布里渊散射是光纤中最容易发生的非线性散射，其应用十分广泛。由于光纤双折射不可消除，由其带来的偏振态随机变化是布里渊系统性能提升的最终瓶颈。本论文从布里渊增益的偏振相关性、双折射测量和布里渊偏振牵引三方面展开，研究了双折射影响下光纤中布里渊散射的偏振相关问题，主要工作与成果包括：针对布里渊作用的偏振相关性，推导了受激布里渊散射的矢量模型，并以此为基础进行了理论研究。在泵浦非耗尽近似下，得到了简化的布里渊矢量模型和基于Stratonovich生成元的理论模型，后者计算效率较前者提高一个数量级。定量分析了泵浦信号光偏振态平均夹角与光纤长度及输入偏振态的关系，并由此解释了布里渊平均增益的偏振相关性。给出了任意双折射下最大和最小增益对应的泵浦信号光偏振态关系，并研究了布里渊放大信号的波动特性，得到了普适的波动范围。理论推导并实验验证了一组新的偏振相关增益矢量模型，相较于已有模型，新模型更简单直观，且计算效率可提高两个数量级。新模型与传统模型对偏振相关增益大小的仿真结果一致，理论验证了其正确性。通过新模型，理论分析了偏振相关增益均值及波动与双折射、泵浦光功率和偏振态及光纤长度的关系。通过实验测试了不同泵浦光功率和光纤长度下的偏振相关增益，其结果与理论预测相符，从而进一步验证了新模型的正确性。基于布里渊散射的偏振相关性，提出并验证了一种基于布里渊增益统计特性的光纤拍长估计的新方法。仿真发现，在一定的光纤拍长范围内，布里渊信号增益的标准差与拍长正相关。基于这一原理，测试了绕制半径不同的单模光纤的拍长，并与利用布里渊增益曲线快速傅里叶变换法测得的拍长进行对比，结果相一致，从而验证了此方法的合理性。相较于已有的双折射测量技术，新方法需要的系统更简单，操作更便利，可实现快速测量。从理论和实验两方面研究了布里渊偏振牵引效果的影响因素。通过邦加球表示，给出了在不同光纤双折射和不同输入泵浦信号光偏振态下，随着泵浦光功率和光纤长度的增加，输出信号光偏振态被牵引的趋势。分别使用输出信号泵浦光偏振态平均夹角和信号光偏振度来衡量固定和任意偏振态信号光输入对应的偏振牵引强度，得到了牵引强度与输入泵浦信号光偏振态和双折射大小的关系。最后，分别实验验证了固定和任意偏振态信号光输入时的偏振牵引效果，其结果与理论仿真相一致，验证了上述仿真结果在实际应用中的合理性。

Stimulated Brillouin scattering is the most common nonlinear scattering in fiber, resulting in its extensive applications. As the fiber birefringence is unavoidable, the induced randomness of polarization is the final limit of the performance of Brillouin system. In this dissertation, in three aspects, viz. the polarization dependence of Brillouin gain, fiber birefringence measurement and Brillouin polarization pulling, the polarization properties of Brillouin scattering with the effect of fiber birefringence are investigated. The main contents are as follows:In order to investigate on the polarization properties of Brillouin scattering, the vector model of stimulated Brillouin scattering is established. With the un-depleted pump approximation, the simplified vector model of Brillouin scattering and the theoretical model based on Stratonovich generator are derived. The latter is an order of magnitude faster than the former in efficiency. The influence of fiber length and input polarization on the average alignment of the polarization of pump and signal waves are quantitatively analyzed, explaining the polarization dependence of Brillouin average gain. The relations of the polarization of pump and signal waves corresponding to maximum and minimum Brillouin gain in fiber with different fiber birefringence are studied and concluded. The fluctuation of the Brillouin amplified signal is studied, and the common range of fluctuation is obtained. A new polarization dependent gain vector model of Brillouin system is theoretically developed and experimentally verified. Comparing to the previous model, this new model is simpler and the corresponding calculation efficiency is increased by two orders of magnitude. The simulated results of polarization dependent gain from the new model and the conventional model are in accord with each other, verifying the validity of the new model. Based on the new model, the influence of fiber birefringence, pump power and polarization and fiber length on the amplitude and fluctuation of polarization dependent gain vector are analyzed. The polarization dependent gain with different pump powers and fiber lengths are experimentally measured. The match of the experimental and theoretical results also verifies the validity of the new model.Based on the polarization dependence of Brillouin scattering, a novel method is proposed to estimate the average polarization beat length of single mode fiber through the analysis of statistical characteristics of stimulated Brillouin amplified signals. It is found that in a certain range of fiber beat length, the standard deviation of Brillouin gain and fiber beat length have a positive correlation. Based on this relation, the beat lengths of coils of single mode fiber with different winding radius are measured, and the results are consistent with the ones from the fast Fourier transform of Brillouin gain curve, which verify the validity of the new method. Compared with the conventional technology of birefringence measurement, this new method is easier to realize and operate, and is less time-consuming.The influence factors on Brillouin polarization pulling are investigated theoretically and experimentally. Through Poincare Sphere presentation, as the increase of pump power and fiber length, the pulling trends of output polarization of signal wave are shown, with the condition of different fiber birefringence and input polarization. In order to investigate on the influence of input polarization and fiber birefringence on the pulling strength, the average alignment of the polarization of pump and signal waves and the degree of polarization of signal wave are used to evaluate the pulling strength corresponding to fixed and random polarization input respectively. Finally, the polarization pulling results corresponding to fixed and random polarization input are experimentally measured, and the consistency of experimental and theoretical results verifies the validity of the simulated results in practical applications.