Fig. 1. Illustration of nonlinear control of a higher-order topological insulator.

a Schematic of corner excitations in a 2D SSH photonic lattice under high nonlinearity, where a focusing nonlinearity leads to corner soliton formation while a defocusing nonlinearity leads to radiation into the bulk/edge. b Illustration of coupling and beating between corner and edge states under weak nonlinearity. c Calculated linear eigenvalues of the SSH lattice β_L as a function of the dimerization parameter c, where the corner and edge states are highlighted with red and green colors in the highly topologically nontrivial regime. d1–d3 Calculated band structures for the nontrivial, square, and trivial lattices, showing the topological phase transition as the dimerization parameter is tuned, where the insets plot the selected mode profiles corresponding to the marked color points. A topological BIC with a characteristic corner-localized mode profile is shown in the upper-right inset of d1, with zero amplitude in the nearest neighboring sites but nonzero amplitude and opposite phase in the NNN sites