Abstract
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 Fr\'echet 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 L\'evy distribution at the threshold and back to the Gaussian well above threshold.
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