Frequency combs induced by phase turbulence.

Wave instability-the process that gives rise to turbulence in hydrodynamics-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. In ring microresonator combs, 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. Here we show that, despite this notion, semiconductor ring lasers with ultrafast gain recovery can enter frequency comb regimes at low pumping levels owing to phase turbulence-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, which produces the needed interplay of dispersive and nonlinear effects. We formulate the instability condition in the framework of the Ginzburg-Landau formalism. 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.