Topological materials, whether in solid state, photonic or acoustic systems, or other domains, are characterized by bulk topological invariants that remain unchanged as long as the relevant spectral gaps remain open. Through the bulk–edge correspondence principle, these invariants predict the presence of robust states that are localized at the termination of the material. A key example is a Chern insulator, which supports backscatter-free edge states that lead to sharply quantized conductance in the electronic case, and allows for robustness against fabrication imperfections in photonic devices. There has been a great deal of research into the linear properties of topological photonic structures, but it has been only recently that interest in the nonlinear domain has bloomed. Nonlinearity has been of particular interest because it is only in nonlinear and interacting systems that the true bosonic character of photons emerges, giving rise to physics with no direct correspondence in solid-state materials. In this Perspective, we discuss recent results concerning nonlinearity in topological photonics—with an emphasis on laser-written waveguide arrays as a model discrete system.

拓扑材料，无论是在固态、光子或声学系统还是其他领域，都具有体拓扑不变量的特征，只要相关的光谱间隙保持开放，体拓扑不变量就保持不变。通过体-边对应原理，这些不变量预测了位于材料末端的鲁棒状态的存在。一个关键的例子是陈绝缘体，它支持无反向散射的边缘态，从而在电子外壳中产生急剧量化的电导，并具有针对光子器件中制造缺陷的鲁棒性。人们对拓扑光子结构的线性特性进行了大量研究，但直到最近人们对非线性领域的兴趣才开始兴起。非线性一直受到特别关注，因为只有在非线性和相互作用的系统中，光子的真正玻色子特性才会出现，从而产生与固态材料没有直接对应的物理学。在本视角中，我们讨论了拓扑光子学中非线性的最新结果，重点是激光写入波导阵列作为模型离散系统。