Observation of nonlinear fractal higher-order topological insulator
arxiv(2024)
摘要
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 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.
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