基于双波片的偏振调控和偏振测量技术
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摘要
针对双波片偏振调控结构,基于Stokes-Mueller矩阵偏振算法,对双1/4波片和双1/2波片的偏振调控机理作了详尽的理论分析,得出调控偏振态与双波片快轴方向之间的关系,并追迹其在庞加莱球上的运动轨迹.基于双波片调控结构搭建偏振测量系统,根据入射和出射Stokes矢量构建了投影关系矩阵算法,完成了待测元件Mueller矩阵的测量,并分析了波片的快轴方向误差和位相延迟误差对Mueller矩阵测量结果以及对出射偏振态调控精度的影响.分析结果表明:波片的快轴方向误差控制在±2°内,位相延迟误差不大于λ/300时,Mueller矩阵的最大测量误差为0.040 2,波片自身误差对测量结果的影响可以忽略不计;波片自身误差所引起的方位角误差不大于0.16rad时,快轴方向误差引起的椭率角误差最大不超过0.032 rad,位相延迟误差导致的椭率角误差小于0.015 rad,且对偏振度无影响.
Based on the Stokes-Mueller matrix polarization algorithm,the polarization control mechanism of a biplate that consists of double quarter wave-plates or double half wave-plates was analyzed in detail.We have derived the analytical relations between the modulated polarization state and the fastaxis direction for the biplate.The movement trajectory of modulated polarization state on the Poincarésphere was obtained.Which helps us to propose a polarization control measurement system using a biplate to complete the measurement of the Mueller matrix based on the projection matrix algorithm for the incident and exiting Stokes vectors.The polarization control accuracy for the exiting Stokes vector was also analysed.For a biplate that the error along the fast axis direction is ± 2 ° and the retardance error is λ/300,the maximum measurement error of Mueller matrix is 0.040 2.When the azimuth error caused by the error of the biplate is less than 0.16 rad,the elliptic angle error caused by the fast axis direction is not more than 0.032 rad,the ellipsometry error caused by the retardance is less than 0.015 rad,and it has no influence on the degree of polarization.
Based on the Stokes-Mueller matrix polarization algorithm,the polarization control mechanism of a biplate that consists of double quarter wave-plates or double half wave-plates was analyzed in detail.We have derived the analytical relations between the modulated polarization state and the fastaxis direction for the biplate.The movement trajectory of modulated polarization state on the Poincarésphere was obtained.Which helps us to propose a polarization control measurement system using a biplate to complete the measurement of the Mueller matrix based on the projection matrix algorithm for the incident and exiting Stokes vectors.The polarization control accuracy for the exiting Stokes vector was also analysed.For a biplate that the error along the fast axis direction is ± 2 ° and the retardance error is λ/300,the maximum measurement error of Mueller matrix is 0.040 2.When the azimuth error caused by the error of the biplate is less than 0.16 rad,the elliptic angle error caused by the fast axis direction is not more than 0.032 rad,the ellipsometry error caused by the retardance is less than 0.015 rad,and it has no influence on the degree of polarization.
引文
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[2]Bashara N M.Ellipsometry and polarized light[M].America and Canada:Elsevier North-Holland,1977.
[3]LIU Qiang,LI Shuang,GONG Ping.Analysis for Influence of Element Deviation to DOLP Measured by Spatial Modulating Spectropolarimeter[J].Acta Optica Sinica(刘强,李双,龚平.空间调制线偏振光谱测量的误差影响仿真分析.光学学报),2014,34(7):105-109.
[4]CUI Gao-Zeng,LIU Tao,LI Guo-Guang,et al.A method to measure the misalignment angle of the optical axes of biplate compensators[J].Laser&Optoelectronics Progress(崔高增,刘涛,李国光,等.一种测量双片波片补偿器中光轴偏差角度的方法.激光与光电子学进展),2013,50(6):89-94.
[5]Gil J J.Polarimetric characterization of light and media[J].European Physical Journal-Applied Physics,2007,40(1):1-47.
[6]He W,Fu Y,Yang Z,et al.Polarization properties of a corner-cube retroreflector with three-dimensional polarization ray-tracing calculus[J].Applied Optics,2013,52(19):4527-4535.
[7]LI Ya-Hong,FU Yue-Gang,HE Wen-Jun.Polarization properties of cat’s eye retroreflector based on three-dimensional Jones matrix method[J].Infrared and Laser Engineering(李亚红,付跃刚,贺文俊.基于三维琼斯矩阵法对“猫眼”逆反射器的偏振特性研究.红外与激光工程),2017,46(4).
[8]ZHAO Wei-Qian,TANG Fang,QIU Li-Rong.Research status and application on the focusing properties of cylindrical vector beams[J].Acta physica sinica(赵维谦,唐芳,邱丽荣.轴对称矢量光束聚焦特性研究现状及其应用.物理学报),2013,62(5):54201-054201.
[9]XI Si-Xing,WANG Xiao-Lei,HUANG Shuai.Generation of vector beams in terms of the partial light modulator of a twisted nematic liquid crystal[J].Acta physica sinica(席思星,王晓雷,黄帅,等.基于扭曲向列液晶空间光调制器的矢量光生成.物理学报),2015,64(11):140-146.
[10]Adam K,Maurer W.Polarization effects in immersion lithography[J].Journal of Microlithography Microfabrication&Microsystems,2005,4(3):329-343.
[11]Mcintyre G R,Kye J W,Levinson H J,et al.Polarization aberrations in hyper-numerical-aperture projection printing:a comparison of various representations[J].Journal of Microlithography Microfabrication&Microsystems,2006,5(3):170-173.
[12]ZHENG Yu-Xiang,CHEN Liang-Yao.Contemporary optics[M].Beijing:Contemporary optics(郑玉祥,陈良尧.近代光学.北京:电子工业出版社),2011.
[13]YAN Ji-Xiang,WEI Guang-Hui,HA Liu-Zhu,et al.Matrix optics[M].Beijing:Enginery Industry Publishing Company(阎吉祥,魏光辉,哈流柱,等.矩阵光学.北京:兵器工业出版社),1995.