Glassy behavior of light in random lasers

A theoretical analysis [Angelani et al., Phys. Rev. Lett. 96, 065702 (2006)] predicts glassy behavior of light in a nonlinear random medium. This implies slow dynamics related to the presence of many metastable states. We consider very general equations (that also apply to other systems, like Bose-Condensed gases) describing light in a disordered nonlinear medium and through some approximations we relate them to a mean-field spin-glass-like model. The model is solved by the replica method, and replica-symmetry breaking phase transition is predicted. The transition describes a mode-locking process in which the phases of the modes are locked to random (history and sample-dependent) values. An extended discussion of possible experimental implications of our analysis is reported.

Figure 1

(Color online) Phase diagram of the model in the $(m,T)$ plane (see Sec. 4D in the text).

Figure 2

The equilibrium complexity $\Sigma \left(T\right)$ as a function of the temperature.

Figure 3

(Color online) Sketch of two experimental signatures of the onset of a glassy transition of light in random lasers: (a) The mode coherence function develops a plateau at high pumping rates, denoting ergodicity breaking. (b) The power density spectrum of the mode instantaneous frequency displays modulation sidebands; this corresponds to the transition from random-mode-phases to phase-locking in one of the metastable states; the sidebands are due to small oscillations in these minima that result in frequency shifts of the mode resonances.