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A superposition of tunable photonic lattices is used to create optical moiré patterns and demonstrate the resulting localization of light waves through a mechanism based on flat-band physics.

Moiré lattices optically induced in photorefractive nonlinear media are used to explain the formation of optical solitons under different geometrical conditions controlled by the twisting angle between the constitutive sublattices.

Higher order topological insulators (HOTIs) can provide an extension of the bulk-boundary correspondence associated with topological insulators, with more exotic physics behind localization of excitations at their boundaries and corners. Here, the authors propose a method for creating a class of HOTIs with unconventional boundary truncations, where the emergence of localized boundary modes of topological origin is associated with fractional Wannier centers and occurs across much broader parameter space in comparison with usual HOTIs.

Localization of light is observed in photonic quasicrystals with various orders of rotational symmetry.

Extending the control over topological system will open the doors to both fundamental studies and applications. Here the authors demonstrate thouless topological transport of light in a bulk tunable moiré lattice.

This research explores Thouless pumping of quadratic solitons in materials that are periodically modulated in both transverse and longitudinal directions. After one cycle of longitudinal modulation, the center of a soliton either does not shift or shifts in the transverse direction by an integer number of transverse lattice periods, with the direction of motion controlled by the topological properties of the refractive index landscape.

By tuning the spatial width, the strength and the frequency of a pump beam in two-dimensional cylindrical microcavities supporting stable, robust photonic snake states, a set of broadband and perfectly synchronized two-dimensional frequency combs can be realized.

Edge states are excitations existing at the boundary of truncated periodic materials with specific spectral degeneracies, and their properties are enriched when materials possess a nonlinear response. Here, the authors provide experimental evidence of edge soliton formation in a nonlinear photonic graphene lattice induced in an atomic vapour cell.

The formation of solitons of topological origin is observed on disclination cores of pentagonal and heptagonal disclination arrays. Nonlinearity profoundly affects localization of such solitons that form as exceptionally robust objects in topological gap.

The nonlinear properties of photonic topological insulators remain largely unexplored, as band topology is linked to linear systems. But nonlinear topological corner states and solitons can form in a second-order topological insulator, as shown by experiments.

Multidimensional self-trapped states exist in many models of physical systems. However, they are highly unstable in media with the universal cubic nonlinearity. We review different mechanisms that may stabilize them, including non-Kerr nonlinearities, spin–orbit coupling and quantum fluctuations, among others.