Prediction and observation of topological modes in fractal nonlinear optics

This item from the News and Views (N&V) category aims to provide a summary of theoretical and experimental results recently published in ref. ²⁴, which demonstrates the creation of corner modes in nonlinear optical waveguides of the higher-order topological insulator (HOTI) type. Actually, these are second-order HOTIs, in which the transverse dimension of the topologically protected edge modes is smaller than the bulk dimension (it is 2, in the case of optical waveguide) by 2, implying zero dimension of the protected modes, which are actually realized as corner or defect ones. Work²⁴ reports the prediction and creation of various forms of the corner modes in a HOTI with a fractal transverse structure, represented by the Sierpiński gasket (SG). The self-focusing nonlinearity of the waveguide's material transforms the corner modes into corner solitons, almost all of which are stable. The solitons may be attached to external or internal corners created by the underlying SG. This N&V item offers an overview of these new findings reported in ref. ²⁴ and other recent works, and a brief discussion of directions for further work on this topic.