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Passively mode-locked lasers are extended one-dimensional dynamical systems subject to noise, with a nonlinear instability and a global power constraint. We use the recent understanding of the importance of entropy in these systems to study mode locking thermodynamically. We show that this class of problems is solvable by a mean field-like theory, where the nonlinear pulse free energy and entropic continuum free energy compete on the available power, and calculate explicitly the pulse power and mode locking, which occurs when the dimensionless scaled interaction strength γ = 9. A transfer matrix calculation shows that the mean field theory is exact in the thermodynamic limit, where the number of active laser modes tends to infinity.

Light-mode locking: a new class of solvable statistical physics systems