We develop a semiclassical theory of laser oscillation into a chiral edge state of a topological photonic system endowed with a frequency-dependent gain. As an archetypal model of this physics, we consider a Harper–Hofstadter lattice embedding population-inverted, two-level atoms as a gain material. We show that a suitable design of the spatial distribution of gain and its spectral shape provides flexible mode-selection mechanisms that can stabilize single-mode lasing into an edge state. Implications of our results for recent experiments are outlined.

中文翻译：

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具有频率相关增益的拓扑激光器中的空间和光谱模式选择效应

我们将激光振荡的半经典理论发展为具有频率相关增益的拓扑光子系统的手征边缘状态。作为该物理学的原型模型，我们将嵌入粒子数反转的两能级原子的 Harper-Hofstadter 晶格视为增益材料。我们表明，增益空间分布及其光谱形状的合适设计提供了灵活的模式选择机制，可以将单模激光稳定到边缘状态。概述了我们的结果对最近实验的影响。