The overall goal of photonics research is to understand and control
light in new and richer ways to facilitate new and richer
applications. Many major developments to this end have relied on
nonlinear optical techniques, such as lasing, mode-locking, and
parametric downconversion, to enable applications based on the
interactions of coherent light with matter. These processes often
involve nonlinear interactions between photonic and material degrees
of freedom spanning multiple spatiotemporal scales. While great
progress has been made with relatively simple optimizations, such as
maximizing single-mode coherence or peak intensity alone, the ultimate
achievement of coherent light engineering is complete,
multidimensional control of light–light and light–matter interactions
through tailored construction of complex optical fields and systems
that exploit all of light’s degrees of freedom. This capability is now
within sight, due to advances in telecommunications, computing,
algorithms, and modeling. Control of highly multimode optical fields
and processes also facilitates quantitative and qualitative advances
in optical imaging, sensing, communication, and information processing
since these applications directly depend on our ability to detect,
encode, and manipulate information in as many optical degrees of
freedom as possible. Today, these applications are increasingly being
enhanced or enabled by both multimode engineering and nonlinearity.
Here, we provide a brief overview of multimode nonlinear photonics,
focusing primarily on spatiotemporal nonlinear wave propagation and,
in particular, on promising future directions and routes to
applications. We conclude with an overview of emerging processes and
methodologies that will enable complex, coherent nonlinear photonic
devices with many degrees of freedom.