实现涡旋光束及光强图样调制的多孔干涉仪设计研究
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摘要
光学涡旋是指具有螺旋状波前的特殊光场。涡旋光场中存在光强为零的点，在这点的光场实部和虚部同时为零，相位具有不确定性，我们称之为涡旋核或相位奇异点。在垂直于光束前进方向的横截面上，光场的相位随相对于涡旋核的方位角呈螺旋型变化。环绕一周，相位的总变化量相对于2π的倍数叫做该光学涡旋的拓扑荷。对于相位按与方位角线性增加或减小的光学涡旋，其所携带的每一光子携带的轨道角动量和拓扑荷成正比。自发现以来，光学涡旋由于其上述相位分布特性以及在动力学方面的应用潜力，得到研究者们的广泛关注，并被应用于光学微操纵、材料科学、原子光学、信息传输、生物医学等众多领域。因此，对于光学涡旋的研究将在其今后应用方面具有较大的实际意义。
在光学领域，对多光束干涉的研究一直受到人们的重视。通过对光束位置、夹角、相位以及振幅等的多种调控，可以实现对所形成光场光强分布精确控制。当前，基于小孔对入射光波的选择透过性的多孔干涉仪，更是由于其简单的构造以及在提供多波面干涉方面的优势更是受到人们的青睐，并被应用于光学涡旋的产生、拓扑荷的探测、光学格子的形成等领域，成为光学研究中一个重要的工具。
本学位论文基于多孔干涉仪对入射光波前的调节，提出了具有螺旋方式排列的小孔阵列。通过对小孔径向位置的精确调节，使得从相邻小孔到观察屏中心的距离逐渐增加或减小且变化总量为入射光波长的整数倍，从而导致各自光波的相位均匀延迟或提前。我们使用平面光波照射螺旋多孔屏，在菲涅耳区的观察面上得到高阶的光学涡旋；使用涡旋光束照明具有螺旋缝的结构，在特定平面获得对入射拓扑荷的调制；使用由少量小孔组成的螺旋孔屏，实现了通过观察面上光强图样同时分辨入射涡旋光拓扑荷的大小和符号；通过调节六孔干涉仪上小孔的径向距离，在平面光波入射的情况下得到干涉仪傅里叶平面上的二阶涡旋阵列分布；通过调节具有等大小孔光子筛上小孔的径向距离，实现了对光波相位的编码，并在观察面获得特定的任意光强图样；使用显微物镜和干涉仪结合的方法，从干涉图样中提取了透射型刻划光栅表面的高度分布。本文共分为七章。
第一章对光学涡旋的研究背景及现状进行了综合型描述。主要内容包括：光学涡旋的发展；光学涡旋的特性分析，包括涡旋的数学描述、所携带光子的轨道角动量、涡旋的传播；光学涡旋的实验室产生方法，主要介绍了常用的几何光学模式转换法、计算全息法、螺旋相位板法、激光直接输出法以及多光束干涉法等主要方法；光学涡旋拓扑荷的探测方法，主要介绍了光学涡旋与平面光波干涉法、计算全息图法、干涉仪法及多孔干涉屏法等。
第二章对非对称螺旋多孔屏在高阶光学涡旋产生方面的应用进行了研究。我们使用方位角均匀排列的多孔衍射屏，根据多孔干涉屏上小孔到共轴观察屏中心处的距离和该小孔到干涉屏中心的面内径向距离之间所具有的二次方关系，调节小孔径向位置，使得相邻小孔到观察屏中心的距离均匀增加或减小且变化总量为波长的整数倍。这种调节导致从各小孔衍射的光波在到达观察屏时具有均匀延迟或提前的相位，并且相位差总量为2π的整数倍。通过这些光波的相互叠加干涉，我们在观察屏上得到具有高阶拓扑荷的光学涡旋。在理论模拟中，我们阐明了螺旋结构多孔屏的设计基础，并验证了这种螺旋机制在涡旋产生方面的可行性；通过多个结果发现，螺旋孔的具体排列方式，即设计之时所遵循的总光程调制量，决定了观察屏上涡旋拓扑荷的大小和方向；模拟结果同时表明，多孔屏上小孔的个数将所能产生的涡旋拓扑荷大小限制在小于或等于小孔个数的一半。我们发现，螺旋多孔屏能否产生规则的光学涡旋，受屏上小孔大小及多孔屏和观察屏之间距离的影响，越小的小孔越能产生较高质量的涡旋。在实验上，我们通过飞秒激光在延平的易拉罐壁上烧蚀了具有螺旋排列的多孔阵列。当平面光波入射时，我们发现在观察屏上出现我们预期的光学涡旋。实验结果和理论模拟相吻合。
第三章研究了螺旋缝屏对入射光学涡旋拓扑荷的调制作用。通过理论模拟我们发现，当涡旋光束照射具有螺旋缝结构的干涉屏后，其衍射光场中的拓扑荷将不同于入射的拓扑荷，并且拓扑荷的变化量决定于螺旋缝的具体结构；通过将螺旋缝换做沿缝的多个小孔，我们实现了通过对屏后衍射光强图样的不同来同时辨别入射光学涡旋的拓扑荷大小和符号。同时，我们分析了实际观察距离和设定观察距离的不同对衍射光场的影响。
第四章设计了具有相位编码的光子筛，并将其应用于特定光强图样的产生。首先，我们将多个等大小的小孔均匀分布在多圈围绕干涉屏中心的圆环上。圆环与屏中心具有特定的径向距离，以保证从各圆环到观察平面中心的距离之间相差波长的整数倍，从而消去该多孔屏衍射中的二次菲涅耳衍射因子。然后，我们通过Gerchberg-Saxton算法进行迭代运算，获得对应于特定光强图样的产生各个小孔处光波所需要的相位分布。最后，通过将相应的小孔沿径向偏移其所在的圆环，使其到观察屏中心的光程发生相应于其所应有相位值的变化，得到具有相位编码的光子筛。在平面波入射这种光子筛后，在观察平面得到了预先设计的光强图样。我们分析了圆环圈数和小孔个数对所称图样质量的影响。在实验中，我们自制了三个具有相位调制的光子筛来作为例子，验证了这种光子筛在图样设计中的可行性。
第五章研究了利用六孔干涉屏产生二阶涡旋阵列的方法。我们将两个具有不同尺寸的正三孔干涉屏叠合，形成对称六孔干涉屏。通过理论分析，我们预测了产生二阶涡旋阵列时，两个三孔屏尺寸之间所应满足的比例。在理论上，我们模拟了多种比例条件下，干涉屏傅里叶平面上的光场分布，验证了这种多孔屏的可行性，并且分析了小孔孔径对这种机制，特别是对光场光强分布的影响。通过具有比例参数4:5的六孔干涉仪的制造，我们从实验上在平面光照明条件下得到了二阶涡旋阵列。
第六章利用显微物镜和干涉仪的结合，提取了透射型刻划光栅表面精确的高度起伏分布。我们利用具有高数值孔径高放大倍数的显微透镜获得光栅表面在微米范围内的放大精细像，通过引入参考光得到其与放大像的干涉图样，根据相位重建理论从干涉图样中得到紧贴光栅后表面光波的相位分布，进而推算处光栅表面的高度分布。通过和利用原子力显微镜获得的光栅表面高度进行对比，验证了我们光学方法的精确度在nm量级。
第七章，我们总结了本学位论文所取得的成果和创新，并对下一步将要进行的工作进行了简单介绍。
Vortex field is a special kind of light field, where the wave fronts have helical variations.In an optical vortex, there exist some points where the intensity vanishes, and we call suchpoints vortex cores. Both the real part and the imaginary part of the field at cores are all zeros,and the phases here are undefined. Around a vortex core, the light phase has a helical variationalong with the increase of azimuthal angle. The total phase variation may be some integermultiples of, and the integer is called the topological charge of the vortex. For a vortex withthe phase increasing strictly linearly to the azimuthal angle, every photon it carries may takethe orbital angular momentum of that is determined by the topological charge. Due to thephase characters mentioned above and the potential use in dynamics, optical vortex hasattracted great attention since proposed. Now, optical vortex has been used in a variety of fieldsranging from optical micromanipulation, material science, quantum optics, opticalcommunication to biomedicine, and so on. Therefore, it is of great practical interest to studythe optical vortex.
In optics, the study of multi-beam interference has also attracted great attention. Byadjusting the positions, incident directions, amplitudes and relative phases in the interferencingbeams, we can accurately control the resultant fields. Nowadays, multipoint interferometers,which are based on the optional selection of incident wave by pinholes, have been well appliedin optical studies. The multipoint interferometers can readily offer multiple waves forinterference, and their fabrications are easy and low-cost. In application, they have been usedin the detection of topological charges, generations of both optical vortices and optical lattices,and they are now a more and more useful tool in optics.
Basing on the modulation of incident wave fronts by multipoint interferometers, weproposed a multipoint interferometer with the pinholes arranged in a helical way. Due to theadjustment of radial positions of the pinholes, the optical paths from adjacent pinholes to theorigin of the observation plane may increase or decrease evenly, and the total variation may bemultiples of the incident wavelength. This results in the specific phase differences between theinterferencing waves. We have illuminated such multipoint interferometers with plane waves,and have obtained high-order optical vortices on the observation plane in Fresnel field. Wehave illuminated the spiral-slit screen with vortex beams, and have realized the conversion oftopological charges of the incident vortex. We have realized the simultaneous distinguishes ofboth the value and the sign of the incident topological charges, by using a spiral pinholeinterferometer with small pinhole numbers. We have obtained second-order vortex arrays by illuminating six-pinhole interferometers of variable radial distances. The phase-encoded photonsieves have been proposed, and we have obtained designed intensity patterns after the sieves.We have also obtained the height variation of two transmissive ruled grating surfaces, using thecombination of a microscope objective and a interferometer. The whole paper is detailed inseven chapters.
Chapter1: Introduction. We describe the background of this paper, and give the generaldescriptions of optical vortices. At the beginning, we show the development of optical vortex.Second, we study the characters of optical vortex, including its mathematical description,orbital angular momentum of photon and its propagation. Third, we review the commonly usedexperimental generation of optical vortex, including mode conversion of laser,computer-generated hologram, spiral phase plate, direct input of laser and multi-beaminterference. At the last, we discuss the methods in detecting of topological charge, includinginterference of vortex and plane wave, holograms, interferometries and multipointinterferometers.
Chapter2: In this chapter, we study the application of spiral multipoint interferometers ingenerating high-order optical vortex. Pinholes are arranged with even azimuthal angleincrement on the multipoint interferometer. According to the quadratic relationship between thedistances from a pinhole to the observation plane origin and the distance from this pinhole tothe interferometer origin, we adjust the pinhole position in radial directions until the opticalpaths from neighboring pinholes to the observation plane origin have constant increment. Thetotal path variation determines the total phase difference in the multiple transmitting waves,which may be integer multiples of. We obtain high-order optical vortices in the interferencefield of the waves. In numerical simulation, we demonstrate the fabrication process of theinterferometer and verify the feasibility of this mechanism. We discover that the topologicalcharge of the generated vortex is determined by the total path variation, e.g., the structure ofthe pinhole arrangement. The simulations show that the possible topological charge of thevortex is confined to be no more than half the pinhole number. We also show that the feasibilityof the interferometer is influenced by the pinhole sizes, and that smaller pinholes are better fora good vortex. In experiment, we fabricate such spiral multipoint interferometers by ablatingpinholes on flattened Coca-Cola cans. The experimental results coincide with the simulationswell.
Chapter3: In this chapter, we study the conversion of topological charge with the use ofspiral-slit screens. When an optical vortex transmits from a designed spiral-slit, its topologicalcharge may be altered. The variation is determined by the structure of the slit. We also replacethe slit by small number of isolated pinholes, and show that both the value and the sign of theincident topological charge could be distinguished simultaneously by reading the differentintensity patterns on the observation plane.
Chapter4: We propose the phase-encoded photon sieves and use them to generate designed intensity patterns. First, we arrange some pinholes of equal size evenly on some ringscentered at the origin. The optical paths from the rings to the observation plane origin differ bymultiples of incident wavelength, and this design eliminates the quadratic phase aberration ofthe sieve in Fresnel diffraction. Then, using the iteration in the Gerchberg-Saxton algorithm,we obtain the required phase value at each pinhole. By deviating the pinhole position fromcorresponding ring, we encode such phase values on the sieve, and obtain the phase-encodedphoton sieve. When such sieves are illuminated by plane wave, the designed intensity patternsare obtained on the observation plane. We have also discussed the influences of pinholenumbers and rings on the quality of the generated patterns. We fabricate three phase-encodedphoton sieves in experiment, and verify their feasibilities.
Chapter5: In this chapter, we generate second-order vortex arrays with six-pinholeinterferometers. The six-pinhole interferometer is fabricated by combining two differentregular three-pinhole interferometers together. In the simulations, we predict the requirement ofsize ratios of the two three-pinhole interferometers to generate second-order vortex arrays. Insimulation, the feasibility of the interferometer is verified, and the influence of the pinholesizes is discussed. By using the self-made six-pinhole interferometer with ratio4:5inexperiment, we obtain second-order vortex arrays under plane wave illumination.
Chapter6: In this chapter, we obtain the height variations of two transmissive ruledgrating surfaces. By using the combination of a Mach-Zende interferometer and an objectivemicroscope of high numerical aperture and high magnification, we obtain the magnified imageof grating surface in small area and distract the phase distribution of the light from theinterferogram. The height variation is deduced from the phase values. We compare the resultswith the ones obtained by a Atomic Force Microscope, and discover that the optical methodrealizes a resolution of nano-scale.
Charpter7: In this chapter, we summarize the results and the innovations of this paper,and describe the future work.
在光学领域，对多光束干涉的研究一直受到人们的重视。通过对光束位置、夹角、相位以及振幅等的多种调控，可以实现对所形成光场光强分布精确控制。当前，基于小孔对入射光波的选择透过性的多孔干涉仪，更是由于其简单的构造以及在提供多波面干涉方面的优势更是受到人们的青睐，并被应用于光学涡旋的产生、拓扑荷的探测、光学格子的形成等领域，成为光学研究中一个重要的工具。
本学位论文基于多孔干涉仪对入射光波前的调节，提出了具有螺旋方式排列的小孔阵列。通过对小孔径向位置的精确调节，使得从相邻小孔到观察屏中心的距离逐渐增加或减小且变化总量为入射光波长的整数倍，从而导致各自光波的相位均匀延迟或提前。我们使用平面光波照射螺旋多孔屏，在菲涅耳区的观察面上得到高阶的光学涡旋；使用涡旋光束照明具有螺旋缝的结构，在特定平面获得对入射拓扑荷的调制；使用由少量小孔组成的螺旋孔屏，实现了通过观察面上光强图样同时分辨入射涡旋光拓扑荷的大小和符号；通过调节六孔干涉仪上小孔的径向距离，在平面光波入射的情况下得到干涉仪傅里叶平面上的二阶涡旋阵列分布；通过调节具有等大小孔光子筛上小孔的径向距离，实现了对光波相位的编码，并在观察面获得特定的任意光强图样；使用显微物镜和干涉仪结合的方法，从干涉图样中提取了透射型刻划光栅表面的高度分布。本文共分为七章。
第一章对光学涡旋的研究背景及现状进行了综合型描述。主要内容包括：光学涡旋的发展；光学涡旋的特性分析，包括涡旋的数学描述、所携带光子的轨道角动量、涡旋的传播；光学涡旋的实验室产生方法，主要介绍了常用的几何光学模式转换法、计算全息法、螺旋相位板法、激光直接输出法以及多光束干涉法等主要方法；光学涡旋拓扑荷的探测方法，主要介绍了光学涡旋与平面光波干涉法、计算全息图法、干涉仪法及多孔干涉屏法等。
第二章对非对称螺旋多孔屏在高阶光学涡旋产生方面的应用进行了研究。我们使用方位角均匀排列的多孔衍射屏，根据多孔干涉屏上小孔到共轴观察屏中心处的距离和该小孔到干涉屏中心的面内径向距离之间所具有的二次方关系，调节小孔径向位置，使得相邻小孔到观察屏中心的距离均匀增加或减小且变化总量为波长的整数倍。这种调节导致从各小孔衍射的光波在到达观察屏时具有均匀延迟或提前的相位，并且相位差总量为2π的整数倍。通过这些光波的相互叠加干涉，我们在观察屏上得到具有高阶拓扑荷的光学涡旋。在理论模拟中，我们阐明了螺旋结构多孔屏的设计基础，并验证了这种螺旋机制在涡旋产生方面的可行性；通过多个结果发现，螺旋孔的具体排列方式，即设计之时所遵循的总光程调制量，决定了观察屏上涡旋拓扑荷的大小和方向；模拟结果同时表明，多孔屏上小孔的个数将所能产生的涡旋拓扑荷大小限制在小于或等于小孔个数的一半。我们发现，螺旋多孔屏能否产生规则的光学涡旋，受屏上小孔大小及多孔屏和观察屏之间距离的影响，越小的小孔越能产生较高质量的涡旋。在实验上，我们通过飞秒激光在延平的易拉罐壁上烧蚀了具有螺旋排列的多孔阵列。当平面光波入射时，我们发现在观察屏上出现我们预期的光学涡旋。实验结果和理论模拟相吻合。
第三章研究了螺旋缝屏对入射光学涡旋拓扑荷的调制作用。通过理论模拟我们发现，当涡旋光束照射具有螺旋缝结构的干涉屏后，其衍射光场中的拓扑荷将不同于入射的拓扑荷，并且拓扑荷的变化量决定于螺旋缝的具体结构；通过将螺旋缝换做沿缝的多个小孔，我们实现了通过对屏后衍射光强图样的不同来同时辨别入射光学涡旋的拓扑荷大小和符号。同时，我们分析了实际观察距离和设定观察距离的不同对衍射光场的影响。
第四章设计了具有相位编码的光子筛，并将其应用于特定光强图样的产生。首先，我们将多个等大小的小孔均匀分布在多圈围绕干涉屏中心的圆环上。圆环与屏中心具有特定的径向距离，以保证从各圆环到观察平面中心的距离之间相差波长的整数倍，从而消去该多孔屏衍射中的二次菲涅耳衍射因子。然后，我们通过Gerchberg-Saxton算法进行迭代运算，获得对应于特定光强图样的产生各个小孔处光波所需要的相位分布。最后，通过将相应的小孔沿径向偏移其所在的圆环，使其到观察屏中心的光程发生相应于其所应有相位值的变化，得到具有相位编码的光子筛。在平面波入射这种光子筛后，在观察平面得到了预先设计的光强图样。我们分析了圆环圈数和小孔个数对所称图样质量的影响。在实验中，我们自制了三个具有相位调制的光子筛来作为例子，验证了这种光子筛在图样设计中的可行性。
第五章研究了利用六孔干涉屏产生二阶涡旋阵列的方法。我们将两个具有不同尺寸的正三孔干涉屏叠合，形成对称六孔干涉屏。通过理论分析，我们预测了产生二阶涡旋阵列时，两个三孔屏尺寸之间所应满足的比例。在理论上，我们模拟了多种比例条件下，干涉屏傅里叶平面上的光场分布，验证了这种多孔屏的可行性，并且分析了小孔孔径对这种机制，特别是对光场光强分布的影响。通过具有比例参数4:5的六孔干涉仪的制造，我们从实验上在平面光照明条件下得到了二阶涡旋阵列。
第六章利用显微物镜和干涉仪的结合，提取了透射型刻划光栅表面精确的高度起伏分布。我们利用具有高数值孔径高放大倍数的显微透镜获得光栅表面在微米范围内的放大精细像，通过引入参考光得到其与放大像的干涉图样，根据相位重建理论从干涉图样中得到紧贴光栅后表面光波的相位分布，进而推算处光栅表面的高度分布。通过和利用原子力显微镜获得的光栅表面高度进行对比，验证了我们光学方法的精确度在nm量级。
第七章，我们总结了本学位论文所取得的成果和创新，并对下一步将要进行的工作进行了简单介绍。
Vortex field is a special kind of light field, where the wave fronts have helical variations.In an optical vortex, there exist some points where the intensity vanishes, and we call suchpoints vortex cores. Both the real part and the imaginary part of the field at cores are all zeros,and the phases here are undefined. Around a vortex core, the light phase has a helical variationalong with the increase of azimuthal angle. The total phase variation may be some integermultiples of, and the integer is called the topological charge of the vortex. For a vortex withthe phase increasing strictly linearly to the azimuthal angle, every photon it carries may takethe orbital angular momentum of that is determined by the topological charge. Due to thephase characters mentioned above and the potential use in dynamics, optical vortex hasattracted great attention since proposed. Now, optical vortex has been used in a variety of fieldsranging from optical micromanipulation, material science, quantum optics, opticalcommunication to biomedicine, and so on. Therefore, it is of great practical interest to studythe optical vortex.
In optics, the study of multi-beam interference has also attracted great attention. Byadjusting the positions, incident directions, amplitudes and relative phases in the interferencingbeams, we can accurately control the resultant fields. Nowadays, multipoint interferometers,which are based on the optional selection of incident wave by pinholes, have been well appliedin optical studies. The multipoint interferometers can readily offer multiple waves forinterference, and their fabrications are easy and low-cost. In application, they have been usedin the detection of topological charges, generations of both optical vortices and optical lattices,and they are now a more and more useful tool in optics.
Basing on the modulation of incident wave fronts by multipoint interferometers, weproposed a multipoint interferometer with the pinholes arranged in a helical way. Due to theadjustment of radial positions of the pinholes, the optical paths from adjacent pinholes to theorigin of the observation plane may increase or decrease evenly, and the total variation may bemultiples of the incident wavelength. This results in the specific phase differences between theinterferencing waves. We have illuminated such multipoint interferometers with plane waves,and have obtained high-order optical vortices on the observation plane in Fresnel field. Wehave illuminated the spiral-slit screen with vortex beams, and have realized the conversion oftopological charges of the incident vortex. We have realized the simultaneous distinguishes ofboth the value and the sign of the incident topological charges, by using a spiral pinholeinterferometer with small pinhole numbers. We have obtained second-order vortex arrays by illuminating six-pinhole interferometers of variable radial distances. The phase-encoded photonsieves have been proposed, and we have obtained designed intensity patterns after the sieves.We have also obtained the height variation of two transmissive ruled grating surfaces, using thecombination of a microscope objective and a interferometer. The whole paper is detailed inseven chapters.
Chapter1: Introduction. We describe the background of this paper, and give the generaldescriptions of optical vortices. At the beginning, we show the development of optical vortex.Second, we study the characters of optical vortex, including its mathematical description,orbital angular momentum of photon and its propagation. Third, we review the commonly usedexperimental generation of optical vortex, including mode conversion of laser,computer-generated hologram, spiral phase plate, direct input of laser and multi-beaminterference. At the last, we discuss the methods in detecting of topological charge, includinginterference of vortex and plane wave, holograms, interferometries and multipointinterferometers.
Chapter2: In this chapter, we study the application of spiral multipoint interferometers ingenerating high-order optical vortex. Pinholes are arranged with even azimuthal angleincrement on the multipoint interferometer. According to the quadratic relationship between thedistances from a pinhole to the observation plane origin and the distance from this pinhole tothe interferometer origin, we adjust the pinhole position in radial directions until the opticalpaths from neighboring pinholes to the observation plane origin have constant increment. Thetotal path variation determines the total phase difference in the multiple transmitting waves,which may be integer multiples of. We obtain high-order optical vortices in the interferencefield of the waves. In numerical simulation, we demonstrate the fabrication process of theinterferometer and verify the feasibility of this mechanism. We discover that the topologicalcharge of the generated vortex is determined by the total path variation, e.g., the structure ofthe pinhole arrangement. The simulations show that the possible topological charge of thevortex is confined to be no more than half the pinhole number. We also show that the feasibilityof the interferometer is influenced by the pinhole sizes, and that smaller pinholes are better fora good vortex. In experiment, we fabricate such spiral multipoint interferometers by ablatingpinholes on flattened Coca-Cola cans. The experimental results coincide with the simulationswell.
Chapter3: In this chapter, we study the conversion of topological charge with the use ofspiral-slit screens. When an optical vortex transmits from a designed spiral-slit, its topologicalcharge may be altered. The variation is determined by the structure of the slit. We also replacethe slit by small number of isolated pinholes, and show that both the value and the sign of theincident topological charge could be distinguished simultaneously by reading the differentintensity patterns on the observation plane.
Chapter4: We propose the phase-encoded photon sieves and use them to generate designed intensity patterns. First, we arrange some pinholes of equal size evenly on some ringscentered at the origin. The optical paths from the rings to the observation plane origin differ bymultiples of incident wavelength, and this design eliminates the quadratic phase aberration ofthe sieve in Fresnel diffraction. Then, using the iteration in the Gerchberg-Saxton algorithm,we obtain the required phase value at each pinhole. By deviating the pinhole position fromcorresponding ring, we encode such phase values on the sieve, and obtain the phase-encodedphoton sieve. When such sieves are illuminated by plane wave, the designed intensity patternsare obtained on the observation plane. We have also discussed the influences of pinholenumbers and rings on the quality of the generated patterns. We fabricate three phase-encodedphoton sieves in experiment, and verify their feasibilities.
Chapter5: In this chapter, we generate second-order vortex arrays with six-pinholeinterferometers. The six-pinhole interferometer is fabricated by combining two differentregular three-pinhole interferometers together. In the simulations, we predict the requirement ofsize ratios of the two three-pinhole interferometers to generate second-order vortex arrays. Insimulation, the feasibility of the interferometer is verified, and the influence of the pinholesizes is discussed. By using the self-made six-pinhole interferometer with ratio4:5inexperiment, we obtain second-order vortex arrays under plane wave illumination.
Chapter6: In this chapter, we obtain the height variations of two transmissive ruledgrating surfaces. By using the combination of a Mach-Zende interferometer and an objectivemicroscope of high numerical aperture and high magnification, we obtain the magnified imageof grating surface in small area and distract the phase distribution of the light from theinterferogram. The height variation is deduced from the phase values. We compare the resultswith the ones obtained by a Atomic Force Microscope, and discover that the optical methodrealizes a resolution of nano-scale.
Charpter7: In this chapter, we summarize the results and the innovations of this paper,and describe the future work.
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