaussian quantum physics, highlighting the need for
sophisticated reduced models that facilitate efficient numerical study while
providing useful physical insight. In this manuscript, we review our recent
efforts in modeling broadband optical systems at varying levels of abstraction
and generality, ranging from multimode extensions of quantum input-output
theory for sync-pumped oscillators to the development of numerical methods
based on a field-theoretic description of nonlinear waveguides. We expect our
work not only to guide ongoing theoretical and experimental efforts towards
next-generation quantum devices but also to uncover essential physics of
broadband quantum photonics.
