利用四元数方法研究各态遍历偏振态发生器

Investigation of Polarization State Generation with Ergodicity of Polarization States Based on the Quaternion Approach

各态遍历偏振态发生器(PSG)是偏振测量不可或缺的基本设备,偏振态和偏振器件的描述对于编写偏振态发生器的控制算法是至关重要的。采用四元数来描述和分析各态遍历偏振态发生器中偏振态与偏振控制器,导出了三级偏振控制器的四元数公式,得到了描述其旋转轴与旋转角度的公式。实验测量了单级偏振控制器的四元数,得到了普通单模光纤受挤压时对应的应力四元数公式以及改变电压时的四元数公式,利用该公式编制的算法,实现了各态遍历的偏振态发生器。

The polarization state generator （PSG） with ergodicity of polarization states （EPS） is an important instrument for measurement of polarization state, and the descriptions of polarization state and polarization devices are the base for control algorithm. A new description of PSG using the quaternion method is proposed and analyzed. A quaternion of three polarization controller is derived, and the equations of rotation axis and rotation angle are obtained. In the experiment, the quaternions of single-stage polarization controller are measured, and the corresponding equations of stress quaternions are obtained when the single-mode fiber is squeezed and the voltage of piezoelectric transducer （PZT） is changed. Finally, using these quaternions, the polarization state generator can be achieved.