# Levy Statistics and the Glassy Behavior of Light in Random Fiber Lasers
## 1 Introduction  
Proposals for the operation of random lasers (RLs) were made five decades ago by [PERSON] and co-workers [1; 2], who visualized the possibility of a new kind of laser that does not require the use of optical cavities. Initially, they reported on the operation of a laser in which one of the cavity mirrors was replaced by a piece of paper that scattered the light in such way that a fraction of the backscattered light was enough to provide feedback for the laser operation. Following the original work, the same group published a series of papers studying the line-narrowing [3], frequency stability [4], and the statistical emission properties [5] of lasers with the so-called nonresonant feedback.  
Apparently, the initial motivation for these studies was the observation of laser emission from interstellar media [6], and the interest of the group on this subject continued in the subsequent years [7; 8; 9].  
For about fifteen years, the majority of research on this theme was pursued by groups that concentrated their effort on the operation of RLs based on microcrystals doped by rare-earth ions [10]. However, the first efficient RL system built in a laboratory environment was reported in 1994 by [PERSON] and co-workers [11], who demonstrated the operation of an RL based on dye molecules dissolved in alcohol with suspended titanium dioxide particles. That report was followed by a great number of papers from different authors that investigated other physical systems for efficient RL operation. A large variety of materials have been tested in the past years, and recent publicationson RLs describe, for example, experiments with dyes dissolved in transparent liquids, gels or liquid crystals with suspended micro or nanoparticles as light scatterers [12; 13; 14; 15; 16; 17], powders of semiconductor quantum dots [18; 19], dielectric nanocrystals doped with rare-earth ions [20; 21], polymers and organic membranes doped by luminescent molecules [22; 23; 24; 25; 26; 27], semiconductor and metallic nanowires structures [28; 29; 30; 31], and even atomic vapors that present interesting analogies with astrophysical lasers [32].  
There is a large literature on RLs motivated by the interest in a deeper understanding of the fundamental properties of RLs [33; 34; 35; 36], as well as reports on their possible application in sensing [37], optofluidics [38; 39], and imaging [40], among other fields [41]. Moreover, although from a fundamental point of view there are many reports focusing on the basic characteristics of RLs and their operation, the analogies between RLs and other complex systems have only recently been investigated by experiments. For example, in the work by [PERSON] and co-authors [42], the analogy between RLs and the spin-glass phenomenon typical of highly-disordered magnetic systems was demonstrated for the first time.  
In the present work, we review the recent advances on the characteristics of random fiber lasers, which have large potential for applications in various areas, as mentioned below. The article is organized as follows. In Section 2, we describe the Materials and Methods used. In Section 3, the experiments with erbium-doped fibers to characterize the RL behavior and the analysis of the intensity fluctuations are presented, along with the theoretical framework to understand the system behavior. Finally, in Section 4, a summary of the article contents and a discussion on perspectives for future work are presented.