We investigate mode-locking processes in lasers displaying a variable degree
of structural randomness, from standard optical cavities to multiple-scattering
media. By employing methods mutuated from spin-glass theory, we analyze the
mean-field Hamiltonian and derive a phase-diagram in terms of the pumping rate
and the degree of disorder. Three phases are found: i) paramagnetic,
corresponding to a noisy continuous wave emission, ii) ferromagnetic, that
describes the standard passive mode-locking, and iii) the spin-glass in which
the phases of the electromagnetic field are frozen in a exponentially large
number of configurations. The way the mode-locking threshold is affected by the
amount of disorder is quantified. The results are also relevant for other
physical systems displaying a random Hamiltonian, like Bose-Einstein
condensates and nonlinear optical beams.Comment: 4 pages, 2 figure
