The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra

Abstract

The behavior of a newly introduced overlap parameter, measuring the correlation between intensity fluctuations of waves in random media, is analyzed in different physical regimes, with varying amount of disorder and non-linearity. This order parameter allows to identify the laser transition in random media and describes its possible glassy nature in terms of emission spectra data, the only data so far accessible in random laser measurements. The theoretical analysis is performed in terms of the complex spherical spin-glass model, a statistical mechanical model describing the onset and the behavior of random lasers in open cavities. Replica Symmetry Breaking theory allows to discern different kinds of randomness in the high pumping regime, including the most complex and intriguing glassy randomness. The outcome of the theoretical study is, eventually, compared to recent intensity fluctuation overlap measurements demonstrating the validity of the theory and providing a straightforward interpretation of qualitatively different spectral behaviors in different random lasers.

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].…”

“…An equilibrium statistical physics approach, with the replica trick applied to , led to a phase diagram for the pumping rate as a function of the disorder strength [78,79]. Photonic paramagnetic, ferromagnetic, phase-locking-wave, and replica-symmetry-breaking (RSB) spin-glass phases have been characterized [78,79], depending on the trend of the disorder to hamper the synchronous oscillation of the modes.…”

“…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 ( ),…”

“…Photonic paramagnetic, ferromagnetic, phase-locking-wave, and replica-symmetry-breaking (RSB) spin-glass phases have been characterized [78,79], depending on the trend of the disorder to hamper the synchronous oscillation of the modes. For example, at low input powers the modes oscillate incoherently in an uncorrelated way.…”

“…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 ( ),…”