四元数偏振光学研究进展
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摘要
全面地介绍了四元数方法在偏振光学中的理论研究进展,包括重新定义的斯托克斯四元数、琼斯四元数、琼斯-穆勒四元数(JMQ),指出了琼斯-穆勒四元数各个分量的物理意义,给出了斯托克斯四元数与琼斯四元数的简单关系。对于各向异性材料,给出了一种直接从各向异性材料的介电张量求出琼斯-穆勒四元数JMQ的方法。证明了多重双折射效应导致的合成双折射满足重新定义的矢量叠加原理,以及使用叠加原理的条件。介绍了四元数偏振光学在保偏光纤应力传感器中的应用,利用四元数方法分析了它们的偏振问题,进行了实验,结果表明,利用四元数方法的理论分析结果与实验结果互相吻合得很好。
This paper presents a comprehensive review of the research progress on the quaternion method in polarization optics which including: redefining Stokes quaternion,Jones quaternion and Jones-Muller Quaternion( JMQ).The physical meaning of each component of JMQ is pointed out,and the simple relationship between Stokes quaternion and Jones quaternion is given. For the anisotropic material,a method for determining the JMQ directly from its dielectric tensor is proposed. It is proved that the synthetic birefringence caused by the multiply birefringence effects is equal to the vector sum of every redefined birefringence vectors,and point out the limitation when using the superposition principle. This paper also describes the application of quaternion polarization optics in polarization-maintaining fibers( PMF). A new type of PMF based stress sensor is proposed,and their polarization problems are analyzed by quaternion method. The experimental results show that the theoretical analysis results using the quaternion method consistent with the experimental results.
This paper presents a comprehensive review of the research progress on the quaternion method in polarization optics which including: redefining Stokes quaternion,Jones quaternion and Jones-Muller Quaternion( JMQ).The physical meaning of each component of JMQ is pointed out,and the simple relationship between Stokes quaternion and Jones quaternion is given. For the anisotropic material,a method for determining the JMQ directly from its dielectric tensor is proposed. It is proved that the synthetic birefringence caused by the multiply birefringence effects is equal to the vector sum of every redefined birefringence vectors,and point out the limitation when using the superposition principle. This paper also describes the application of quaternion polarization optics in polarization-maintaining fibers( PMF). A new type of PMF based stress sensor is proposed,and their polarization problems are analyzed by quaternion method. The experimental results show that the theoretical analysis results using the quaternion method consistent with the experimental results.
引文
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[2] LE Bihan N,MARS J. Singular value decomposition of quaternion matrices:a new tool for vector-sensor signal processing[J]. Signal processing,2004,84(7):1177-1199.
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[7] SHU J-J,LI Y. Hypercomplex cross-correlation of DNA sequences[J]. Journal of Biological Systems,2010,18(04):711-725.
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[12]张薇,陈新桥,柴佳,等.基于多幅值多时隙编码的120Gb/s光偏振复用系统设计[J].激光杂志,2018,39(02):56-59.
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[14]刘岚岚,吴重庆,李政勇.利用四元数方法研究各态遍历偏振态发生器[J].光学学报,2014,34:0306002.
[15] LIU Lanlan,WU Chongqing,SHANG Chao,et al. Quaternion approach to the Measurement of the Local Birefringence Distribution in Optical Fibers[J]. IEEE Photonics Journal,2015,7(4):1-15.
[16] LIU Lanlan,WU Chongqing,SHANG Chao,et al. Quaternion approach to solve CNSE and crosstalk of QPSK signals in Pol M systems[J]. Chinese Physics Letters 2015,32(8):084202-1-5.
[17]吴重庆,四元数偏振光学及在光纤中的应用(特邀报告)(C)://中国光学学会光电技术专业委员会2015高端学术交流会(重庆),2015,10,30.
[18]吴重庆,四元数偏振光学及在光纤P-OTDR应用(特邀报告)(C)://第十七次光纤通信暨第十八届集成光学学术会议,2015,12.
[19] WU Chongqing,ZHANG Xianfeng,HUANG Zejia. The Quaternion Method Study on Polarization Maintaining Fiber Multiple Effects(C)://15th International Conference on Optical Communications and Networks,2016,9,24.
[20] HUANG Zejia,WU Chongqing,WANG Zhi,Stress Direction Measurement Based on Polarization State in Optical Fibers Using the Quaternion Method[J]. IEEE Photonics Journal,2017,9(7):1-11.
[21] HUANG Zejia,WU Chongqing,WANG Zhi,et al. Distributed measurement of polarization mode coupling in fiber ring based on P-OTDR complete polarization state detection[J]. Optics express 2018,26(4):4798-4806.
[22] HUANG Zejia,WU Chongqing,WANG Zhi,et al. Distributed measurement of axes misaligned splicing and multistress in polarization-maintaining fiber based on polarization-OTDR[J]. Optics Communications 2018,4(23):96-99.
[23]黄泽铗.保偏光纤传感器与光纤敏感环模耦合研究[D].北京:北京交通大学,2018.
[24] WILLIAMS. Bickel and Wilbur M. Bailey. Stokes vectors Mueller matrices and polarized light scattering[J]. Am. J.Phys.,1985,53(5):468-478.
[25] H. Mueller. The foundation of optics[J]. J. Opt. Soc.Am.(A),1948,38:661.
[26] R. C. Jones. Anew calculus for the treatment ofoptical systems[J]. J. Opt. Soc. Am.,1941,31:488-493.
[27]张显峰,吴重庆,盛新志.保偏光纤应力传感特性的理论分析[J].激光杂志,2016,37(9):19-26.
[2] LE Bihan N,MARS J. Singular value decomposition of quaternion matrices:a new tool for vector-sensor signal processing[J]. Signal processing,2004,84(7):1177-1199.
[3]许方官,四元数物理学[M].北京:北京大学出版社,2012.
[4]肖尚彬.四元数方法及其应用[J].力学进展,1993,23(2):249-260.
[5]柴卫华,侯芸.捷联惯导系统姿态算法研究[J].现代防御技术,2001,29(4):249-260.
[6] B P Ickes. A new method for performing digital control system attitude computations[J]. AIAA J,1970,8(1):13-17
[7] SHU J-J,LI Y. Hypercomplex cross-correlation of DNA sequences[J]. Journal of Biological Systems,2010,18(04):711-725.
[8] SHU J-J,OUW L S. Pairwise alignment of the DNA sequence using hypercomplex number representation[J].Bulletin of Mathematical Biology,2004,66(5):1423-1438.
[9] GUO S,ZHANG J,WANG L,et al. Depth-resolved birefringence and differential optical axis orientation measurements with fiber-based polarization-sensitive optical coherence tomography[J]. Optics Letters,2004,29(17):2025-2027.
[10]田博,徐恭勤,黄宏纬,等.径向偏振涡旋光束经轴棱锥后的传输特性[J].激光杂志,2018,39(08):6-10.
[11]丁光涛.偏振光的四元数表示[J].黄淮学刊,1993,9(1):43-48.
[12]张薇,陈新桥,柴佳,等.基于多幅值多时隙编码的120Gb/s光偏振复用系统设计[J].激光杂志,2018,39(02):56-59.
[13]丁光涛.偏振光学的四元数方法[J].光学学报,2013,33(7):0726001.
[14]刘岚岚,吴重庆,李政勇.利用四元数方法研究各态遍历偏振态发生器[J].光学学报,2014,34:0306002.
[15] LIU Lanlan,WU Chongqing,SHANG Chao,et al. Quaternion approach to the Measurement of the Local Birefringence Distribution in Optical Fibers[J]. IEEE Photonics Journal,2015,7(4):1-15.
[16] LIU Lanlan,WU Chongqing,SHANG Chao,et al. Quaternion approach to solve CNSE and crosstalk of QPSK signals in Pol M systems[J]. Chinese Physics Letters 2015,32(8):084202-1-5.
[17]吴重庆,四元数偏振光学及在光纤中的应用(特邀报告)(C)://中国光学学会光电技术专业委员会2015高端学术交流会(重庆),2015,10,30.
[18]吴重庆,四元数偏振光学及在光纤P-OTDR应用(特邀报告)(C)://第十七次光纤通信暨第十八届集成光学学术会议,2015,12.
[19] WU Chongqing,ZHANG Xianfeng,HUANG Zejia. The Quaternion Method Study on Polarization Maintaining Fiber Multiple Effects(C)://15th International Conference on Optical Communications and Networks,2016,9,24.
[20] HUANG Zejia,WU Chongqing,WANG Zhi,Stress Direction Measurement Based on Polarization State in Optical Fibers Using the Quaternion Method[J]. IEEE Photonics Journal,2017,9(7):1-11.
[21] HUANG Zejia,WU Chongqing,WANG Zhi,et al. Distributed measurement of polarization mode coupling in fiber ring based on P-OTDR complete polarization state detection[J]. Optics express 2018,26(4):4798-4806.
[22] HUANG Zejia,WU Chongqing,WANG Zhi,et al. Distributed measurement of axes misaligned splicing and multistress in polarization-maintaining fiber based on polarization-OTDR[J]. Optics Communications 2018,4(23):96-99.
[23]黄泽铗.保偏光纤传感器与光纤敏感环模耦合研究[D].北京:北京交通大学,2018.
[24] WILLIAMS. Bickel and Wilbur M. Bailey. Stokes vectors Mueller matrices and polarized light scattering[J]. Am. J.Phys.,1985,53(5):468-478.
[25] H. Mueller. The foundation of optics[J]. J. Opt. Soc.Am.(A),1948,38:661.
[26] R. C. Jones. Anew calculus for the treatment ofoptical systems[J]. J. Opt. Soc. Am.,1941,31:488-493.
[27]张显峰,吴重庆,盛新志.保偏光纤应力传感特性的理论分析[J].激光杂志,2016,37(9):19-26.