Random fiber lasers have recently attracted a great deal of attention due to their novel underlying physics and great potential applications [1–5]. Different from the conventional lasers that require a cavity with a fixed length to trap light, random fiber lasers make use of the multiple scattering of photons in a disordered medium to provide optical feedback. Lasing occurs when the total gain in the random cavity overcomes the total loss. The characteristics of random lasers are determined by the radiation buildup by multiple scattering of the disordered medium and the light amplifying process in the gain medium, resulting in versatile unique output properties in different random fiber laser schemes. The first demonstration of the random fiber laser was based on random nanoparticles scattering in colloidal suspension inserted in the hollow-core fiber [6], which was then followed by the realization of the coherent random fiber laser in a similar configuration [7]. Recent research found the statistical turbulence signatures in the distribution of intensity fluctuations in a continuous wave pumped erbium-based random fiber laser with random Bragg grating scatters [8,9], which provide a platform to study the challenging turbulent behavior in photonics. Replica symmetry breaking was demonstrated in random fiber lasers, where the transition from a photonic paramagnetic to a photonic spin-glass phase was verified and indicated the glassy random fiber laser behavior [10]. Near lasing threshold, the statistical distribution of the random fiber laser was characterized by a power law tailed function consistent with a Lévy α-stable distribution as a universal existence of such statistical properties in random lasing systems [11,12]. The simple architecture of the random fiber laser has provided a perfect photonics platform to study the fundamental physics in various random systems. Since there is no need to form a precise microcavity, the production cost of the random fiber laser is low, which makes great potential applications in fiber sensing [13–15] and low-noise fiber lasers [16–19]. However, for many applications, the current performance of the random fiber laser has to be improved, especially due to its large intensity noise [20,21]. Different from the conventional fiber lasers, a large number of random modes are formed in random fiber lasers, making it difficult to describe their dynamic process. Though wave kinetic theory was developed to describe the random lasers with a large number of generation modes [22], the fundamental physics behind random fiber lasers remains unclear in many phenomena, such as the Lévy statistics [23,24], spectral correlations [25], and optical rogue waves [26] in random fiber lasers. Stimulated Brillouin scattering (SBS) is a major noise source in various random fiber laser systems, especially with Raman gain medium-based random laser, which has a higher threshold than the SBS threshold. The stochastic behavior of the random fiber laser originated from SBS process was studied in a random fiber laser based on Raman gain recently [27]. At the same time, SBS can be utilized as the gain mechanism to build the random fiber laser [28,29], which provides a good platform to study the noise characteristic of the SBS process enhanced by the multiple scattering in disordered media. The intrinsic spectral width and intensity dynamics of the acoustic wave in a polarized Brillouin random fiber laser were characterized experimentally [30]. The characterization mechanism was based on the polarization-dependent central wavelength of the acoustic-wave-induced dynamic grating, which was similar to the population-inversion-based dynamic grating in an open-cavity Yb-doped fiber laser with distributed feedback [31]. However, the distributed spatial information of the acoustic wave still remains unclear because a single-frequency continuous probe wave was used in the previous characterization. By either linearly sweeping the probe light frequency (optical frequency domain reflectometry, OFDR) [32,33] or using the pulsed probe light (optical time domain reflectometry, OTDR) [34,35], the distributed spatial information can be obtained, which provides a visual picture of acoustic wave evolution in the spatial domain for us to further understand the acoustic wave noise properties. The requirement of the frequency sweeping in the OFDR technique usually takes a long time, thus hindering its dynamic applications (up to kilohertz) in the distributed sensing. By sending a series of probe pulses and measuring the time-resolved traces in the oscilloscope, OTDR is a good technique for the distributed static and dynamic detection of the acoustic wave in Brillouin random fiber lasers.

In this paper, the acoustic wave in a Brillouin gain fiber generated by a Brillouin random fiber laser (BRFL) is measured by the OTDR technique for the first time. A dynamic grating is introduced by the acoustic wave, where its detection is an SBS-enhanced polarization-decoupled four-wave mixing (FWM) process. Based on the measurement time of one detection process, the distributed detection can be divided into static measurement and dynamic measurement. The static measurement characterizes the time-averaged property of the acoustic wave, in which the frequency of the probe light is swept in several minutes. In dynamic measurement, a series of pulsed probe lights with 10 kHz repetition rate at fixed optical frequency under the phase matching condition is launched into the Brillouin gain fiber, and thus the fast change of the acoustic wave intensity is obtained. The static measurement results find that the Brillouin gain of BRFL depletes exponentially along the Brillouin gain fiber. In addition, the Brillouin gain depletes more quickly at the initial part of the Brillouin gain fiber when the photons of the probe light absorb energy from the acoustic wave. The dynamic detection reveals that the noise source of the BRFL first appears at the initial part of the Brillouin gain fiber and the phase noise of the random laser induces the nonlinear change of the interference dark spots in the spatial-time map. The distributed measurement results provide a new perspective to study the performance and noise properties of the BRFL, which enhances our understanding about the fundamental physics behind random fiber lasers.

The distributed detection of the acoustic wave generated by the BRFL is realized based on the OTDR technique for the first time. The detection is an SBS-enhanced polarization-decoupled FWM process where the probe light experiences maximum reflection when phase matching condition is satisfied. Photons of the probe light can either give energy to the acoustic phonons or absorb energy from the acoustic phonons, depending on the relative propagation direction of the acoustic wave and the probe light. In the static measurement, the distributed dynamic grating spectra are obtained by sweeping the frequency of the probe light. The Brillouin gain depletes exponentially along the Brillouin gain fiber in the BRFL. When the photons of the probe light absorb energy from the acoustic wave, a quick depletion of the Brillouin gain is observed in the experiment. The SBS-induced birefringence variations are estimated to be approximately 10−7 to 10−6 by measuring the central frequency change of the dynamic grating spectra. In the dynamic measurements, the intensity noise of the laser is found to first occur at the highest gain position of the Brillouin gain fiber. The phase noise of the BRFL leads to wavelength variation of the beat pattern, which further leads to nonlinear dark spot change in the spatial-time acoustic wave intensity map. The spatial-time acoustic wave intensity map provides a new method to characterize the phase noise of the BRFL and to study its dynamic evolution process. Optical RWs are found near the lasing threshold of the BRFL, where the nonlinear transfer function of the SBS process modifies the temporal intensity probability distribution of the mixing noisy Stokes light and lasing Stokes light. Above the lasing threshold, the temporal intensity at the high gain position exhibits more events with high peak intensity fluctuation than the temporal intensity at the low gain position, which is caused by the SBS nonlinear transfer function and the localized gain in the BRFL. The detection results enhance our understanding on the BRFL, paving the way for its performance improvement in future applications in the fields of communication, high-precision metrology, sensing, and spectroscopy.