# Levy Statistics and the Glassy Behavior of Light in Random Fiber Lasers
## 3 Results  
### Characterization of the FBG-Based Er-RFL Explored as a Statistical-Physics Experimental Platform  
As reported by [PERSON] and [PERSON] [45], a unique FBG was produced by writing an exceptionally high number of gratings (\(>\)1000) over a 30 cm length fiber. A polarization-maintaining erbium-doped fiber from CorActive (peak absorption 28 dB/m at 1530 nm, NA 0.25, mode field diameter 5.7 \(\upmu\)m) was employed, in which the randomly distributed phase errors grating was written, instead of a random array of gratings as in [44]. It was realized in [45] that during the movement of the translation stage, the friction between the fiber and the mount introduced irregularities in the grating spectrum that could be controlled by managing the air flow from the vacuum. Such irregularities were perceived as small phase errors, randomly but continuously distributed along the grating profile being inscribed. Thanks to this procedure, a high number of modes were observed, which is very important for several applications, as we will see later. The Er-RFL described in [45] had a very low threshold of 3 mW, with a throughput efficiency of -4.5% for 100 mW pump power. The number of emitted modes was dependent on the pump power and fiber length (20 or 30 cm fiber lengths were characterized in [45]), and a single or few modes were observed, limited by the system measurement resolution [69]. For the experiments described here, the 30 cm long fiber was employed with the experimental setup shown in Figure 1, reproduced from ref. [68]. The pump source was a semiconductor laser operating in the CW regime at 1480 nm, delivering 150 mW output power at the fiber pigtail. The Er-RFL output was split, through a 1480 nm/1550 nm wavelength-division multiplexer (WDM),with a split ratio of 10/90 for 1480 nm and 1550 nm, respectively, to a power meter and a spectrometer. The employed fiber splices were lossy, if compared to the original work [45], leading to a higher threshold. The spectrometer (SpectraPro 300i, Acton Research, Acton, MA, USA), coupled to a liquid-N\({}_{2}\) cooled InGaAs CCD camera, had a nominal resolution of 0.1 nm. Figure 2a shows the Er-RFL output spectrum for intensities below and above the RFL threshold, while Figure 2b shows the linewidth narrowing (left y-axis) and emitted Er-RFL intensity (right y-axis) as a function of the pump power \(P\) normalized to the threshold power \(P_{th}\). The threshold power was \(P_{th}\) = 16.30 \(\pm\) 0.05 mW [68], which is higher than in the original work of ref. [45] due to the lossy components employed. However, this fact did not affect the experimental studies, and the output was typically around 1-2 mW. Besides the routine characterization illustrated in Figure 2, two other analyzes were performed in order to show that the laser is multimode, i.e., with many longitudinal modes, and that the intensity fluctuations do not depend on the pump laser fluctuations. First, in order to demonstrate the multimode characteristic of the Er-RFL, we employed the technique of speckle contrast [69], following the work of refs. [40; 70; 71]. To generate the speckle,  
Figure 1: Experimental setup for the erbium-based random fiber laser (Er-RFL) system. (1) Fiber pigtailed semiconductor laser operating in the continuous-wave (CW) regime. (2) Fiber connector. (3) Er-doped RFL. (4) Wavelength-division multiplexer (WDM) 1480-1550. (5) Power meter to measure the output power \(P_{out}\) at 1480 nm. (6) RFL emission out to the spectrometer. (7) Spectrometer. (8) Liquid-N\({}_{2}\) cooled InGaAs CCD camera. (Reproduced with permission from ref. [68]). Figure 2: (a) Emitted spectrum of Er-RFL before (red) and after (blue) the laser threshold; (b) Emitted intensity (squares) and FWHM (triangles) of the Er-RFL system as a function of the normalized input power. The measured threshold power was \(P_{th}\) = 16.30 \(\pm\) 0.05 mW. The dotted lines are a guide to the eyes. (Reproduced with permission from ref. [68]).