Title: Turbulence Hierarchy in a Random Fibre Laser,
Abstract: 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.