Turbulence is a challenging feature common to a wide range of complex phenomena. Random fibre lasers are a special class of lasers in which the feedback arises from multiple scattering in a one-dimensional disordered cavity-less medium. Here we report on statistical signatures of turbulence in the distribution of intensity fluctuations in a continuous-wave-pumped erbium-based random fibre laser, with random Bragg grating scatterers. The distribution of intensity fluctuations in an extensive data set exhibits three qualitatively distinct behaviours: a Gaussian regime below threshold, a mixture of two distributions with exponentially decaying tails near the threshold and a mixture of distributions with stretched-exponential tails above threshold. All distributions are well described by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence, which includes energy cascade and the intermittence phenomenon. Our findings have implications for explaining the remarkably challenging turbulent behaviour in photonics, using a random fibre laser as the experimental platform.

The photonic analog of the paramagnetic to spin-glass phase transition in disordered magnetic systems, signaled by the phenomenon of replica symmetry breaking, has been reported using random lasers as the photonic platform. We report here a demonstration of replica symmetry breaking in a one-dimensional photonic system consisting of an erbium-doped random fiber laser operating in the continuous-wave regime. The system is based on a unique random fiber grating system which plays the role of random scattering, providing the disordered feedback mechanism. The clear transition from a photonic paramagnetic to a photonic spin-glass phase, characterized by the Parisi overlap parameter, was verified and indicates the glassy random-fiber-laser behavior.

We report on measurements of the statistical fluctuations of the output intensity in a continuous-wave-pumped erbium-doped one-dimensional random fiber laser (RFL), with specially designed Bragg grating scatterers. Transitions from Gaussian to Lévy-like and back to the Gaussian regime, similar to those observed in three-dimensional random lasers, are described as the input excitation power increases from below to above the RFL threshold. Our results are consistent with theoretical predictions for the sequence of statistical regimes of output intensity in random laser systems. We also discuss experimental and theoretical connections with the photonic spin-glass behavior of the erbium-doped RFL, which displays a replica-symmetry-breaking phase above the threshold.

We report on the extreme-value statistics of output intensities in a one-dimensional cw-pumped erbium-doped random fiber laser, with a strongly scattering disordered medium consisting of randomly spaced Bragg gratings. The experimental findings from the analysis of a large number of emission spectra are well described by the Gumbel distribution below and above the laser threshold, whereas the Fréchet distribution, typical of strongly fluctuating extreme events with heavy power-law probability tails, provides a nice support to the data near the threshold. We establish a close connection, relying on theoretical arguments, between the reported extreme-value statistics and the shifts in the statistics of intensity fluctuations, from the Gaussian to the Lévy distribution at the threshold and back to the Gaussian well above threshold.