晶体双折射退偏器的光波叠加分析方法与优化设计
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摘要
退偏器是将偏振光转化为非偏振光的一种偏光器件。随着偏光技术和激光应用的发展，退偏器被越来越广泛地应用于天文仪器、激光加工、激光医学、光纤通信等各种光学探测和通信系统，因此退偏器性能及优化设计的研究具有重要的现实意义。本文研究的对象是双折射晶体材料的退偏器，即晶体双折射退偏器。该类型的退偏器不能真正把偏振光转化为非偏振光，只是使透射光的偏振态按一定规律做周期性分布，只要周期足够小，其总的平均效果即表现为退偏。因此该类型退偏器属于伪退偏器。晶体双折射退偏器利用晶体的双折射性质可以实现偏振光在空域和频域的退偏，其中，最早的退偏器——Lyot型退偏器便属于频域退偏，而本文研究的其它退偏器均属于空域退偏。频域退偏基于复色光透过退偏器后产生随频率连续变化的相位差，而不同相位差又对应不同偏振态，这些不同偏振态的叠加效果即表现为退偏；空域退偏则一般靠一个或多个晶体楔面（简称晶楔）的组合，产生随空间连续变化的相位差来实现退偏。尽管有所不同，但其退偏原理均可表述为相位差变化造成的不同偏振态的光的叠加。
退偏器性能的分析长期以来采用矩阵方法，包括Mueller矩阵、相干矩阵。尽管这两种方法的科学性、合理性毋庸置疑，却也有自身难以避免的缺点：过程比较复杂，物理意义比较抽象。为克服这些缺点，本文直接从光的波动本性出发，根据退偏原理，提出光波叠加分析方法。该方法避免了矩阵方法中过多元素带来的繁琐运算，并可充分沿用椭圆偏振光的分析公式或结论，加上对相位的合理、灵活处理，大大简化了数学过程；分析过程的每一步都与退偏的光学过程直接相关，物理意义非常清晰，因此可以揭示矩阵方法难以涉及的退偏机制。
本文的研究工作主要包括以下三个方面：
1、利用光波叠加方法分析四种已有形式的退偏器：Lyot改进型退偏器、Lyot型退偏器、HV退偏器、双巴比涅退偏器，并与传统矩阵方法进行对比。
2、利用光波叠加方法分析四种新设计的退偏器：晶体光轴扇形分布退偏器、正反应用不同特性退偏器、四元优化设计退偏器、Lyot单色光退偏器。其中，后两种属于优化设计形式：四元优化设计退偏器是在光波叠加分析结论基础上，结合双巴比涅退偏器、晶体光轴扇形分布退偏器、正反应用不同特性退偏器等四元结构退偏器的优点而实现完美退偏；而Lyot单色光退偏器是根据光波叠加方法对Lyot型退偏器分析结果，进一步推理得到的一种可以实现对单色线偏振光退偏的退偏器，性能大大优于单个1/4波片形式的单色光退偏器。
3、制作石英晶体材料的样品，并建立退偏度测试需要的实验系统，对样品性能进行测试。主要测试样品对线偏振光的退偏度，包括偏振度随方位角、入射角的变化情况。除此之外，在探索的基础阶段，做了大量相关的实验工作，如研究退偏器的透射光点分布规律，圆形光阑孔径大小对退偏度的影响，楔角对退偏度的影响，激光波长对退偏度的影响，不同平面内退偏度随入射角的变化规律，光屏上叠加条纹可见度随方位角及光屏位置的变化规律，等。
本文的主要创新点有：
1、提出了退偏器的光波叠加分析的思想和方法。
2、对已有形式的退偏器分析中得到有意义的新结论，如首次推导得到Lyot改进型退偏器和HV退偏器对单色线偏振光的退偏度表达式，统一了不同文献所给的Lyot型退偏器的理想退偏条件，等。
3、设计并分析了四种新型退偏器，其中四元优化设计退偏器、Lyot单色光退偏器具有各自优越性，完全可以得到推广应用。
4、实验研究了退偏度随晶楔楔角的变化规律，提出了退偏度对楔角的“饱和性”概念，为退偏器的设计、加工提供了重要依据；提出了受楔角及光屏位置影响的退偏度的“边缘效应”。
5、根据光波叠加分析的结论，总结了晶体双折射退偏器的理想退偏条件，将成为该类型退偏器设计、分析的基本理论。
6、研究了退偏度随入射角的实验规律，提出通过微调入射角改善退偏度的方法。
Depolarizer is a type of polarization devices that can realize the transformation frompolarized light to unpolarized light. Along with the development of polarizing technology andlaser application, depolarizers have an increasingly wide utilization in optical detection andcommunication system, such as astronomical instruments, laser processing, laser medicine,optical fiber communication, etc. So it is significant to study the performance of depolarizer andits optimal design. In this paper, the depolarizers made by crystal birefringent, namely crystalbirefringent depolarizers, are selected as the major objects. Such a depolarizer can’t transformincident wave to unpolarized light in real sense, but cause the periodic variation of transmittedpolarization states, and it seems as depolarization for average effect when the cycle is smallenough. Therefore the depolarizer is a type of pseudodepolarizer. Using the birefringentcharacteristics of crystal, the crystal birefringent depolarizer realize the depolarization of spatialor frequency domain. The Lyot depolarizer which is the earliest depolarizer belongs to thefrequency depolarizer and the others belongs to the spatial depolarizer. Operation principle of thefrequency depolarizer bases on the different phase difference caused by the transmittedpolychromatic lights and the different phase differences lead to the different polarization states.The behavior of the superposition of the different polarization states is just depolarization. Thedepolarization of the spatial depolarizer based on the continuously varying spatial phasedifferences caused by one or more crystal wedge surfaces (short for crystal wedge). Though thedifferences between the above two depolarizers, their depolarization principle can be expressedas the same as the superposition of lights of different polarization states caused by the differentphase differences.
For a long time, matrix is adopted as the analytical method of depolarizers, includingMueller matrix and coherency matrix. Though their scientificity is certainly reliable, they stillhave some inevitable defects, such as complicated procedure and abstract physical meaning. Toovercome the defects, considering directly the wave properties of lights, we put forward ananalytical method based on superposition of lights. The method avoids the complicatecalculation caused by the excessive matrix elements, moreover, most of the formulas andconclusions to analyze elliptically polarized light can be cited adequately by the procedure, andthe reasonable and flexible treatments of the phase in addition, the mathematical procedure ismuch simplified. The procedure has very clear physical meaning for every analysis sequence isrelated directly to the optical process of depolarization. So the new method can disclose somedepolarization mechanisms that difficult to be covered by the matrix method.
This paper mainly includes the following research contents in three fields:
1. Using the superposition of lights method, four existed depolarizers were analyzed,including the improved Lyot depolarizer, the Lyot depolarizer, the HV depolarizer, and the dualBabinet compensator depolarizer. The contrasts between it with the traditional methods weregiven.
2. Using the superposition of lights method, four new designed depolarizers were analyzed,including the optical axes of crystal fan-shaped-distribution depolarizer, the different propertiesof forward-reverse applications depolarizer, the quarternary optimal design depolarizer, the Lyotmonochromatic depolarizer, among which the last two are the optimal designs. Based on thestudy conclusions of the superposition of lights, combined the advantages of the dual Babinetcompensator depolarizer, the optical axes of crystal fan-shaped-distribution depolarizer and thedifferent properties of forward-reverse applications depolarizer, the quarternary optimal designdepolarizer can achieve perfect depolarization. By further discursion based on the studyconclusions of the Lyot depolarizer by the superposition of lights, the Lyot monochromaticdepolarizer was derived to realize the depolarization of monochromatic linearly polarized light,whose performance is much better than depolarizer acted by one quarter-wave plate.
3. Experiment system was set up to test the performance of samples made by quartz crystal.The main test aim is the degree of depolarization (short for D), including the variation of the Dwith azimuth angle and incident angle. In addition, lots of related experiments were conducted inthe exploratory stage. For example, the study of distribution regularities of transmitted light spots,and the dependence of the D on the size of round diaphragm aperture, wedge angle, laser wavelength, incident angle in different plane, and the dependence of the degree of visibility ofsuperposed stripes on the azimuth angle and the position of optical screen.
The major innovations of this paper include the following areas:
1. The idea and method of the superposition of lights are put forward to analyze depolarizer.
2. The new significant conclusions were derived from the analysis of the existeddepolarizers, such as the D of the improved Lyot depolarizer and the HV depolarizer for linearlypolarized light were deduced firstly, the different ideal conditions of depolarization from someearly literature were united, etc.
3. Four new depolarizers were designed and analyzed, among which the quarternary optimaldesign depolarizer and the Lyot monochromatic depolarizer can be applied widely for their ownsuperiorities.
4. The dependence of the D on the wedge angle was studied through experiments, and the“saturability” of the D on the wedge angle was put forward as a result, which is an importantground for the design and machining. The “edge effect” of the D which is dependent on thewedge angle and the position of optical screen were also mentioned.
5. Based on the analysis of the superposition of lights, the ideal condition of depolarizationof the crystal birefringent depolarizer was concluded, which will be a fundamental theory usedfor the design and analysis of such depolarizer.
6. The dependence of the D on the incident angle was studied through experiments, and takeminor adjustment of incident angle as the way to improve the D.
退偏器性能的分析长期以来采用矩阵方法，包括Mueller矩阵、相干矩阵。尽管这两种方法的科学性、合理性毋庸置疑，却也有自身难以避免的缺点：过程比较复杂，物理意义比较抽象。为克服这些缺点，本文直接从光的波动本性出发，根据退偏原理，提出光波叠加分析方法。该方法避免了矩阵方法中过多元素带来的繁琐运算，并可充分沿用椭圆偏振光的分析公式或结论，加上对相位的合理、灵活处理，大大简化了数学过程；分析过程的每一步都与退偏的光学过程直接相关，物理意义非常清晰，因此可以揭示矩阵方法难以涉及的退偏机制。
本文的研究工作主要包括以下三个方面：
1、利用光波叠加方法分析四种已有形式的退偏器：Lyot改进型退偏器、Lyot型退偏器、HV退偏器、双巴比涅退偏器，并与传统矩阵方法进行对比。
2、利用光波叠加方法分析四种新设计的退偏器：晶体光轴扇形分布退偏器、正反应用不同特性退偏器、四元优化设计退偏器、Lyot单色光退偏器。其中，后两种属于优化设计形式：四元优化设计退偏器是在光波叠加分析结论基础上，结合双巴比涅退偏器、晶体光轴扇形分布退偏器、正反应用不同特性退偏器等四元结构退偏器的优点而实现完美退偏；而Lyot单色光退偏器是根据光波叠加方法对Lyot型退偏器分析结果，进一步推理得到的一种可以实现对单色线偏振光退偏的退偏器，性能大大优于单个1/4波片形式的单色光退偏器。
3、制作石英晶体材料的样品，并建立退偏度测试需要的实验系统，对样品性能进行测试。主要测试样品对线偏振光的退偏度，包括偏振度随方位角、入射角的变化情况。除此之外，在探索的基础阶段，做了大量相关的实验工作，如研究退偏器的透射光点分布规律，圆形光阑孔径大小对退偏度的影响，楔角对退偏度的影响，激光波长对退偏度的影响，不同平面内退偏度随入射角的变化规律，光屏上叠加条纹可见度随方位角及光屏位置的变化规律，等。
本文的主要创新点有：
1、提出了退偏器的光波叠加分析的思想和方法。
2、对已有形式的退偏器分析中得到有意义的新结论，如首次推导得到Lyot改进型退偏器和HV退偏器对单色线偏振光的退偏度表达式，统一了不同文献所给的Lyot型退偏器的理想退偏条件，等。
3、设计并分析了四种新型退偏器，其中四元优化设计退偏器、Lyot单色光退偏器具有各自优越性，完全可以得到推广应用。
4、实验研究了退偏度随晶楔楔角的变化规律，提出了退偏度对楔角的“饱和性”概念，为退偏器的设计、加工提供了重要依据；提出了受楔角及光屏位置影响的退偏度的“边缘效应”。
5、根据光波叠加分析的结论，总结了晶体双折射退偏器的理想退偏条件，将成为该类型退偏器设计、分析的基本理论。
6、研究了退偏度随入射角的实验规律，提出通过微调入射角改善退偏度的方法。
Depolarizer is a type of polarization devices that can realize the transformation frompolarized light to unpolarized light. Along with the development of polarizing technology andlaser application, depolarizers have an increasingly wide utilization in optical detection andcommunication system, such as astronomical instruments, laser processing, laser medicine,optical fiber communication, etc. So it is significant to study the performance of depolarizer andits optimal design. In this paper, the depolarizers made by crystal birefringent, namely crystalbirefringent depolarizers, are selected as the major objects. Such a depolarizer can’t transformincident wave to unpolarized light in real sense, but cause the periodic variation of transmittedpolarization states, and it seems as depolarization for average effect when the cycle is smallenough. Therefore the depolarizer is a type of pseudodepolarizer. Using the birefringentcharacteristics of crystal, the crystal birefringent depolarizer realize the depolarization of spatialor frequency domain. The Lyot depolarizer which is the earliest depolarizer belongs to thefrequency depolarizer and the others belongs to the spatial depolarizer. Operation principle of thefrequency depolarizer bases on the different phase difference caused by the transmittedpolychromatic lights and the different phase differences lead to the different polarization states.The behavior of the superposition of the different polarization states is just depolarization. Thedepolarization of the spatial depolarizer based on the continuously varying spatial phasedifferences caused by one or more crystal wedge surfaces (short for crystal wedge). Though thedifferences between the above two depolarizers, their depolarization principle can be expressedas the same as the superposition of lights of different polarization states caused by the differentphase differences.
For a long time, matrix is adopted as the analytical method of depolarizers, includingMueller matrix and coherency matrix. Though their scientificity is certainly reliable, they stillhave some inevitable defects, such as complicated procedure and abstract physical meaning. Toovercome the defects, considering directly the wave properties of lights, we put forward ananalytical method based on superposition of lights. The method avoids the complicatecalculation caused by the excessive matrix elements, moreover, most of the formulas andconclusions to analyze elliptically polarized light can be cited adequately by the procedure, andthe reasonable and flexible treatments of the phase in addition, the mathematical procedure ismuch simplified. The procedure has very clear physical meaning for every analysis sequence isrelated directly to the optical process of depolarization. So the new method can disclose somedepolarization mechanisms that difficult to be covered by the matrix method.
This paper mainly includes the following research contents in three fields:
1. Using the superposition of lights method, four existed depolarizers were analyzed,including the improved Lyot depolarizer, the Lyot depolarizer, the HV depolarizer, and the dualBabinet compensator depolarizer. The contrasts between it with the traditional methods weregiven.
2. Using the superposition of lights method, four new designed depolarizers were analyzed,including the optical axes of crystal fan-shaped-distribution depolarizer, the different propertiesof forward-reverse applications depolarizer, the quarternary optimal design depolarizer, the Lyotmonochromatic depolarizer, among which the last two are the optimal designs. Based on thestudy conclusions of the superposition of lights, combined the advantages of the dual Babinetcompensator depolarizer, the optical axes of crystal fan-shaped-distribution depolarizer and thedifferent properties of forward-reverse applications depolarizer, the quarternary optimal designdepolarizer can achieve perfect depolarization. By further discursion based on the studyconclusions of the Lyot depolarizer by the superposition of lights, the Lyot monochromaticdepolarizer was derived to realize the depolarization of monochromatic linearly polarized light,whose performance is much better than depolarizer acted by one quarter-wave plate.
3. Experiment system was set up to test the performance of samples made by quartz crystal.The main test aim is the degree of depolarization (short for D), including the variation of the Dwith azimuth angle and incident angle. In addition, lots of related experiments were conducted inthe exploratory stage. For example, the study of distribution regularities of transmitted light spots,and the dependence of the D on the size of round diaphragm aperture, wedge angle, laser wavelength, incident angle in different plane, and the dependence of the degree of visibility ofsuperposed stripes on the azimuth angle and the position of optical screen.
The major innovations of this paper include the following areas:
1. The idea and method of the superposition of lights are put forward to analyze depolarizer.
2. The new significant conclusions were derived from the analysis of the existeddepolarizers, such as the D of the improved Lyot depolarizer and the HV depolarizer for linearlypolarized light were deduced firstly, the different ideal conditions of depolarization from someearly literature were united, etc.
3. Four new depolarizers were designed and analyzed, among which the quarternary optimaldesign depolarizer and the Lyot monochromatic depolarizer can be applied widely for their ownsuperiorities.
4. The dependence of the D on the wedge angle was studied through experiments, and the“saturability” of the D on the wedge angle was put forward as a result, which is an importantground for the design and machining. The “edge effect” of the D which is dependent on thewedge angle and the position of optical screen were also mentioned.
5. Based on the analysis of the superposition of lights, the ideal condition of depolarizationof the crystal birefringent depolarizer was concluded, which will be a fundamental theory usedfor the design and analysis of such depolarizer.
6. The dependence of the D on the incident angle was studied through experiments, and takeminor adjustment of incident angle as the way to improve the D.
引文
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