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Optical nonlinearities are known to provide a coherent coupling between theamplitude and phase of the light, which can result in the formation of periodicwaveforms. Lasers that emit such waveforms are referred to as optical frequencycombs. Here we show that Bloch gain - a nonclassical phenomenon that was firstpredicted in the 1930s - plays an essential role in comb formation in quantumcascade lasers (QCLs). We develop a self-consistent theoretical model thatconsiders all aspects of comb formation: bandstructure, electron transport, andcavity dynamics. It reveals that Bloch gain gives rise to a giant Kerrnonlinearity and serves as the physical origin of the linewidth enhancementfactor in QCLs. Using a master equation approach, we explain how frequencymodulated combs can be produced in Fabry-P\'{e}rot QCLs over the entire biasrange. In ring resonators, Bloch gain triggers phase turbulence and theformation of soliton-like patterns.

Frequency comb generation by Bloch gain induced giant Kerr nonlinearity