Rapidly growing demands for fast information processing have launched a race
for creating compact and highly efficient optical devices that can reliably
transmit signals without losses. Recently discovered topological phases of
light provide a novel ground for photonic devices robust against scattering
losses and disorder. Combining these topological photonic structures with
nonlinear effects will unlock advanced functionalities such as nonreciprocity
and active tunability. Here we introduce the emerging field of nonlinear
topological photonics and highlight recent developments in bridging the physics
of topological phases with nonlinear optics. This includes a design of novel
photonic platforms which combine topological phases of light with appreciable
nonlinear response, self-interaction effects leading to edge solitons in
topological photonic lattices, nonlinear topological circuits, active photonic
structures exhibiting lasing from topologically-protected modes, and harmonic
generation from edge states in topological arrays and metasurfaces. We also
chart future research directions discussing device applications such as mode
stabilization in lasers, parametric amplifiers protected against feedback, and
ultrafast optical switches employing topological waveguides.Comment: 21 pages, 12 figure
