Observation of Square‐Root Higher‐Order Topological States in Photonic Waveguide Arrays

Abstract

Recently, higher-order topological insulators (HOTIs), accompanied by topologically nontrivial boundary states with a codimension larger than one, have been extensively explored because of unconventional bulk-boundary correspondences. As a novel type of HOTIs, very recent works have explored the square-root HOTIs, where the topologically nontrivial nature of bulk bands stems from the square of the Hamiltonian. In this paper, 2D square-root HOTIs are experimentally demonstrated in photonic waveguide arrays written in glass using femtosecond laser direct-write techniques. Edge and corner states are clearly observed at visible light spectra. The dynamical evolutions of topological boundary states are experimentally demonstrated, which verify the existence of photonic corner states in two band gaps. The symmetry-protected corner states in the photonic square-root HOTI may have potential applications in information processing and lasing.

光波导阵列中拓扑态及其应用的研究进展

“…随后, 如图3(c)所 示, 一种新型的square-root HOTIs被提出. 与一维squre-root模型类似, 这种拓扑绝缘体体带的非平庸特性源于 系统哈密顿量的平方, 图3(d)展示了在耦合光波导阵列 中square-root HOTIs非平庸相的零维角态 [49] . HOTIs遵 循非常规的体-边对应关系, 为实现拓扑保护的光学局 域态调控提供了新的研究思路.…”

“…(c) 高阶拓扑 光波导阵列. (d) 拓扑非平庸和等间距晶格中光从端面出射结果 [49] Figure 3 (Color online) Two-dimensional topological waveguide arrays. (a) Floquet topological waveguide arrays [27] .…”

Tunable Localization of Higher‐Order Bound States in Non‐Hermitian Optical Waveguide Lattices

“…It is, therefore, difficult to obtain high performance in the extremely diminutive topological device designed with higher‐order topological corner states, because the reduction of size will inevitably lead to the weakening of the corner state localization. [ 25 ] Even several newly emerged higher‐order topological structures (e.g., graphdiyne [ 26 ] and decorated honeycomb models [ 27 ] ) are not immune from this finite‐size effect.…”

Observation of Topologically Distinct Corner States in “Bearded” Photonic Kagome Lattices

“…[22][23][24][25] The HOTI features germinating from the BKLs have also been extended to the nonlinear regime, [24] as well as to the square-root HOTIs for which the Kagome lattice acts as a "parent" lattice. [26][27][28] Quite recently, p-orbital HOTIs based on the BKLs have been proposed and demonstrated in photonics. [29,30] Whilst the number of experimental realizations of HOTI corner states based on BKLs is still increasing, the origin and classification with respect to their higher-order topology have been extensively investigated.…”

“…[ 22–25 ] The HOTI features germinating from the BKLs have also been extended to the nonlinear regime, [ 24 ] as well as to the square‐root HOTIs for which the Kagome lattice acts as a “parent” lattice. [ 26–28 ] Quite recently, p ‐orbital HOTIs based on the BKLs have been proposed and demonstrated in photonics. [ 29,30 ]…”