双折射晶体与偏光器件的温度特性
摘要
偏光镜是用以获得偏振光的光学器件，在现代激光技术中使用最广的是双折射晶体制作的偏光棱镜，与其它种类的偏光器件相比，它们具有一系列非常突出的优点，例如具有高的消光比和大的抗光损伤阈值。按照激光应用特点设计的偏光镜的种类繁多，大体可分为棱镜起偏器、偏光分束镜以及相位延迟器和退偏器四种类型。温度对任何仪器、设备乃至器件性能的影响一直是人们十分关注的问题；由冰洲石晶体及其它晶体等双折射材料制作的偏尤器件也不例外。由于我国激光技术的迅速发展，对偏光棱镜的需求越来越大，应用到各种温度下的机会也越来越多，使得对偏光器件温度效应的研究成为紧要的任务。这些双折射晶体(材料)不但光学性质是各向异性的，而且热学性质也是各向异性的，显然温度对这类器件性能的影响更是复杂，也更是不客被忽视的。温度对晶体宏观光学性质的影响，主要反映在晶体折射率的变化上。这种变化虽然很小，却足以改变光在晶体中传播的许多特性。对大多数光学元件来讲．热尤系数是有害的。由于折射率的变化，将使器件的透射比、消光比及透射光强发生改变，从而影响器件的工作特性；另外，因为晶体温度的变化或晶体中存在不均匀的温度分布，将使光波发生畸变，或使透射尤的强度分布不均匀。
本论文着重以冰洲石晶体为例，研完冰洲石晶体的温度特性及冰洲石晶体制作的空气隙格兰棱镜的温度效应。全文概括起来包括以下几个方面的内容：
第一章主要介绍了偏振器件的发展概况和器件的温度效应简介，以及对这一课题进行研究的重要意义。第二章首先介绍了棱镜起偏原理的基本概念，引入了斯涅耳定理及全反射公式，并给出了s振动和p振动的反射比公式；然后分别介绍了偏光棱镜起偏器如格兰·汤姆逊棱镜、格兰·泰勒棱镜的结构、起偏原理，偏光分束镜如渥拉斯顿棱镜和洛匈棱镜的分束原理，片式相位延迟器的原理、特点和消色差相位延迟器的作用原理及分类，最后简单介绍了退偏器件。
摘 要 第2页
为了更精确的确定各个波长和各个温度下的冰洲石晶体的折射率
值；在第三章中，首先介绍了冰洲石晶体的材料性质，引入了色散的
概念及修正的％11。e i er方程；文中精确地求解出Sellmeier方程的
各常数表达式，这些常数可通过不同波长所对应的折射率值求解。在
可见光区将四组不同的波长和对应的折射率代入常数表达式中，然后
通过重复的迭代得到最佳的常数值；使用线形插值的办法得到了不同
波长的折射率温度系数，从而可得出不同温度的 S el line i e r方程常数
值，这样可以很容易求出各个温度下各波长所对应的折射率值。将其
与实验值相比较，发现得到的 Sel lmeiCF方程较好地表达了冰洲石晶
体的色散关系和温度效应。
由冰洲石晶体制作而成的器件在温度变化时，器件的各参量如透
射比、消光比和透射光强曲线也要发生变化。第四章中，首先根据透
射比测量原理和消光比定义，建立了温度对格兰棱镜性能影响的测试
系统，并利用该系统对格兰·泰勒棱镜的透射比、消光比的温度效应
进行了测试，结果各棱镜的透射比和消光比都随着温度的升高而有所
降低；但并不是温度越低越对器件使用有利，各种偏光镜和偏光分束
镜的温度破坏性实验证实在较低温度下，棱镜的结构和胶合层均有被
破坏现象。这些实验均取得了有价值的结果，为在各种温度下使用器
件提供了理论和实验依据。其次系统分折了温度对格兰·泰勒棱镜和
格兰·付科棱镜的透射光强曲线的影响，利用光的干涉原理和不同振
动形式的反射比公式，得到了格兰棱镜在同一入射波长、温度改变时
的扰动因子极大值点的移动量以及相同的温度改变、不同人射波长时
扰动困子极大值点的移动量。这为在不同温度、不同波长下使用的偏
光器件提出了最优化的设计方案，为偏光器件设计提供了有利的理论
依据。
Polarizing prisms are the optical devices to generate polarized light. A kind of birefringent polarizing prism is widely used in the modem laser technology, which has many prominent merits such as the high extinction ratio and the big anti-light injury threshold in contrast with other kinds of prisms. Polarizers, beam splitters, phase retarders and depolarizers are the most commonly used polarizing prisms. Temperature affects the performance of the instrument, equipment and devices. Much attention has been paid to this problem for a long time. One example is the thermal effects on the polarizing devices that are made up with Iceland crystal or other birefringent materials. With the rapid developments of the laser technology in our country, polarizing prisms are used in more and more areas. So researches on thermal effects of the polarizing devices are becoming very important. Not only the thermal properties but also the optical properties of these birefringent crystals (materials) are anisotrop
ic. So how the temperature affects the properties of these devices is very complicated, and shouldn't be neglected. The effects on the macroscopical optical property of the crystal with the variation of the temperature mainly behave as the variation of the refractive index. Although the changes are small, they are big enough to alter a great deal of characteristics when the ray propagates in the crystal. The thermo-optical effect is harmful to a majority of the optical devices. The transmittance, the extinction ratio and the transmitted intensity are all changed due to the alteration of the refractive index, hi addition, optical waves will be distorted or the intensity of the transmitted waves will be non-homogeneously distributed because of the change of the crystal's temperature as well as the uneven temperature distribution.
The dissertation puts emphasis on the Iceland crystal and the
air-spaced Glan-type polarizing prisms made of the Iceland crystal. Thermal effects on the devices are also presented.
The first chapter mainly introduces the general development of the polarizing devices and the importance of the researches on this subject. The second chapter firstly presents the basic conception of the polarizing principles of the prisms, and introduces the Snell theorem and the total reflection formula. The reflectivity formula of the s vibration as well as the p vibration is given. Structures and polarization principles of the polarizing prisms such as the Glan-Thompson prism or the Glan-Taylor prism, beam splitter prisms such as the Wollaston prism or the Rochon prism and their beam splitting principles, the operating principle and features of the phase delay plate, the operating principle and the classification of the achromatic phase delay devices, along with the depolarization devices are all presented.
Chapter 3 is arranged in the following sequence to acquire the refractive index of the Iceland crystal for different values of the wavelength and the temperature. Firstly, the properties of the Iceland crystal are described. The notion of the dispersion and the Sellmeier equation are presented. Secondly, constants in the Sellmeier equation are analytically calculated out and expressed as the function of four different groups of values of the wavelength and the refractive index. The optimal constants are obtained using the iterative method in the visible range of the light. Thirdly, we calculate out the refractive index as a function of the temperature for different values of the wavelength with the interpolation method, by which we obtain the constants of the Sellmeier equation for different values of the temperature. Then we can easily obtain the values of the refractive index for different values of the wavelength and the temperature.
When the temperature changes, several device parameters such as the transmittance, the extinction ratio and the curve of the transmitted
intensity will change accordingly for devices made of the Iceland crystal. At the beginning of chapter 4 we cons
本论文着重以冰洲石晶体为例，研完冰洲石晶体的温度特性及冰洲石晶体制作的空气隙格兰棱镜的温度效应。全文概括起来包括以下几个方面的内容：
第一章主要介绍了偏振器件的发展概况和器件的温度效应简介，以及对这一课题进行研究的重要意义。第二章首先介绍了棱镜起偏原理的基本概念，引入了斯涅耳定理及全反射公式，并给出了s振动和p振动的反射比公式；然后分别介绍了偏光棱镜起偏器如格兰·汤姆逊棱镜、格兰·泰勒棱镜的结构、起偏原理，偏光分束镜如渥拉斯顿棱镜和洛匈棱镜的分束原理，片式相位延迟器的原理、特点和消色差相位延迟器的作用原理及分类，最后简单介绍了退偏器件。
摘 要 第2页
为了更精确的确定各个波长和各个温度下的冰洲石晶体的折射率
值；在第三章中，首先介绍了冰洲石晶体的材料性质，引入了色散的
概念及修正的％11。e i er方程；文中精确地求解出Sellmeier方程的
各常数表达式，这些常数可通过不同波长所对应的折射率值求解。在
可见光区将四组不同的波长和对应的折射率代入常数表达式中，然后
通过重复的迭代得到最佳的常数值；使用线形插值的办法得到了不同
波长的折射率温度系数，从而可得出不同温度的 S el line i e r方程常数
值，这样可以很容易求出各个温度下各波长所对应的折射率值。将其
与实验值相比较，发现得到的 Sel lmeiCF方程较好地表达了冰洲石晶
体的色散关系和温度效应。
由冰洲石晶体制作而成的器件在温度变化时，器件的各参量如透
射比、消光比和透射光强曲线也要发生变化。第四章中，首先根据透
射比测量原理和消光比定义，建立了温度对格兰棱镜性能影响的测试
系统，并利用该系统对格兰·泰勒棱镜的透射比、消光比的温度效应
进行了测试，结果各棱镜的透射比和消光比都随着温度的升高而有所
降低；但并不是温度越低越对器件使用有利，各种偏光镜和偏光分束
镜的温度破坏性实验证实在较低温度下，棱镜的结构和胶合层均有被
破坏现象。这些实验均取得了有价值的结果，为在各种温度下使用器
件提供了理论和实验依据。其次系统分折了温度对格兰·泰勒棱镜和
格兰·付科棱镜的透射光强曲线的影响，利用光的干涉原理和不同振
动形式的反射比公式，得到了格兰棱镜在同一入射波长、温度改变时
的扰动因子极大值点的移动量以及相同的温度改变、不同人射波长时
扰动困子极大值点的移动量。这为在不同温度、不同波长下使用的偏
光器件提出了最优化的设计方案，为偏光器件设计提供了有利的理论
依据。
Polarizing prisms are the optical devices to generate polarized light. A kind of birefringent polarizing prism is widely used in the modem laser technology, which has many prominent merits such as the high extinction ratio and the big anti-light injury threshold in contrast with other kinds of prisms. Polarizers, beam splitters, phase retarders and depolarizers are the most commonly used polarizing prisms. Temperature affects the performance of the instrument, equipment and devices. Much attention has been paid to this problem for a long time. One example is the thermal effects on the polarizing devices that are made up with Iceland crystal or other birefringent materials. With the rapid developments of the laser technology in our country, polarizing prisms are used in more and more areas. So researches on thermal effects of the polarizing devices are becoming very important. Not only the thermal properties but also the optical properties of these birefringent crystals (materials) are anisotrop
ic. So how the temperature affects the properties of these devices is very complicated, and shouldn't be neglected. The effects on the macroscopical optical property of the crystal with the variation of the temperature mainly behave as the variation of the refractive index. Although the changes are small, they are big enough to alter a great deal of characteristics when the ray propagates in the crystal. The thermo-optical effect is harmful to a majority of the optical devices. The transmittance, the extinction ratio and the transmitted intensity are all changed due to the alteration of the refractive index, hi addition, optical waves will be distorted or the intensity of the transmitted waves will be non-homogeneously distributed because of the change of the crystal's temperature as well as the uneven temperature distribution.
The dissertation puts emphasis on the Iceland crystal and the
air-spaced Glan-type polarizing prisms made of the Iceland crystal. Thermal effects on the devices are also presented.
The first chapter mainly introduces the general development of the polarizing devices and the importance of the researches on this subject. The second chapter firstly presents the basic conception of the polarizing principles of the prisms, and introduces the Snell theorem and the total reflection formula. The reflectivity formula of the s vibration as well as the p vibration is given. Structures and polarization principles of the polarizing prisms such as the Glan-Thompson prism or the Glan-Taylor prism, beam splitter prisms such as the Wollaston prism or the Rochon prism and their beam splitting principles, the operating principle and features of the phase delay plate, the operating principle and the classification of the achromatic phase delay devices, along with the depolarization devices are all presented.
Chapter 3 is arranged in the following sequence to acquire the refractive index of the Iceland crystal for different values of the wavelength and the temperature. Firstly, the properties of the Iceland crystal are described. The notion of the dispersion and the Sellmeier equation are presented. Secondly, constants in the Sellmeier equation are analytically calculated out and expressed as the function of four different groups of values of the wavelength and the refractive index. The optimal constants are obtained using the iterative method in the visible range of the light. Thirdly, we calculate out the refractive index as a function of the temperature for different values of the wavelength with the interpolation method, by which we obtain the constants of the Sellmeier equation for different values of the temperature. Then we can easily obtain the values of the refractive index for different values of the wavelength and the temperature.
When the temperature changes, several device parameters such as the transmittance, the extinction ratio and the curve of the transmitted
intensity will change accordingly for devices made of the Iceland crystal. At the beginning of chapter 4 we cons
引文
[1] West C D and Jones R C. J. Opt. Soc. Am. 41,976 (1951)
[2] Harem R.N. MacRac R.A. and Arakawa E.T. J. Opt. Soc. Am. 55, 1460 (1965)
[3] Schledermamn M and Skibowsdi M. Appl. Opt. 10,321(1971)
[4] Driscoll W.G. Vaughan W. Handbook of Optics, New York The Kingsport Press.10～87(1978)
[5] Kestutis Norvaisa, Concord and Richard F. Patented Feb. 9. 3, 56.81 (1971)
[6] 李景镇等编，光学手册．陕西科学出版社，(1986)
[7] E. Ealing Beck Prism polarizers McGraw-Hill Book Co. 190～192 (1972)
[8] 李国华，“偏光棱镜研究”：山东激光，Vol．1，No．1，20～26(1979)
[9] 李国华，“棱镜偏光技术与器件”，应用激光联刊，Vol．12，No．1，60～64 (1982)
[10] 李国华，“激光偏光镜与偏光分束镜”，曲师大学报，Vol．8，No．34，20～26 (1982)
[11] 李国华，“格兰型偏光棱镜”，曲师大学报，Vol．9，No．4，20～26 (1989)
[12] 李国华，李继仲，“棱镜偏光技术与器件”，光电工程，Vol．17，No．4，1～6 (1989)
[13] 李国华，肖胜安，李继仲等，“Wollaston棱镜用于会聚光束中的位相延迟研究”，中国激光，Vol．19，No．7，512～516(1992)
[14] 徐娴，蔡昕，张志利“改进型Wollaston棱镜设计”，光学 精密工程，Vol．9，No．2，131～134(2001)
[15] 肖定全，王民编，晶体物理学，四川大学出版社，(1989)
[16] 李国华，李继仲，“冰洲石红外偏光透射谱测量及其应用”，光谱
学与光谱分析，Vol．11，No．1，18～20(1991)
[17] 李国华，李继仲，“冰洲石红外二向色偏光器件的研究”，中国激光，Vol．18，No．2，94～97(1991)
[18] M．玻恩，E．沃而夫，光学原理，上册，科学出版社，(1978)
[19] Swartz, J.F. and Taylor, A.M., J. Opt. Soc. Am., 58,1427 (1968)
[20] E. Olive, S. Gennari. etal., "Optical metarials for near infrared Wollaston prisms" A&A supplement series., Vol. 123, May2 179～182 (1997)
[21] Kelvin Wagner, "Crystal Optics experiment No. 12", Optics Lab-Ecen 5606 A.M., Department of Electrical and Computer Engineering University of Colorado at Boulder, 1～9 (2001)
[22] 李国华，吴福全，于德洪，“可调分束棱镜的分束角与入射角的关系”，曲阜师范大学学报，Vol．17，No。2， 54～56(1991)
[23] 苏昌林，万光毅等，“渥拉斯顿棱镜出射光线夹角的测量”，计量技术，No．11，23～24(1994)
[24] 张琢，刘丽华等，“Wollaston棱镜方位对激光干涉测量精度的影响”，理论与实践，Vol．19，No．1，4～7(1999)
[25] 黄家寅，尹慧，吴福全，“方解石棱镜分束角高度对称性的设计”，应用光学，Vol．15，No．5，16～20(1994)
[26] 金国藩，李景镇，激光测量学，科学出版社(1998)
[27] Jingshan Wang, Haimin Wang, etal, "Optic design of a near-infrared birefringent flitter system and measurement on birefringence index of calcite", Appl. Opt., Vol. 15, No. 5, 1621～1640 (2001)
[28] 小川智哉著，崔承甲译，应用晶体物理学，科学出版社，(1985)
[29] 蒋民华编，晶体物理，山东科学技术出版社，(1980)
[30] 寥延彪编，物理光学，电子工业出版社，(1986)
[31] Z.D. Zeng, H.Y. Shen et al "Measurement of the refractive
index and thermal refractive index coefficients of Nd:YAP crystal" Appl. Opt. Vol. 29, No. 9, 1281-1280 (1990)
[32] Gorachand Ghosh, "Sellmeier coefficients and dispersion of thermo-optic coefficients for some optical glasses"Appl. Opt. Vol. 36, No. 7, 1540-1546 (1997)
[33] Gorachand Ghosh, "Temperature dispersion in KTP for Nonlinear Devices" IEEE Pho. Tech. Letters. Vol. 7, No. 1, 68～70 (1995)
[34] Gorachand Ghosh, "Sellmeier coefficients for the birefringence and refractive indices of ZnGeP_2 nonlinear crystal at different temperatures" Appl. Opt. Vol. 37, No. 7, 1205～1212 (1998)
[35] Tang Zhou, Jin-feng Zhang et. al. "Measurements of the thermo-optic coefficient ora barium fluoride single crystal" Appl. Opt. Vol. 33, No. 13, 2620～2623 (1994)
[36] David W. Rush, Brian M. Dugan et. al. "Temperature-dependent index-of-refraction changes in BaTiO_3" Opties Letters. Vol. 16, No. 17, 1295～1297 (1991)
[37] Z. D. Zeng, H. Y. Shen et al "Measurement of refractive indices and thermal refractive index coefficients of the Ti:Mg:LiNbO_3 crystal"J. Opt. Soc. Am.B Vol. 10, No. 3, 551-553 (1993)
[38] 徐浩，沈鸿元等，“Ti：Mg：LiNbO_3晶体的折射率温度系数表示式”，激光技术，Vol．19，No．1，1～6(1995)
[39] 周建华、黄燕编，MATLAB 5.3学习教程，北京大学出版社，(2000)
[40] 尹泽明、丁春利等编，精通MATLAB6，清华大学出版社，(2000)
[41] 李国华，赵明山，吴福全等，“高消光比测试系统的研究”，中国激光，Vol．17，No．1，51～53(1990)
[42] 黄建余，季家熔，“偏振干涉法用于偏振器消尤比的测量”，应用激光，Vol．16，No．6，267～268(1996)
[43] 刘训章，黎高平，杨照金等，“用单1／4波片法测量晶体消光比的研究”，中国激光，Vol．26，No．7，589～601(1999)
[44] 王召兵，李国华，陆书龙等，“消光比自动测试系统的实验研究”，中国激光，Vol．A27，No．5，415～418(2000)
[45] 李建利，王英伟，李艳红等，“冰洲石晶体偏光器件性能研究人工晶体学报”Vol．31，No．4，413～416(2002)
[46] Bennett J M Handbook of Optics Vol 2, ed M Bass New York: McGraw-Hill chap3 (1995)
[47] Born M and Wolf E Principles of Optics Cambridge: Cambridge University Press p44 (2001)
[2] Harem R.N. MacRac R.A. and Arakawa E.T. J. Opt. Soc. Am. 55, 1460 (1965)
[3] Schledermamn M and Skibowsdi M. Appl. Opt. 10,321(1971)
[4] Driscoll W.G. Vaughan W. Handbook of Optics, New York The Kingsport Press.10～87(1978)
[5] Kestutis Norvaisa, Concord and Richard F. Patented Feb. 9. 3, 56.81 (1971)
[6] 李景镇等编，光学手册．陕西科学出版社，(1986)
[7] E. Ealing Beck Prism polarizers McGraw-Hill Book Co. 190～192 (1972)
[8] 李国华，“偏光棱镜研究”：山东激光，Vol．1，No．1，20～26(1979)
[9] 李国华，“棱镜偏光技术与器件”，应用激光联刊，Vol．12，No．1，60～64 (1982)
[10] 李国华，“激光偏光镜与偏光分束镜”，曲师大学报，Vol．8，No．34，20～26 (1982)
[11] 李国华，“格兰型偏光棱镜”，曲师大学报，Vol．9，No．4，20～26 (1989)
[12] 李国华，李继仲，“棱镜偏光技术与器件”，光电工程，Vol．17，No．4，1～6 (1989)
[13] 李国华，肖胜安，李继仲等，“Wollaston棱镜用于会聚光束中的位相延迟研究”，中国激光，Vol．19，No．7，512～516(1992)
[14] 徐娴，蔡昕，张志利“改进型Wollaston棱镜设计”，光学 精密工程，Vol．9，No．2，131～134(2001)
[15] 肖定全，王民编，晶体物理学，四川大学出版社，(1989)
[16] 李国华，李继仲，“冰洲石红外偏光透射谱测量及其应用”，光谱
学与光谱分析，Vol．11，No．1，18～20(1991)
[17] 李国华，李继仲，“冰洲石红外二向色偏光器件的研究”，中国激光，Vol．18，No．2，94～97(1991)
[18] M．玻恩，E．沃而夫，光学原理，上册，科学出版社，(1978)
[19] Swartz, J.F. and Taylor, A.M., J. Opt. Soc. Am., 58,1427 (1968)
[20] E. Olive, S. Gennari. etal., "Optical metarials for near infrared Wollaston prisms" A&A supplement series., Vol. 123, May2 179～182 (1997)
[21] Kelvin Wagner, "Crystal Optics experiment No. 12", Optics Lab-Ecen 5606 A.M., Department of Electrical and Computer Engineering University of Colorado at Boulder, 1～9 (2001)
[22] 李国华，吴福全，于德洪，“可调分束棱镜的分束角与入射角的关系”，曲阜师范大学学报，Vol．17，No。2， 54～56(1991)
[23] 苏昌林，万光毅等，“渥拉斯顿棱镜出射光线夹角的测量”，计量技术，No．11，23～24(1994)
[24] 张琢，刘丽华等，“Wollaston棱镜方位对激光干涉测量精度的影响”，理论与实践，Vol．19，No．1，4～7(1999)
[25] 黄家寅，尹慧，吴福全，“方解石棱镜分束角高度对称性的设计”，应用光学，Vol．15，No．5，16～20(1994)
[26] 金国藩，李景镇，激光测量学，科学出版社(1998)
[27] Jingshan Wang, Haimin Wang, etal, "Optic design of a near-infrared birefringent flitter system and measurement on birefringence index of calcite", Appl. Opt., Vol. 15, No. 5, 1621～1640 (2001)
[28] 小川智哉著，崔承甲译，应用晶体物理学，科学出版社，(1985)
[29] 蒋民华编，晶体物理，山东科学技术出版社，(1980)
[30] 寥延彪编，物理光学，电子工业出版社，(1986)
[31] Z.D. Zeng, H.Y. Shen et al "Measurement of the refractive
index and thermal refractive index coefficients of Nd:YAP crystal" Appl. Opt. Vol. 29, No. 9, 1281-1280 (1990)
[32] Gorachand Ghosh, "Sellmeier coefficients and dispersion of thermo-optic coefficients for some optical glasses"Appl. Opt. Vol. 36, No. 7, 1540-1546 (1997)
[33] Gorachand Ghosh, "Temperature dispersion in KTP for Nonlinear Devices" IEEE Pho. Tech. Letters. Vol. 7, No. 1, 68～70 (1995)
[34] Gorachand Ghosh, "Sellmeier coefficients for the birefringence and refractive indices of ZnGeP_2 nonlinear crystal at different temperatures" Appl. Opt. Vol. 37, No. 7, 1205～1212 (1998)
[35] Tang Zhou, Jin-feng Zhang et. al. "Measurements of the thermo-optic coefficient ora barium fluoride single crystal" Appl. Opt. Vol. 33, No. 13, 2620～2623 (1994)
[36] David W. Rush, Brian M. Dugan et. al. "Temperature-dependent index-of-refraction changes in BaTiO_3" Opties Letters. Vol. 16, No. 17, 1295～1297 (1991)
[37] Z. D. Zeng, H. Y. Shen et al "Measurement of refractive indices and thermal refractive index coefficients of the Ti:Mg:LiNbO_3 crystal"J. Opt. Soc. Am.B Vol. 10, No. 3, 551-553 (1993)
[38] 徐浩，沈鸿元等，“Ti：Mg：LiNbO_3晶体的折射率温度系数表示式”，激光技术，Vol．19，No．1，1～6(1995)
[39] 周建华、黄燕编，MATLAB 5.3学习教程，北京大学出版社，(2000)
[40] 尹泽明、丁春利等编，精通MATLAB6，清华大学出版社，(2000)
[41] 李国华，赵明山，吴福全等，“高消光比测试系统的研究”，中国激光，Vol．17，No．1，51～53(1990)
[42] 黄建余，季家熔，“偏振干涉法用于偏振器消尤比的测量”，应用激光，Vol．16，No．6，267～268(1996)
[43] 刘训章，黎高平，杨照金等，“用单1／4波片法测量晶体消光比的研究”，中国激光，Vol．26，No．7，589～601(1999)
[44] 王召兵，李国华，陆书龙等，“消光比自动测试系统的实验研究”，中国激光，Vol．A27，No．5，415～418(2000)
[45] 李建利，王英伟，李艳红等，“冰洲石晶体偏光器件性能研究人工晶体学报”Vol．31，No．4，413～416(2002)
[46] Bennett J M Handbook of Optics Vol 2, ed M Bass New York: McGraw-Hill chap3 (1995)
[47] Born M and Wolf E Principles of Optics Cambridge: Cambridge University Press p44 (2001)