Unraveling the origin of frequency modulated combs using active cavity mean-field theory

In many laser systems, frequency combs whose output is frequency-modulated (FM) can form, producing light whose frequency sweeps linearly. While this intriguing result has been replicated experimentally and numerically, a compact description of the core physics has remained elusive. By creating a mean-field theory for active cavities analogous to the Lugiato–Lefever equation, we show that these lasers are described by a nonlinear Schrödinger equation with a potential proportional to the phase of the electric field. This equation can be solved analytically and produces a field with quasi-constant intensity and piecewise quadratic phase. We refer to these nondispersive waves as extendons , and they describe both fundamental FM combs and harmonic states. Our results apply to many lasers, explaining the ubiquity of this phenomenon, and our new theory unifies many experimental observations.