利用四元数方法研究各态遍历偏振态发生器
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摘要
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.
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.
引文
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17 Zhang Ze,Duan Guangren,Sun Yong.Algorithm for relative position and attitude of RVD based on dual-quaternion[J].J Shanghai Jiaotong University,2011,45(3):398-402.张泽,段广仁,孙勇.基于对偶四元数的交会对接相对位姿测量算法[J].上海交通大学学报,2011,45(3):398-402.
18 Li Zhengyong,Wu Chongqing,Shang Chao,et al..Muellermatrix-based differential rotation method for precise measurement of fiber birefringence vector[J].Chin Phys Lett,2010,27(10):104201.
2 He Wen,Jinxin Liao,Xiaoping Zheng,et al..160-Gb/s polarization-multiplexing optical NRZ-DQPSK transmission using differential detection[J].Chin Opt Lett,2011,9(10):100607.
3 Tiecheng Wang,Shoufeng Lan,Junfeng Jiang,et al..A novel method of polarization state control for polarization division multiplexing system[J].Chin Opt Lett,2008,6(11):812-814.
4 Tang Zhilie,Li Ming,Wei Zhengjun,et al..The quantum key distribution system based on polarization states produced by phase modulation[J].Acta Physica Sinica,2005,56(6):2534-2539.唐志列,李铭,魏正军,等.相位-偏振编码的量子保密通信系统的研究[J].物理学报,2005,56(6):2534-2539.
5 Zhang Guangyu,Yang Zhe,Zhang Chenglong,et al..Dynamic polarization-basis compensation for free-space quantum communications[J].China Communications,2013,10(2):27-32.
6 Wei Jia,Jing Hongmei,Zhou Jing,et al..One channel hit-miss transform with zero threshold by polarization encoding[J].Acta Optica Sinica,2006,26(10):1479-1482.韦嘉,景红梅,周静,等.利用偏振编码实现取零阈值的单通道击中与否运算[J].光学学报,2006,26(10):1479-1482.
7 Li Jianzhong,Rao Yunjiang,Ran Zengling.Distributed fiberoptic intrusion sensor system based on POTDR[J].Acta Photonica Sinica,2009,38(11):2789-2794.李建中,饶云江,冉曾令.POTDR分布式光纤传感及其在安防监测中的应用[J].光子学报,2009,38(11):2789-2794.
8 Qian Shuo,Dai Zhiyong,Zhang Xiaoxia,et al..Distributed optic fiber sensors based on polarization-optical time domain reflectometry[J].Laser&Infrared,2012,42(11):1205-1209.钱铄,代志勇,张晓霞,等.基于偏振光时域反射技术的分布式光纤传感器[J].激光与红外,2012,42(11):1205-1209.
9 Yang Shuangshou,Wu Chongqing,Li Zhengyong,et al..Measurement of bend radius based on PPC-assisted POTDR[J].J China Railway Society,2012,34(2):47-51.杨双收,吴重庆,李政勇,等.基于压电偏振控制器辅助POTDR的光纤弯曲半径测量研究[J].铁道学报,2012,34(2):47-51.
10 Zhou Xiaojun,Gong Junjie,Liu Yongzhi,et al..Analysis of white-light interference distributed optic fiber sensor by polarized modes coupling[J].Acta Optica Sinica,2004,24(5):605-608 .周晓军,龚俊杰,刘永智,等.白光干涉偏振模耦合分布式光纤传感器分析[J].光学学报,2004,24(5):605-608.
11 Gao Hongfang,Ren Yuxuan,Liu Weiwei,et al..Rotation dynamics of yeast cell in vortex optical tweezers[J].Chinese J Lasers,2011,38(4):0404002.高红芳,任煜轩,刘伟伟,等.酵母细胞在涡旋光阱中的旋转动力学研究[J].中国激光,2011,38(4):0404002.
12 Dai Yuehua,Tai Shunzhang,Wang Chong.Content determination of sisomicin in sisomicin sulfate and sodium chloride injection by polarimetry[J].China Pharmacy,2012,23(41):3906-3907.戴月华,邰顺章,王冲.旋光法测定硫酸西索米星氯化钠注射液中西索米星的含量[J].中国药房,2012,23(41):3906-3907.
13 Yin Yuying.The helix structure and opticity activity[J].Chemistry,1993,(10):1-9.尹玉英.螺旋结构和旋光性[J].化学通报,1993,(10):1-9.
14 Ding Guangtao.Quaternion method in polarization optics[J].Acta Optica Sinica,2013,33(7):0726001.丁光涛.偏振光学的四元数方法[J].光学学报,2013,33(7):0726001.
15 M Karlsson,M Petersson.Quaternion approach to PMD and PDL phenomena in optical fiber systems[J].J Lightwave Technol,2004,22(4):1137-1146.
16 Chen Guimin,Song Wenchao,Jia Jianyuan.Quaternion representation of reflection and refraction laws[J].OptoElectronic Engineering,2006,33(3):141-144.陈贵敏,宋文超,贾建援.四元数方法表示的反射和折射定律[J].光电工程,2006,33(3):141-144.
17 Zhang Ze,Duan Guangren,Sun Yong.Algorithm for relative position and attitude of RVD based on dual-quaternion[J].J Shanghai Jiaotong University,2011,45(3):398-402.张泽,段广仁,孙勇.基于对偶四元数的交会对接相对位姿测量算法[J].上海交通大学学报,2011,45(3):398-402.
18 Li Zhengyong,Wu Chongqing,Shang Chao,et al..Muellermatrix-based differential rotation method for precise measurement of fiber birefringence vector[J].Chin Phys Lett,2010,27(10):104201.