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.

中文翻译：

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布里渊随机光纤激光器中声波的分布静态和动态检测

随机激光器和增益介质之间的相互作用对于理解随机光纤激光器中的噪声源很重要。在此，使用光时域反射法，对由布里渊随机光纤激光器（BRFL）产生的时间分辨分布声波进行表征。声波的动态特性反映了BRFL的增益动态。该原理基于偏振解耦的受激布里渊散射（SBS）增强的四波混合过程，其中当满足相位匹配条件时，探测光会经历最大反射。静态测量结果显示，沿着BRFL中的增益介质，布里渊增益呈指数衰减，这表明最大局部增益区域中的局部随机SBS频率变化，动态测量表明，随时间变化会产生随机的激光噪声。SBS引起的布里渊增益光纤中的双折射变化约为${10}^{-7}$ 至 ${10}^{-6}$。首次通过时间和空间变化的声波强度直接在随机激光增益介质内部观察到BRFL的相位噪声。通过计算时间强度统计分布，可以在BRFL的激射阈值附近检测到光学流氓波。发现高，低增益位置的时间强度统计分布不同，这是由SBS非线性传递函数和局部增益引起的。本文中的分布式表征方法为研究随机激光器与增益介质之间的相互作用提供了一个新的平台，为我们提供了一个新的视角，以了解随机激光过程的基本物理学及其噪声特性。