Statistical physics of multimode ordered and disordered lasers

The adoption of a statistical mechanical framework in optics provides realistic models for multimode laser systems, whose experimental implications are presented and critically analyzed. A model for passive mode locking lasers is analyzed beyond the mean-field approximation, accounting for the presence of many well-resolved frequencies of the lasing modes. The inhomogeneous structure in the nonlinear "mode locked" interaction network is shown to yield short pulses and phase waves with nontrivial slopes, corresponding to a phase delay of the pulsed laser signal. The analytic solution of a mean field-model for multimode laser in open and irregular cavities will be, afterwards, addressed. The complete phase diagram, in terms of degree of disorder, pumping rate of the source and strength of nonlinearity, consists of four different photonic regimes: incoherent fluorescence, mode locking, random lasing and the novel "phase locking wave". A replica symmetry breaking transition occurs at the random lasing threshold. For a high enough strength of nonlinearity, a whole region with nonvanishing complexity anticipates the transition and the light in the disordered medium displays typical glassy behavior.