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In certain lasers, frequency combs can form whose output is frequency-modulated (FM) linearly in time. While this result has been replicated numerically, the core physics have remained elusive. By deriving a mean-field theory for lasers analogous to the Lugiato-Lefever equation, we efficiently describe the dynamics of light in nonlinear laser cavities. This equation can be solved analytically with some weak assumptions, simplifying to the nonlinear Schrodinger equation with a phase potential. The phase of its solution is piecewise quadratic in time|an FM comb. Our results apply to nearly any laser and explain the diverse experimental observations.
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