Discrete nonlinear topological photonics

Topological materials, whether in solid state, photonic or acoustic systems, or other domains, are characterized by bulk topological invariants that remain unchanged as long as the relevant spectral gaps remain open. Through the bulk–edge correspondence principle, these invariants predict the presence of robust states that are localized at the termination of the material. A key example is a Chern insulator, which supports backscatter-free edge states that lead to sharply quantized conductance in the electronic case, and allows for robustness against fabrication imperfections in photonic devices. There has been a great deal of research into the linear properties of topological photonic structures, but it has been only recently that interest in the nonlinear domain has bloomed. Nonlinearity has been of particular interest because it is only in nonlinear and interacting systems that the true bosonic character of photons emerges, giving rise to physics with no direct correspondence in solid-state materials. In this Perspective, we discuss recent results concerning nonlinearity in topological photonics—with an emphasis on laser-written waveguide arrays as a model discrete system.