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.

Topological photonics, accompanied by the ability to manipulate light, has emerged as a rapidly growing field of research. More platforms for displaying novel topological photonic states are being explored, thus offering efficient strategies for the realization of robust photonic devices. Optical waveguide arrays, described as a (n+1)‐dimensional system, are ideal platforms for studying topological photonics because of the characteristic that can exhibit light dynamics. Here, this work reviews the experimental implementations of the various topological phases in the optical waveguide arrays, and specifically discusses novel physical phenomena arising from the combination of topology with non‐Hermitianity and nonlinearity. It is believed that topological waveguide arrays provide powerful support for enriching topological physics and promoting the development of topological photonic integrated devices.

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