Zhong Hua, Kompanets Victor O, Zhang Yiqi, Kartashov Yaroslav V, Cao Meng, Li Yongdong, Zhuravitskii Sergei A, Skryabin Nikolay N, Dyakonov Ivan V, Kalinkin Alexander A, Kulik Sergei P, Chekalin Sergey V, Zadkov Victor N
Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, 710049, Xi'an, China.
Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia.
Light Sci Appl. 2024 Sep 20;13(1):264. doi: 10.1038/s41377-024-01611-1.
Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states, whose dimensionality is at least by 2 lower than that of the bulk. Topological states in such insulators may be strongly confined in their corners which 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 the 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 spatial 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.
高阶拓扑绝缘体（HOTIs）是一种独特的材料，其承载着拓扑保护态，这些态的维度比主体材料至少低2维。此类绝缘体中的拓扑态可能会被强烈限制在其角上，这导致涉及这些态的非线性过程显著增强。然而，到目前为止所展示的所有非线性HOTIs都是基于周期性主体晶格材料构建的。在此，我们展示了首个具有分形起源的非线性光子HOTI。尽管它们具有分数有效维度，但在此基于两种不同类型的谢尔宾斯基垫片波导阵列构建的HOTIs，即使在传统HOTIs变得平凡的参数区域，也可能在出乎意料的宽耦合强度范围内支持拓扑角态。我们展示了非线性分形HOTIs中从角态分叉出的无阈值空间孤子，并表明它们的局域化可以通过输入光束功率有效地控制。我们观察到在这些分形材料所代表的外拐角和多个内拐角及边缘上，非线性光局域化存在明显差异。我们的发现不仅代表了非线性拓扑绝缘体的一种新范式，还为分形材料控制光流的潜在应用开辟了新途径。
