The optical rogue wave (RW), known as a short-lived extraordinarily high amplitude dynamics phenomenon with small appearing probabilities, plays an important role in revealing and understanding the fundamental physics of nonlinear wave propagations in optical systems. The random fiber laser (RFL), featured with cavity-free and “modeless” structure, has opened up new avenues for fundamental physics research and potential practical applications combining nonlinear optics and laser physics. Here, the extreme event of optical RW induced by noise-driven modulation instability that interacts with the cascaded stimulated Brillouin scattering, the quasi-phase-matched four-wave mixing as well as the random mode resonance process is observed in a Brillouin random fiber laser comb (BRFLC). Temporal and statistical characteristics of the RWs concerning their emergence and evolution are experimentally explored and analyzed. Specifically, temporally localized structures with high intensities including chair-like pulses with a sharp leading edge followed by a trailing plateau appear frequently in the BRFLC output, which can evolve to chair-like RW pulses with adjustable pulse duration and amplitude under controlled conditions. This investigation provides a deep insight into the extreme event of RWs and paves the way for RW manipulation for its generation and elimination in RFLs through adapted laser configuration.

A Brillouin dynamic grating (BDG) can be used for distributed birefringence measurement in optical fibers, offering high sensitivity and spatial resolution for sensing applications. However, it is quite a challenge to simultaneously achieve dynamic measurements with both high accuracy and high spatial resolution. In this work, we propose a sensing mechanism to achieve distributed phase-matching measurement using a chirped pulse as a probe signal. In BDG reflection, the peak reflection corresponds to the highest four-wave mixing (FWM) conversion efficiency, and it requires the Brillouin frequency in the fast and slow axes to be equal, which is called the phase-matching condition. This condition changes at different fiber positions, which requires a range of frequency injection for the probe wave. The proposed method uses a chirped pulse as a probe wave to cover this frequency range associated with distributed birefringence inhomogeneity. This allows us to detect distributed phase matching for birefringence changes that are introduced by temperature and strain variations. Thanks to the single shot and direct time delay measurement capability, the acquisition rate in our system is only limited by the fiber length. Notably, unlike conventional BDG spectrum recovery-based systems, the spatial resolution here is determined by both the frequency chirping rate of the probe pulse and the birefringence profile of the fiber. In the experiments, an acquisition rate of 1 kHz (up to fiber length limits) and a spatial resolution of 10 cm using a 20 ns probe pulse width are achieved. The minimum detectable temperature and strain variation are 5.6 mK and 0.37 με along a 2 km long polarization-maintaining fiber (PMF).

The interaction of random laser and gain medium is important to understand the noise origin in random fiber lasers. Here, using the optical time domain reflectometry method, the time-resolved distributed acoustic wave generated by a Brillouin random fiber laser (BRFL) is characterized. The dynamic property of the acoustic wave reflects the gain dynamics of the BRFL. The principle is based on the polarization-decoupled stimulated Brillouin scattering (SBS)-enhanced four-wave mixing process, where the probe light experiences maximum reflection when the phase match condition is satisfied. Static measurements present exponentially depleted Brillouin gain along the gain medium in the BRFL, indicating the localized random SBS frequency change in the maximum local gain region, which varies with time to contribute random laser noise as revealed in the dynamic measurement. The SBS-induced birefringence change in the Brillouin gain fiber is approximately 10-7 to 10-6. The phase noise of the BRFL is observed directly inside the random laser gain medium for the first time via time and spatially varied acoustic wave intensity. By counting the temporal intensity statistical distribution, optical rogue waves are detected near the lasing threshold of the BRFL. Different temporal intensity statistical distribution at high and low gain positions is found, which is caused by the SBS nonlinear transfer function and localized gain. The distributed characterization methods in the paper provide a new platform to study the interaction of random lasers and gain medium, giving us a new perspective to understand the fundamental physics of the random lasing process and its noise property.

To obtain high spatial resolution over a long sensing distance in Brillouin optical correlation domain reflectometry (BOCDR), a broad laser spectrum and high pump power are used to improve the signal-to-noise ratio (SNR). In this Letter, we use a noise-modulated laser to study the variation of the Brillouin spectrum bandwidth and its impact on the coherent length of BOCDR quantitatively. The result shows that the best spatial resolution (lowest coherent length) is achieved by the lowest pump power with the highest noise-modulation spectrum. Temperature-induced changes in the Brillouin frequency shift along a 253.1 m fiber are demonstrated with a 19 cm spatial resolution.