# Levy Statistics and the Glassy Behavior of Light in Random Fiber Lasers
## 2 Materials and Methods  
### Random Fiber Lasers  
Random fiber lasers (RFLs) are akin to RLs, being the one-dimensional (1D) or quasi-1D version of the 2D or 3D RLs. They bear the same nonconventional remarkable characteristic: the optical feedback is provided by a scattering medium, rather than by fixed mirrors or fiber Bragg gratings (FBGs), as in conventional fiber lasers. Similarly to conventional fiber lasers, a gain medium is excited by an appropriate optical pump source.  
The first demonstrated RFL, by [PERSON] and co-workers in 2007 [43], can be seen as a quasi-1D extension of the colloidal-based RL reported by [PERSON] and co-workers in 1994 [11]. In [43], the hollow core of a photonic crystal fiber was filled with a colloid al consisting of Rhodamine 6 G and 250 nm rutile (TiO\({}_{2}\)) particles suspended in ethylene glicol. By transversely pumping with nanosecond pulses from the second harmonic of a Nd:YAG laser, directional emission was generated axially, and the feedback was due to the TiO\({}_{2}\) scatterers. Shortly after the report of ref. [43], [PERSON] and co-authors [44] and [PERSON] and [PERSON] [45] demonstrated the operation of a continuous-wave (CW) pumped erbium-based RFL (Er-RFL), with random FBGs providing the scattering mechanism. We anticipate that this special type of RFL will be exploited as the photonic platform for all of the work described here, and will be detailed later.  
A new breakthrough in the research of RFL systems occurred in 2010, when [PERSON] and co-workers [46] first reported on the operation of an RFL system which exploits Rayleigh scattering as the optical feedback mechanism in rather long (\(\sim\)83 km) conventional single-mode optical fibers. In this pioneer work, the gain mechanism was the stimulated Raman scattering excited in the fiber.  
We observe that following this work, the interest in RFL systems and applications has fantastically grown, as reviewed in refs. [47; 48]. Indeed, by further exploiting the Rayleigh scattering due to refractive index fluctuations as the mechanism for the multiple light scattering, a myriad of novel types of RFL systems have been demonstrated using a stimulated Raman or Brillouin scattering process.  
As most of the works between 2007 and 2014 have been reviewed in refs. [47; 48], including polymer-based optical fibers or plasmonically-enhanced RFLs, we highlight here the diversity of works reported over the years 2015 and 2016 (see [49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66] and references therein). As examples, we mention that a Q-switched operation has been reported using Brillouin scattering [56], with pulses as short as 42 ns at 100 kHz being demonstrated. Regarding the fiber length, since the first observation of RFL made using conventional fibers with 83 km [46], RFLs with fiber lengths as short as 120 m have been reported [58], also providing 200 W of output power. Other recent features of RFLs include tunability using graphene-based devices [56] or high-order Raman scattering [57], second harmonic generation [59], polarized emission from disordered polymer optical fibers [60], and photonic turbulence [67].