Fig. 2: Nonlinear corner excitations in dimerized kagome lattices.

Experimental images are shown in the top three rows, whereas corresponding continuous simulations are shown in the bottom three rows. Given the scaling of the nonlinear response with the overall coupling strength in the system, experimental as well as numerical powers are provided in the normalized form. First column (Δ = 0.20): in the strongly topological regime, linear corner excitations predominantly populate the HOTI state. Increasing the power leads to an intermediate nonlinear phase matching to bulk modes, until at higher powers, a tightly localized corner soliton forms. Second column (Δ = 0.45): since the weakly topological regime features HOTI states that extend far into the lattice (third panel in Fig. 1c), linear corner excitations yield considerable bulk diffraction, and the additional action of nonlinearity is required to form a localized corner state. Nevertheless, this contraction occurs faster than in the trivial case (middle column, Δ = 0.50). The weakly dimerized trivial regime (fourth column, Δ = 0.55) is instead characterized by intra-unit cell dynamics that yield two separate localization steps as the power is increased. In the strongly dimerized trivial regime (fifth column, Δ = 0.80), the intermediate localization in the three guides of the corner unit cell is even more pronounced.