Statistical physical theory of mode-locking laser generation with a frequency comb

A study of the mode-locking lasing pulse formation in closed cavities is presented within a statistical-mechanical framework where the onset of laser coincides with a thermodynamic phase transition driven by the optical power pumped into the system. Electromagnetic modes are represented by classical degrees of freedom of a Hamiltonian model at equilibrium in an effective ensemble corresponding to the stationary laser regime. By means of optimized Monte Carlo numerical simulations, the system properties are analyzed while varying mode interaction dilution, gain profile, and number of modes. Properties of the resulting mode-locking laser phase are presented that were not observed in previous approaches based on mean-field approximations. For strong dilution of the nonlinear interaction network, power condensation occurs as the total optical intensity is taken by a few electromagnetic modes, whose number does not depend on the size of the system. For all reported cases, laser thresholds, intensity spectra, phase waves, and ultrafast electromagnetic pulses are computed.