Abstract
Random lasers have been recently exploited as a photonic platform for studies of complex systems. This cross-disciplinary approach opened up new important avenues for the understanding of random-laser behavior, including Lévy-type distributions of strong intensity fluctuations and phase transitions to a photonic spin-glass phase. In this work, we employ the Nd:YBO random laser system to unveil, from a single set of measurements, the physical origin of the complex correspondence between the Lévy fluctuation regime and the replica-symmetry-breaking transition to the spin-glass phase. A novel unexpected finding is also reported: the trend to suppress the spin-glass behavior for high excitation pulse energies. The present description from first principles of this correspondence unfolds new possibilities to characterize other random lasers, such as random fiber lasers, nanolasers and small lasers, which include plasmonic-based, photonic-crystal and bio-derived nanodevices. The statistical nature of the emission provided by random lasers can also impact on their prominent use as sources for speckle-free laser imaging, which nowadays represents one of the most promising applications of random lasers, with expected progress even in cancer research.
Highlights
In ref. 19 a replica-symmetry-breaking (RSB) transition to the SG phase was experimentally reported for the first time in a Random lasers1–3 (RLs) employing a functionalized thiophene-based oligomer (T5OCx) in amorphous solid state with planar geometry
The above description matches with recent results on RL systems which report on[7,8,9,10,11,12]: (i) a prelasing weakly-fluctuating Gaussian regime at low pump energies, corresponding in refs 15–22 to the photonic paramagnetic phase with qmax = 0; followed by (ii) an abrupt change in αat the RL threshold to the strongly-fluctuating Lévy-like regime at intermediate pump energies, signaled in[15,16,17,18,19,20,21,22] by the RSB transition to the glassy regime with qmax ≠ 0; and (iii) a subsequent crossover at high pump energies to the so-called self-averaged RL regime, with qmax ≠ 0 and Gaussian statistics of emitted intensities[7,8,9,10,11,12]. This latter Gaussian regime taking place deep in the glassy RL phase has not been anticipated in refs 15–22, since the scope of these works did not include the analysis of the statistics of intensity fluctuations
The experimental investigation on the above-discussed correspondence is possible through measurements in actual RL systems of the parameter qmax, whose behavior identifies the boundary between the prelasing paramagnetic and RL glassy phases, and the Lévy index α, that defines the statistics of the intensity fluctuations as being Gaussian or Lévy-type
Summary
The complex correspondence between the RSB transition to the photonic SG phase and the changes in the statistics of intensity fluctuations in RLs can be explained within the same framework. An equilibrium statistical physics approach, with the replica trick applied to R in terms of the slow-amplitude modes ak, led[21,22] to a phase diagram for the pumping rate as a function of the disorder strength. By expressing the optical noise as the sum of additive and multiplicative statistically independent stochastic processes[34], so that Fk(t) = Fk(0)(t) + ak(t)Fk(1)(t), and considering slow-amplitude modes ak(t) (if compared to the rapidly evolving phase dynamics), we obtain the Fokker-Planck equation[13,34] for the probability density function (PDF) of emission intensity.
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