基于邦加球轨迹的穆勒矩阵测量法
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摘要
提出了基于邦加球轨迹的穆勒矩阵测量法,将极分解得到的矩阵与其在邦加球上的轨迹联系起来,通过输入光和输出光的偏振态在邦加球上的位置关系,直接获取非消偏元件的双折射矩阵和二向色性矩阵。结果表明:基于所提方法,偏振控制系统只需要一个可旋转起偏器,在测试前后提供两个确定的偏振态,即可直接获得光纤器件的双折射矩阵和二向色性矩阵,且在测量过程中无需改变待测光纤的状态。
A measurement method of Müller matrix is proposed based on the trajectories on the Poincare sphere.A matrix obtained by the polar decomposition is related to its trajectories on the Poincare sphere.Therefore,the birefringence and dichroism matrices of a nondepolarizing unit are directly obtained via the position relationship of the input and output light polarization states on the Poincare sphere.The results show that,based on the proposed method,only one rotatable polarizer is required in the polarization control system.With the measurement of two polarization states determined before and after tests,not only the birefringence and dichroism matrices can be directly obtained,but also the state of the fiber to detect does not need change during the measuring process.
A measurement method of Müller matrix is proposed based on the trajectories on the Poincare sphere.A matrix obtained by the polar decomposition is related to its trajectories on the Poincare sphere.Therefore,the birefringence and dichroism matrices of a nondepolarizing unit are directly obtained via the position relationship of the input and output light polarization states on the Poincare sphere.The results show that,based on the proposed method,only one rotatable polarizer is required in the polarization control system.With the measurement of two polarization states determined before and after tests,not only the birefringence and dichroism matrices can be directly obtained,but also the state of the fiber to detect does not need change during the measuring process.
引文
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[15]Gil J J,Bernabeu E.Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix[J].Optik,1987,76(2):67-71.
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[17]Ossikovski R.Interpretation of nondepolarizing Mueller matrices based on singular-value decomposition[J].Journal of the Optical Society of America A,2008,25(2):473-482.
[18]Xiao Y Y,Yang H X,Xu H B,et al.Measuring Jones matrix of arbitrary orthogonal basic vectors based on Stokes space[J].Laser&Optoelectronics Progress,2016,53(9):092604.肖悦娱,杨辉祥,徐怀宝,等.基于斯托克斯空间的任意正交基矢下琼斯矩阵的测量[J].激光与光电子学进展,2016,53(9):092604.
[19]Mi J,Zhang C X,Li Z,et al.Measuring the beatlength of polarization maintaining fiber by broadband light source and conoscopic interference[J].Journal of Optoelectronics·Laser,2006,17(9):1074-1077.米剑,张春熹,李铮,等.利用宽谱光源及偏光干涉测量保偏光纤拍长[J].光电子·激光,2006,17(9):1074-1077.
[2]Yang J,Yuan Y G,Yu Z J,et al.Optical coherence domain polarimetry technology and its application in measurement for evaluating components of high precision fiber-optic gyroscopes[J].Acta Optica Sinica,2018,38(3):0328007.杨军,苑勇贵,喻张俊,等.光学相干域偏振测量技术及其在高精度光纤陀螺器件测量中的应用[J].光学学报,2018,38(3):0328007.
[3]Goossens J W,Yousefi M I,Jaou3n Y,et al.Polarization-division multiplexing based on the nonlinear Fourier transform[J].Optics Express,2017,25(22):26437-26452.
[4]Li S S,Hao X,Bai J J,et al.Terahertz singlepolarization single-mode photonic crystal fiber with tunable polarization[J].Chinese Journal of Lasers,2016,43(9):0901005.李珊珊,郝霞,白晋军,等.偏振可调的太赫兹单偏振单模光子晶体光纤[J].中国激光,2016,43(9):0901005.
[5]Li P C,Liu K,Jiang J F,et al.Research on polarization control of distributed optical fiber sensing system based on FPGA[J].Chinese Journal of Lasers,2017,45(5):051002.李鹏程,刘琨,江俊峰,等.基于FPGA的分布式光纤传感系统偏振控制研究[J].中国激光,2017,45(5):051002.
[6]Xie Z,Yang Y H,Yan H,et al.Estimation of distributed polarization coupling error in optic fiber coil of fiber optic gyroscope[J].Chinese Journal of Lasers,2017,44(10):1006004.谢泽,杨远洪,闫晗,等.光纤陀螺光纤环分布偏振耦合误差预估[J].中国激光,2017,44(10):1006004.
[7]Li C S,Zhang C Y,Sun H J,et al.Effect of polarization crosstalk of polarization-maintaining delay optical fiber coil on the fiber-optic current sensor[J].Chinese Journal of Lasers,2014,41(11):1105008.李传生,张朝阳,孙海江,等.保偏延迟光纤环偏振串音对光纤电流互感器的影响[J].中国激光,2014,41(4):1105008.
[8]Gao Y Y,Zhou W N,Lei L L,et al.Research on polarization characteristics of SLD start-up used in fiber optic gyroscope and its effect[J].Laser&Optoelectronics Progress,2015,52(11):112302.高洋洋,周卫宁,雷莉莉,等.光纤陀螺用超辐射发光二极管启动偏振特性及其影响研究[J].激光与光电子学进展,2015,52(11):112302.
[9]Yao X S,Chen X J,Liu T G.High accuracy polarization measurements using binary polarization rotators[J].Optics Express,2010,18(7):6667-6685.
[10]Huang S,Zhao H F,Yu T,et al.Improved Jones matrix eigenanalysis method in measuring PMD[J].Journal of Optoelectronics·Laser,2004,15(1):120-122.黄山,赵华凤,俞涛,等.对琼斯矩阵测量PMD的改进[J].光电子·激光,2004,15(1):120-122.
[11]Xu Z X,Yao X S,Ding Z Y,et al.Accurate measurements of circular and residual linear birefringences of spun fibers using binary polarization rotators[J].Optics Express,2017,25(24):30780-30792.
[12]Huang A X,Zhang H,Qiu Y S,et al.Application of Stokes vector method on the full-fiber current sensor[J].Acta Photonica Sinica,2013,42(6):699-704.黄爱显,张昊,邱怡申,等.斯托克斯矢量法在全光纤电流传感器中的应用[J].光子学报,2013,42(6):699-704.
[13]Chen L G.Smart measurement of the Muller matrix of polarization devices[D].Qufu:Qufu Normal University,2004.陈立刚.偏光器件Muller矩阵的智能化测量[D].曲阜:曲阜师范大学,2004.
[14]Cloude S R.Group theory and polarization algebra[J].Optik,1986,31(11):26-36.
[15]Gil J J,Bernabeu E.Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix[J].Optik,1987,76(2):67-71.
[16]Lu S Y,Chipman R A.Interpretation of Mueller matrices based on polar decomposition[J].Journal of the Optical Society of America A,1996,13(5):1106-1113.
[17]Ossikovski R.Interpretation of nondepolarizing Mueller matrices based on singular-value decomposition[J].Journal of the Optical Society of America A,2008,25(2):473-482.
[18]Xiao Y Y,Yang H X,Xu H B,et al.Measuring Jones matrix of arbitrary orthogonal basic vectors based on Stokes space[J].Laser&Optoelectronics Progress,2016,53(9):092604.肖悦娱,杨辉祥,徐怀宝,等.基于斯托克斯空间的任意正交基矢下琼斯矩阵的测量[J].激光与光电子学进展,2016,53(9):092604.
[19]Mi J,Zhang C X,Li Z,et al.Measuring the beatlength of polarization maintaining fiber by broadband light source and conoscopic interference[J].Journal of Optoelectronics·Laser,2006,17(9):1074-1077.米剑,张春熹,李铮,等.利用宽谱光源及偏光干涉测量保偏光纤拍长[J].光电子·激光,2006,17(9):1074-1077.