非线性分形高阶拓扑绝缘体的观测
Observation of nonlinear fractal higher-order topological insulator
AI总结：
研究首次实现了基于分形起源的非线性光子高阶拓扑绝缘体，发现其在宽耦合强度范围内支持拓扑角态并存在无阈值孤子，为非线性拓扑绝缘体及分形材料控制光流提供了新范式。
摘要：
高阶拓扑绝缘体（HOTIs）是独特的材料，其承载的拓扑保护态的维度比其体态的维度至少低2倍。此类绝缘体中的拓扑态可能被强烈地限制在角上，从而导致涉及此类态的非线性过程得到显著增强。然而，迄今为止展示的所有非线性HOTIs均构建于周期性体晶格材料之上。在此，我们展示了首个具有分形起源的非线性光子HOTI。尽管其具有分数有效维度，但在此基于两种不同类型的Sierpiński垫片波导阵列构建的HOTIs，可以在出乎意料的宽耦合强度范围内支持拓扑角态，甚至在常规HOTIs变得平庸的参数区域也是如此。我们展示了在非线性分形HOTIs中从角态分叉出的无阈值孤子，并表明其局域化可以通过输入光束功率进行有效控制。我们观察到在这些分形材料所特有的外角和多个内角及边缘上，非线性光局域化存在显著差异。我们的发现不仅代表了非线性拓扑绝缘体的新范式，也为分形材料在控制光流方面的潜在应用开辟了新途径。
英文摘要：
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 \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.
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