Glassy behavior of light in random lasers

Abstract

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 non-linear 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.

Lévy Statistics and Glassy Behavior of Light in Random Fiber Lasers

“…On the other hand, in the RL regime above the threshold the modes acquire phase coherence and nontrivial correlations (see below), similarly to the spin-glass phase at low temperatures in disordered magnets. Moreover, as also reported for spin-glass systems [84], the RL regime presents the property of RSB [73][74][75][76][77][78][79][80].…”

“…The restricted sum in the quartic coupling generally involves three classes of mode combinations [73,86]:  =  and  =  ,  =  and  =  , and the remaining possibilities satisfying the frequency-matching conditions, which have been usually disregarded [73,86]. We consider the diagonal contribution in the quadratic coupling to dominate over the off-diagonal part.…”

“…A great advance in the theoretical understanding of the combined effect of amplification, nonlinearity, and disorder in RL systems was put forward in a series of articles [73][74][75][76][77][78][79][80][81][82] published along the last decade. We start by reviewing the theoretical background [73][74][75][76][77][78][79][80] underlying the variety of photonic behaviors displayed by RLs, which relies its basis on the Langevin equations that drive the dynamics of the complex slow-amplitudes modes ( ),…”

“…We start by reviewing the theoretical background [73][74][75][76][77][78][79][80] underlying the variety of photonic behaviors displayed by RLs, which relies its basis on the Langevin equations that drive the dynamics of the complex slow-amplitudes modes ( ),…”

Non-locality and collective emission in disordered lasing resonators

“…The small frequency differences can be embedded in the time-dependent a j (t), which corresponds to letting a j R a j exp [2i(v 0 2v i )t]. The coupled mode equations 23,34,35 are written as:…”