Lévy spectral intensity statistics in a Raman random fiber laser

The statistical behavior of spectral intensity fluctuations in a Raman gain random fiber laser is investigated for the first time, to the best of our knowledge. Through a fiber Fabry–Perot tunable filter, the intensity of the filtered single wavelength from random laser (RL) spectra is measured at different pump powers. The probability density function (PDF) of spectral intensity values is analyzed. Well below the lasing threshold, the intensity of a single wavelength is stable in the time domain, and the PDF exhibits a typical Gaussian behavior. However, around the threshold, strong fluctuations in intensity emerge. In this case, the statistical distribution is characterized by a power-law-tailed function consistent with a Levy α-stable distribution. We identify the statistical evolution as the injected pump power increases, from a Gaussian to a Levy and then back to a Gaussian distribution, which is similar to the case of RLs with a strong disorder due to the presence of photon scatterers and gain related to electronic transitions in the active medium, indicating the universal existence of such statistical properties in random lasing systems.