In comparison with conventional lasers, topological lasers are more robust and can be immune to disorder or defects if lasing occurs in topologically protected states. Previously reported topological lasers were almost exclusively based on the first-order photonic topological insulators. Here, we show that lasing can be achieved in the zero-dimensional corner state in a second-order photonic topological insulator, which is based on the Kagome waveguide array with a rhombic configuration. If gain is present in the corner of the structure, where the topological corner state resides, stable lasing in this state is achieved, with the lowest possible threshold, in the presence of uniform losses and two-photon absorption. When gain acts in other corners of the structure, lasing may occur in edge or bulk states, but it requires substantially larger thresholds, and transition to stable lasing occurs over much larger propagation distances, sometimes due to instabilities, which are absent for lasing in corner states. We find that increasing two-photon absorption generally plays strong stabilizing action for nonlinear lasing states. The transition to stable lasing stimulated by noisy inputs is illustrated. Our work demonstrates the realistic setting for corner state lasers based on higher-order topological insulators realized with waveguide arrays.

中文翻译：

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Kagome波导阵列中的拓扑角状态激光理论

与常规激光器相比，拓扑激光器更坚固，如果在拓扑保护状态下发射激光，则可以抵抗混乱或缺陷。先前报道的拓扑激光器几乎完全基于一阶光子拓扑绝缘体。在这里，我们表明可以在具有二维菱形配置的Kagome波导阵列的二阶光子拓扑绝缘体中，在零维角状态下实现激光发射。如果在存在拓扑拐角状态的结构的拐角处存在增益，则在存在均匀损耗和双光子吸收的情况下，以最低可能的阈值可以在此状态下获得稳定的激光发射。当增益作用在结构的其他角落时，可能会在边缘或整体状态下产生激光，但是它需要大得多的阈值，并且有时由于不稳定性（在转角状态下不存在激射），会在更大的传播距离上过渡到稳定的激射。我们发现，增加双光子吸收通常对非线性激射态起很强的稳定作用。示出了由噪声输入刺激的向稳定激光的过渡。我们的工作演示了基于角阵激光器的现实设置，该角阵激光器基于通过波导阵列实现的高阶拓扑绝缘体。示出了由噪声输入刺激的向稳定激光的过渡。我们的工作演示了基于角阵激光器的现实设置，该角阵激光器基于通过波导阵列实现的高阶拓扑绝缘体。示出了由噪声输入刺激的向稳定激光的过渡。我们的工作演示了基于角阵激光器的现实设置，该角阵激光器基于通过波导阵列实现的高阶拓扑绝缘体。