  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 varying
mode interaction dilution, gain profile and number of modes. Novel properties
of the resulting mode-locking laser phase are presented, not observable by
previous mean-field approaches. For strong dilution of the nonlinear
interaction network, power condensation occurs as the whole 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,
and ultra-fast electromagnetic pulses are computed.
