光学涡旋的衍射特性、生成及检测方法的研究
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摘要
光学涡旋是一种具有螺旋相位结构的光场,是现代奇点光学的一个重要研究分支。光学涡旋的动力学特性、轨道角动量特性和独特的拓扑结构在光学微操纵、散斑场的研究以及量子通信领域都具有重要的研究价值,已经受到越来越广泛的关注。
一方面,光学涡旋具有轨道角动量,可以传递给俘获粒子,使粒子产生旋转等比较独特的动力学效应。在相同的激光参数下,采用光学涡旋的光镊系统轴向束缚力是聚焦高斯光束的几倍。利用光学涡旋可以实现对粒子的二维或三维的实时动态操纵,利用阵列光学涡旋可以实现对微小颗粒的驱动,组装微流体系统的介观泵,和制作纳米合成材料与器件等。
另一方面,光学涡旋的螺旋相位结构使其具有一系列特殊的物理性质,如强度呈环状分布、具有很小的中心暗斑尺寸、无加热效应等,可以实现较低激光功率条件下对生物细胞的俘获与操纵,这对于减少被俘获细胞受破坏的危险性是非常重要的。近年来已经在激光光学、微粒波导、生物医学、原子光学和分子光学中得到广泛的研究和应用。如利用光学涡旋中空的光束结构作为“势管”实现了对超冷原子的束缚及中性原子的俘获等。
此外,光学涡旋的拓扑结构还是天文学、超流体、散斑场甚至拓扑数学的一个重要研究内容。光子的轨道角动量特性和量子纠缠效应,在量子计算、光学通信、光电子学以及远程传感等领域的潜在应用也正在受到越来越多的关注。
光学涡旋的研究与应用虽然只有数十年的时间,但已经显示出极具潜力的应用前景。随着研究的深入,光学涡旋的研究内容及相关应用技术开发还会更加丰富。上述研究工作都需要对光学涡旋的光场分布和角动量特性有较深刻的理解,在光学涡旋的衍射特性及其动力学行为,光学涡旋及阵列的产生方法,以及对光学涡旋性质的检测技术方面还需要进行更深入的理论分析和实验研究。
本文通过对光学涡旋研究背景的系统总结,深入考察了光学涡旋的研究进展情况,包括光学涡旋的自旋与轨道角动量特性,强度梯度力与相位梯度力等动力学行为和光子轨道角动量态的量子纠缠,并对现有的生成光学涡旋的方法进行了总结,包括模式变换法、计算全息法、相位板法和利用液晶空间光调制器等几种常见的方法,为我们在实验中获得和研究光学涡旋的性质奠定了基础。我们还分析了干涉法和螺旋相位滤波法等产生光学涡旋阵列的方法。
本论文在此研究基础之上,讨论了光学涡旋的聚焦环带结构和在线性介质中的传播特性,提出了利用分数Talbot效应制作阵列照明器产生光学涡旋阵列的产生方法,并对光学涡旋轨道角动量和波前检测技术方面进行了研究,取得了一些创新性的研究成果,主要内容和结果如下:
1.利用流体力学的研究方法分析了光学涡旋在介质中的传播,发现局域性的tanh光学涡旋在高斯背景光束中的旋转角速度与核间距的平方成反比,要远大于Gouy相移,而全局性的r型光学涡旋具有不同的传播特性,旋转角度与涡旋间的距离无关。我们还进一步的讨论了阵列光学涡旋的传播特性,分析了其中局域光学涡旋的演变和传播特性,发现在距离分数Talbot面的一个离焦面上存在相衬效应,在一定的衍射距离时具有最佳的聚焦强度,这种相衬现象在实现光学微操纵时具有很重要的意义。
2.首次提出基于分数Talbot效应的倒格矢理论生成阵列光学涡旋的方法。我们利用倒格矢理论研究了分数Talbot效应,提出利用分数Talbot效应来制作称为“光学涡旋Talbot阵列照明器”(OVTAI)的衍射光学元件,通过对入射光波的调制实现波分复用,从而产生高度聚焦的光学涡旋阵列。该方法因为不需要复杂的透镜系统,光路设计简单,实用性较高。我们详细的讨论了设计正交长方、有心立方和六角三种阵列结构的OVTAI的基本原理和设计参数,将设计的OVTAI显示到纯相位液晶空间光调制器上,实验验证了该方法的可行性。
3.系统分析了干涉法测量光学涡旋轨道角动量的方法,提出利用球面波与光学涡旋干涉测量光学涡旋轨道角动量的方法,发现利用该方法可以测量一定范围内的光学涡旋拓扑荷的总量,并通过模拟验证了该方法的可行性。同时,分析了光学涡旋之间的干涉,研究了共轭光学涡旋干涉条纹的形成机制和测量原理。
4.首次提出利用多针孔干涉仪定量测量光学涡旋轨道角动量的算法。我们发现透过多针孔板的远场衍射图样包含透过多针孔的复振幅信息。通过适当的算法可以从远场衍射图样的逆傅里叶变换中提取这些信息。根据提取出的相位值,可以进一步的确定光学涡旋轨道角动量。我们把这种方法叫做多针孔干涉仪。我们对该方法的基本原理进行了理论推导,通过计算机模拟和实验验证了该方法的可行性,简单讨论了该方法存在的系统误差和解决方法。
5.首次提出利用行扫描多针孔干涉仪实现光学涡旋波前的三维重建。对波前的三维重建,基于对波前的精确测量。在多针孔干涉仪的理论基础上,我们认识到,透过多针孔的远场衍射图样包含了透过这些针孔的复振幅信息,通过适当的方法可以将这些信息准确的提取出来。如果我们改变多针孔的位置对整个波面进行扫描,就可以得到整个波面的抽样复振幅信息。如何确定多针孔板的设计原则和高效的实现扫描是问题的关键。我们在理论分析的基础上提出了行扫描多针孔干涉法。该方法可以使理论分析更加简明,波前测量更加精密,实验结果更加直观。我们利用该方法成功的对光学涡旋的波前实现了三维重建。
The special helical phase structure of an optical vortex leads to an intriguing study in modern singular optics. Due to the dynamics properties, unique topological structure, and orbital angular momentum carrying of photos, opitcal vorties have get more and more attentions in the study of optical micromanipulation, speckle field and quantum communications.
Firstly, opitcal vortex has orbital anglure momentum that can be transered to the trapped particles and rotate them. Optical vortex trap has axial gradient force times of the focus Gauss beam under same laser parameters. When focused strongly enough, such helical modes form toroidal optical traps known as optical vortices, whose properties present novel opportunities for scientific research and technological applications. For example, optical vortices can dynamically trap and modulate mesoscopic particles in 2D and 3D, and optical vortex array trapping systems have shown a promising ability to assemble colloidal particles into mesoscopic pumps for microfluidic systems, and offered new applications in nanotechnology, and manufacturing.
Secondly, the optical vortex with spiral phase possesses series of unique properties, such as ring distribution of the intensity, small size of the dark spot, no heating effect, and so on. It can trap and manipulate biologic cells in lower power of laser for decreasing the destructive fatalness. Recently, it has been widely used in the area such as laser optics, micro particle waveguiding, biomedicine, atom optics and molecule optics. The manipulation of the Doppler cooling atoms by the hollow intensity configurations of optical vortex potential trap was accomplished.
Thirdly, the topological structure of the optical vortices and phase singularities is an important research area in astronomy, superfluid, spekle field and topological arithmetics. The orbital angular momentum of the photos and its quantum entanglement brings widespread applications ranging from carrying more information in quantum information processing, quantum calculation, to optical infromation processing, optoelectronics, and cryptography, and so on.
The studies on optical vortices become an intriguing research area which has tremendous potencial application, though the history of the studies is only several decades. Following the further research of the optical vortex, the content and the technology would be more meaningful and rewarding. The further studies need the profound understanding and acknowledgement of the distributions of the optical vortex and the angular momentum properties. The diffractive properties, generation, and the methods for examining the properties of optical vortices need developing theoretically and experimentally, too.
We systematically analysized the history and development of the optical vortices in the dissertation, including the fundamental mathematically description, the properties of spin and orbital angular momentum of the photos, the dynamics properties of intensity gradient force and phase gradient force, and the quantum entanglement of the photo carrying orbital angular momentum. Further, we summarized the different methods of generation of optical vortex, such as using mode convertion, by computer generation holography, spiral phase plate and liquid crystal spatial light modulator. The studies above found the experimental and theoretical base for our further research in these areas. Furthermore, we introduced the methods of multi-beams interference and helical phase spatial filtering for generation of optical vortex array.
Based on the studies above, we discussed the focus ring structure and the diffractive properties of the optical vortices in linear meadium, presented the method for generating optical vortex array based on fractional Talbot effection, and developped the examing technology for measuring the orbital angular momentum and three-dimensional reconstuction of the wavefront of an optical vortex. The main innovative researches and conclusion are demonstrated as follows:
1. We analysed the propagation of the optical vortex solitions in the linear medium based on two of the principal equations in hydromechanics: the Bernoulli and the continuity equations.We found contrasting differences between the trajectories for r vortices that have globally distributed core functions and tanh vortices that have localized core functions when the beam propagates through a linear medium. In particular, we discussed the propogation of the optical vortex array. We found the localized optical vortices enlarging their own field, overlapping with the adjacent vortices, and forming new enlarged local area which can be regarded as a new optical vortex. At last, they degenerated to a new array of optical vortex. Moreover, in comparison with the reconstructed vortex array at the fractional Talbot distance, we found the vortex cells focused into a sharp ringed structure with higher contrast at a defocusing Talbot plane. The phase contrast phenomenon can be useful in optical micromanipulations.
2. We presented the method for generating optical vortex array based on the reciprocal vector theory for the fractional Talbot effection. We studied the reciprocal vector theory detailedly, and introdued the method for designing phase-only diffractive element named optical vortex Talbot array illumination (OVTAI) An array of optical vortex with high compress ratio is generated by the wave division multiplex. As our method need not use splitters and reflectors, the optical system is simple and with high practicability. We discussed the fundamental principle and design parameters analytically for OVTAI of rectangular array, centered-square array, and hexagonal array. As an example, an OVTAI for generating a hexagonal array of optical vortices is designed and demonstrated through displaying the OVTAI on a programmable liquid crystal spatial light modulator. The vortex array generated by the OVTAI are observed and analyzed.
3. We studied the methods of interferometer for measuring the orbital angular momentum (OAM) detailedly, and introduced the method by a spherical reference wave. We found the total topological charge of the optical vortex in an area can be defined by the recognization of the closed interference pattern or the number of the spiral stripes. Digital simulations prove the feasibility of the method. Furthermore, we used another reference optical vortex wave and studied the procedure forming the interference pattern, and found that it also defined the location and the topological charge of the phase dislocation.
4. We presented the arithmetics for retrieval the complex amplitude passing through a multi-pinhole interferometer (MPI), and demonstrated the method for measurement of the OAM of an optical vortex in a background beam. We found the far-field diffraction pattern involves imformation sampled by the multi-pinhole (MP) plate, which can be extracted by inverse Fourier transform of the far-field pattern with a properly arithmetics. We can further use the extracted phase to determine the OAM of the illuminated optical vortex. We have deduced the principle of the method analytically, and demonstrated by digital simulations and experimental result. The error of the systerm was also discussed.
5. We introduced a method for three dimensional reconstruction of the wavefront of optical vortex by a line scanning multi-pinhole interferometer (LS-MPI). The reconstruction of the wavefront requires the precise measurement of the phase passing through the MP plate. The method we presented can be resolved by the principle of MPI. If scan the whole wavefront by such a MP plate, we can extracted the sampled complex amplitude of the whole wavefront and further reconstruct the wavefront. We deduced the principle of the method, and found it can be descibed simpler, the inverse Fourier transform pattern can be distinguished more clearly, the sampled data is more precise, and the unwrap operation is easier. The digital simulations demonstrate the feasibility of the mothod.
一方面,光学涡旋具有轨道角动量,可以传递给俘获粒子,使粒子产生旋转等比较独特的动力学效应。在相同的激光参数下,采用光学涡旋的光镊系统轴向束缚力是聚焦高斯光束的几倍。利用光学涡旋可以实现对粒子的二维或三维的实时动态操纵,利用阵列光学涡旋可以实现对微小颗粒的驱动,组装微流体系统的介观泵,和制作纳米合成材料与器件等。
另一方面,光学涡旋的螺旋相位结构使其具有一系列特殊的物理性质,如强度呈环状分布、具有很小的中心暗斑尺寸、无加热效应等,可以实现较低激光功率条件下对生物细胞的俘获与操纵,这对于减少被俘获细胞受破坏的危险性是非常重要的。近年来已经在激光光学、微粒波导、生物医学、原子光学和分子光学中得到广泛的研究和应用。如利用光学涡旋中空的光束结构作为“势管”实现了对超冷原子的束缚及中性原子的俘获等。
此外,光学涡旋的拓扑结构还是天文学、超流体、散斑场甚至拓扑数学的一个重要研究内容。光子的轨道角动量特性和量子纠缠效应,在量子计算、光学通信、光电子学以及远程传感等领域的潜在应用也正在受到越来越多的关注。
光学涡旋的研究与应用虽然只有数十年的时间,但已经显示出极具潜力的应用前景。随着研究的深入,光学涡旋的研究内容及相关应用技术开发还会更加丰富。上述研究工作都需要对光学涡旋的光场分布和角动量特性有较深刻的理解,在光学涡旋的衍射特性及其动力学行为,光学涡旋及阵列的产生方法,以及对光学涡旋性质的检测技术方面还需要进行更深入的理论分析和实验研究。
本文通过对光学涡旋研究背景的系统总结,深入考察了光学涡旋的研究进展情况,包括光学涡旋的自旋与轨道角动量特性,强度梯度力与相位梯度力等动力学行为和光子轨道角动量态的量子纠缠,并对现有的生成光学涡旋的方法进行了总结,包括模式变换法、计算全息法、相位板法和利用液晶空间光调制器等几种常见的方法,为我们在实验中获得和研究光学涡旋的性质奠定了基础。我们还分析了干涉法和螺旋相位滤波法等产生光学涡旋阵列的方法。
本论文在此研究基础之上,讨论了光学涡旋的聚焦环带结构和在线性介质中的传播特性,提出了利用分数Talbot效应制作阵列照明器产生光学涡旋阵列的产生方法,并对光学涡旋轨道角动量和波前检测技术方面进行了研究,取得了一些创新性的研究成果,主要内容和结果如下:
1.利用流体力学的研究方法分析了光学涡旋在介质中的传播,发现局域性的tanh光学涡旋在高斯背景光束中的旋转角速度与核间距的平方成反比,要远大于Gouy相移,而全局性的r型光学涡旋具有不同的传播特性,旋转角度与涡旋间的距离无关。我们还进一步的讨论了阵列光学涡旋的传播特性,分析了其中局域光学涡旋的演变和传播特性,发现在距离分数Talbot面的一个离焦面上存在相衬效应,在一定的衍射距离时具有最佳的聚焦强度,这种相衬现象在实现光学微操纵时具有很重要的意义。
2.首次提出基于分数Talbot效应的倒格矢理论生成阵列光学涡旋的方法。我们利用倒格矢理论研究了分数Talbot效应,提出利用分数Talbot效应来制作称为“光学涡旋Talbot阵列照明器”(OVTAI)的衍射光学元件,通过对入射光波的调制实现波分复用,从而产生高度聚焦的光学涡旋阵列。该方法因为不需要复杂的透镜系统,光路设计简单,实用性较高。我们详细的讨论了设计正交长方、有心立方和六角三种阵列结构的OVTAI的基本原理和设计参数,将设计的OVTAI显示到纯相位液晶空间光调制器上,实验验证了该方法的可行性。
3.系统分析了干涉法测量光学涡旋轨道角动量的方法,提出利用球面波与光学涡旋干涉测量光学涡旋轨道角动量的方法,发现利用该方法可以测量一定范围内的光学涡旋拓扑荷的总量,并通过模拟验证了该方法的可行性。同时,分析了光学涡旋之间的干涉,研究了共轭光学涡旋干涉条纹的形成机制和测量原理。
4.首次提出利用多针孔干涉仪定量测量光学涡旋轨道角动量的算法。我们发现透过多针孔板的远场衍射图样包含透过多针孔的复振幅信息。通过适当的算法可以从远场衍射图样的逆傅里叶变换中提取这些信息。根据提取出的相位值,可以进一步的确定光学涡旋轨道角动量。我们把这种方法叫做多针孔干涉仪。我们对该方法的基本原理进行了理论推导,通过计算机模拟和实验验证了该方法的可行性,简单讨论了该方法存在的系统误差和解决方法。
5.首次提出利用行扫描多针孔干涉仪实现光学涡旋波前的三维重建。对波前的三维重建,基于对波前的精确测量。在多针孔干涉仪的理论基础上,我们认识到,透过多针孔的远场衍射图样包含了透过这些针孔的复振幅信息,通过适当的方法可以将这些信息准确的提取出来。如果我们改变多针孔的位置对整个波面进行扫描,就可以得到整个波面的抽样复振幅信息。如何确定多针孔板的设计原则和高效的实现扫描是问题的关键。我们在理论分析的基础上提出了行扫描多针孔干涉法。该方法可以使理论分析更加简明,波前测量更加精密,实验结果更加直观。我们利用该方法成功的对光学涡旋的波前实现了三维重建。
The special helical phase structure of an optical vortex leads to an intriguing study in modern singular optics. Due to the dynamics properties, unique topological structure, and orbital angular momentum carrying of photos, opitcal vorties have get more and more attentions in the study of optical micromanipulation, speckle field and quantum communications.
Firstly, opitcal vortex has orbital anglure momentum that can be transered to the trapped particles and rotate them. Optical vortex trap has axial gradient force times of the focus Gauss beam under same laser parameters. When focused strongly enough, such helical modes form toroidal optical traps known as optical vortices, whose properties present novel opportunities for scientific research and technological applications. For example, optical vortices can dynamically trap and modulate mesoscopic particles in 2D and 3D, and optical vortex array trapping systems have shown a promising ability to assemble colloidal particles into mesoscopic pumps for microfluidic systems, and offered new applications in nanotechnology, and manufacturing.
Secondly, the optical vortex with spiral phase possesses series of unique properties, such as ring distribution of the intensity, small size of the dark spot, no heating effect, and so on. It can trap and manipulate biologic cells in lower power of laser for decreasing the destructive fatalness. Recently, it has been widely used in the area such as laser optics, micro particle waveguiding, biomedicine, atom optics and molecule optics. The manipulation of the Doppler cooling atoms by the hollow intensity configurations of optical vortex potential trap was accomplished.
Thirdly, the topological structure of the optical vortices and phase singularities is an important research area in astronomy, superfluid, spekle field and topological arithmetics. The orbital angular momentum of the photos and its quantum entanglement brings widespread applications ranging from carrying more information in quantum information processing, quantum calculation, to optical infromation processing, optoelectronics, and cryptography, and so on.
The studies on optical vortices become an intriguing research area which has tremendous potencial application, though the history of the studies is only several decades. Following the further research of the optical vortex, the content and the technology would be more meaningful and rewarding. The further studies need the profound understanding and acknowledgement of the distributions of the optical vortex and the angular momentum properties. The diffractive properties, generation, and the methods for examining the properties of optical vortices need developing theoretically and experimentally, too.
We systematically analysized the history and development of the optical vortices in the dissertation, including the fundamental mathematically description, the properties of spin and orbital angular momentum of the photos, the dynamics properties of intensity gradient force and phase gradient force, and the quantum entanglement of the photo carrying orbital angular momentum. Further, we summarized the different methods of generation of optical vortex, such as using mode convertion, by computer generation holography, spiral phase plate and liquid crystal spatial light modulator. The studies above found the experimental and theoretical base for our further research in these areas. Furthermore, we introduced the methods of multi-beams interference and helical phase spatial filtering for generation of optical vortex array.
Based on the studies above, we discussed the focus ring structure and the diffractive properties of the optical vortices in linear meadium, presented the method for generating optical vortex array based on fractional Talbot effection, and developped the examing technology for measuring the orbital angular momentum and three-dimensional reconstuction of the wavefront of an optical vortex. The main innovative researches and conclusion are demonstrated as follows:
1. We analysed the propagation of the optical vortex solitions in the linear medium based on two of the principal equations in hydromechanics: the Bernoulli and the continuity equations.We found contrasting differences between the trajectories for r vortices that have globally distributed core functions and tanh vortices that have localized core functions when the beam propagates through a linear medium. In particular, we discussed the propogation of the optical vortex array. We found the localized optical vortices enlarging their own field, overlapping with the adjacent vortices, and forming new enlarged local area which can be regarded as a new optical vortex. At last, they degenerated to a new array of optical vortex. Moreover, in comparison with the reconstructed vortex array at the fractional Talbot distance, we found the vortex cells focused into a sharp ringed structure with higher contrast at a defocusing Talbot plane. The phase contrast phenomenon can be useful in optical micromanipulations.
2. We presented the method for generating optical vortex array based on the reciprocal vector theory for the fractional Talbot effection. We studied the reciprocal vector theory detailedly, and introdued the method for designing phase-only diffractive element named optical vortex Talbot array illumination (OVTAI) An array of optical vortex with high compress ratio is generated by the wave division multiplex. As our method need not use splitters and reflectors, the optical system is simple and with high practicability. We discussed the fundamental principle and design parameters analytically for OVTAI of rectangular array, centered-square array, and hexagonal array. As an example, an OVTAI for generating a hexagonal array of optical vortices is designed and demonstrated through displaying the OVTAI on a programmable liquid crystal spatial light modulator. The vortex array generated by the OVTAI are observed and analyzed.
3. We studied the methods of interferometer for measuring the orbital angular momentum (OAM) detailedly, and introduced the method by a spherical reference wave. We found the total topological charge of the optical vortex in an area can be defined by the recognization of the closed interference pattern or the number of the spiral stripes. Digital simulations prove the feasibility of the method. Furthermore, we used another reference optical vortex wave and studied the procedure forming the interference pattern, and found that it also defined the location and the topological charge of the phase dislocation.
4. We presented the arithmetics for retrieval the complex amplitude passing through a multi-pinhole interferometer (MPI), and demonstrated the method for measurement of the OAM of an optical vortex in a background beam. We found the far-field diffraction pattern involves imformation sampled by the multi-pinhole (MP) plate, which can be extracted by inverse Fourier transform of the far-field pattern with a properly arithmetics. We can further use the extracted phase to determine the OAM of the illuminated optical vortex. We have deduced the principle of the method analytically, and demonstrated by digital simulations and experimental result. The error of the systerm was also discussed.
5. We introduced a method for three dimensional reconstruction of the wavefront of optical vortex by a line scanning multi-pinhole interferometer (LS-MPI). The reconstruction of the wavefront requires the precise measurement of the phase passing through the MP plate. The method we presented can be resolved by the principle of MPI. If scan the whole wavefront by such a MP plate, we can extracted the sampled complex amplitude of the whole wavefront and further reconstruct the wavefront. We deduced the principle of the method, and found it can be descibed simpler, the inverse Fourier transform pattern can be distinguished more clearly, the sampled data is more precise, and the unwrap operation is easier. The digital simulations demonstrate the feasibility of the mothod.
引文
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