Switching on topology: Ways to control and design topological features in various systems are being studied intensively because the resulting properties tend to be robust against things such as scattering and defects, endowing the system with topological protection. Maczewsky et al. now look to another regime in optics to show that optical nonlinearity can induce a topological change in the properties of a photonic lattice. At low excitation power, probe light uniformly leaks into the rest of the lattice, an optically trivial phase. Above a threshold power, optical nonlinearity induces a topological change in the properties of the photonic lattice, and probe light is confined to propagate along the edge of the structure. These results illustrate a route to dynamically control the propagation of light. Science , this issue p. 701

Higher-order topological insulators are a novel topological phase beyond the framework of conventional bulk–boundary correspondence^1,2. In these peculiar systems, the topologically non-trivial boundary modes are characterized by a co-dimension of at least two^3,4. Despite several promising preliminary considerations regarding the impact of nonlinearity in such systems^5,6, the flourishing field of experimental higher-order topological insulator research has thus far been confined to the linear evolution of topological states. As such, the observation of the interplay between nonlinearity and the dynamics of higher-order topological phases in conservative systems remains elusive. Here we experimentally demonstrate nonlinear higher-order topological corner states. Our photonic platform enables us to observe nonlinear topological corner states as well as the formation of solitons in such topological structures. Our work paves the way towards the exploration of topological properties of matter in the nonlinear regime, and may herald a new class of compact devices that harnesses the intriguing features of topology in an on-demand fashion.

We describe topological edge solitons in a continuous dislocated Lieb array of helical waveguides. The linear Floquet spectrum of this structure is characterized by the presence of two topological gaps with edge states residing in them. A focusing nonlinearity enables families of topological edge solitons bifurcating from the linear edge states. Such solitons are localized both along and across the edge of the array. Due to the nonmonotonic dependence of the propagation constant of the edge states on the Bloch momentum, one can construct topological edge solitons that either propagate in different directions along the same boundary or do not move. This allows us to study collisions of edge solitons moving in opposite directions. Such solitons always interpenetrate each other without noticeable radiative losses; however, they exhibit a spatial shift that depends on the initial phase difference.

We theoretically introduce a type of topological dipole soliton propagating in a Floquet topological insulator based on a kagome array of helical waveguides. Such solitons bifurcate from two edge states belonging to different topological gaps and have bright envelopes of different symmetries: fundamental for one component, and dipole for the other. The formation of dipole solitons is enabled by unique spectral features of the kagome array which allow the simultaneous coexistence of two topological edge states from different gaps at the same boundary. Notably, these states have equal and nearly vanishing group velocities as well as the same sign of the effective dispersion coefficients. We derive envelope equations describing the components of dipole solitons and demonstrate in full continuous simulations that such states indeed can survive over hundreds of helix periods without any noticeable radiation into the bulk.

We observe linear and nonlinear light localization at the edges and in the corners of truncated moiré arrays created by the superposition of periodic mutually twisted at Pythagorean angles square sublattices. Experimentally exciting corner linear modes in the femtosecond-laser written moiré arrays we find drastic differences in their localization properties in comparison with the bulk excitations. We also address the impact of nonlinearity on the corner and bulk modes and experimentally observe the crossover from linear quasilocalized states to the surface solitons emerging at the higher input powers. Our results constitute the first experimental demonstration of localization phenomena induced by truncation of periodic moiré structures in photonic systems.