Observation of nonlinear fractal higher-order topological insulator

Abstract

Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states, whose dimensionality is at least by a factor of 2 lower than that of the bulk. Topological states in such insulators may be strongly confined in their corners that leads to considerable enhancement of nonlinear processes involving such states. However, all nonlinear HOTIs demonstrated so far were built on periodic bulk lattice materials. Here we demonstrate first \textit{nonlinear photonic} HOTI with the fractal origin. Despite their fractional effective dimensionality, the HOTIs constructed here on two different types of the Sierpiński gasket waveguide arrays, may support topological corner states for unexpectedly wide range of coupling strengths, even in parameter regions where conventional HOTIs become trivial. We demonstrate thresholdless solitons bifurcating from corner states in nonlinear fractal HOTIs and show that their localization can be efficiently controlled by the input beam power. We observe sharp differences in nonlinear light localization on outer and multiple inner corners and edges representative for these fractal materials. Our findings not only represent a new paradigm for nonlinear topological insulators, but also open new avenues for potential applications of fractal materials to control the light flow.

10 pages, 5 figures

References in corpus (16)

• Topological Photonics
• Topological Crystalline Insulators
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Photonic Floquet topological insulators in a fractal lattice
• Inner Skin Effects on Non-Hermitian Topological Fractals
• Observation of edge solitons in topological trimer arrays
• Higher-order topological phases on fractal lattices
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• Weakly nonlinear topological gap solitons in Su-Schrieffer-Heeger photonic lattices
• Observation of nonlinear disclination states
• Corner modes of the breathing kagome lattice: origin and robustness
• Observation of $\pi$ solitons in oscillating waveguide arrays
• Fractal-like photonic lattices and localized states arising from singular and nonsingular flatbands
• Topological Random Fractals
• Observation of squeezed Chern insulator in an acoustic fractal lattice
• Observation of topologically distinct corner states in "bearded" photonic Kagome lattices

Cited by in corpus (12)

• Observation of nonlinear topological corner states originating from different spectral charges
• Solitons in Quasiperiodic Lattices with Fractional Diffraction
• Observation of edge solitons and transitions between them in a trimer circuit lattice
• Observation of nonlinear higher-order topological insulators with unconventional boundary truncations
• Observation of Light Localization at the Edges of Quasicrystal Waveguide Arrays
• Thresholdless corner vortex solitons in fractal Sierpiński topological insulators
• Vortex solitons in disclination quasicrystals
• Nonlinear quadrupole topological insulators
• Quadratic solitons in higher-order topological insulators
• Self-Accelerating Topological Edge States
• Stable vortex soliton arrays in disclination-fractal systems
• Fractal Polariton Topological Insulator