Wave instability—the process that gives rise to turbulence in hydrodynamics 1 —represents the mechanism by which a small disturbance in a wave grows in amplitude owing to nonlinear interactions. In photonics, wave instabilities result in modulated light waveforms that can become periodic in the presence of coherent locking mechanisms. These periodic optical waveforms are known as optical frequency combs 2 – 4 . In ring microresonator combs 5 , 6 , an injected monochromatic wave becomes destabilized by the interplay between the resonator dispersion and the Kerr nonlinearity of the constituent crystal. By contrast, in ring lasers instabilities are considered to occur only under extreme pumping conditions 7 , 8 . Here we show that, despite this notion, semiconductor ring lasers with ultrafast gain recovery 9 , 10 can enter frequency comb regimes at low pumping levels owing to phase turbulence 11 —an instability known to occur in hydrodynamics, superconductors and Bose–Einstein condensates. This instability arises from the phase–amplitude coupling of the laser field provided by linewidth enhancement 12 , which produces the needed interplay of dispersive and nonlinear effects. We formulate the instability condition in the framework of the Ginzburg–Landau formalism 11 . The localized structures that we observe share several properties with dissipative Kerr solitons, providing a first step towards connecting semiconductor ring lasers and microresonator frequency combs 13 . Wave destabilization is demonstrated in semiconductor ring lasers operating at low pumping levels, where ultrafast gain recovery leads to the emergence of a frequency comb regime owing to phase turbulence.

中文翻译：

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相位湍流引起的频率梳

波浪不稳定性——在流体动力学 1 中引起湍流的过程——代表了由于非线性相互作用，波浪中的小扰动在振幅上增长的机制。在光子学中，波的不稳定性会导致调制光波形在存在相干锁定机制的情况下变得周期性。这些周期性的光波形被称为光频梳 2 – 4 。在环形微谐振器梳5、6中，注入的单色波由于谐振器色散和组成晶体的克尔非线性之间的相互作用而变得不稳定。相比之下，环形激光器的不稳定性被认为仅在极端泵浦条件下发生 7, 8。在这里，我们表明，尽管有这个概念，具有超快增益恢复 9 的半导体环形激光器，由于相位湍流 11，10 可以在低泵浦水平下进入频率梳状态 - 一种已知发生在流体动力学、超导体和玻色-爱因斯坦凝聚物中的不稳定性。这种不稳定性是由线宽增强 12 提供的激光场的相位-幅度耦合引起的，它产生了所需的色散和非线性效应的相互作用。我们在 Ginzburg-Landau 形式主义 11 的框架内制定了不稳定条件。我们观察到的局部结构与耗散克尔孤子共享几个特性，为连接半导体环形激光器和微谐振器频率梳 13 提供了第一步。在低泵浦水平下运行的半导体环形激光器中证明了波不稳定，