高斯相关随机表面光散射散斑场的相位奇异
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摘要
随机散斑场是相干光波经过随机介质或随机表面散射后而形成的一种复杂的随机光场。理论和实验证明散斑场中散斑颗粒和光强零点的个数相等,所以在散斑场中有大量的相位奇异。光强零值点处的相位都不能确定,光强零值点称为相位奇异点,相位奇异点也叫光学涡旋,散斑涡旋的类型在光学涡旋中也最为复杂和最具代表性,散斑相位涡旋的研究在光学奇异的研究中具有引领作用。其普遍存在于众多物理领域之中,诸如氢原子的角动量本证态、II型超导体的迈斯纳态、超流体的涡旋状态、波色—爱因斯坦凝聚和晶体学等领域,并在光学微控、量子纠缠、信息传输等众多等领域也得到了重要而广泛的应用。近几年来,由于相位奇异现象具有潜在的应用价值,使得人们对相位奇异的研究兴趣迅速增加。然而,现有文献都仅限于散斑光场实部和虚部零值线相交而形成的相位涡旋。众所周知,由于散斑场的复杂性,其实部零值线和虚部零值线还可以相切、重合。研究随机散斑场相位涡旋的性质不仅是散斑相位涡旋中的新课题,而且对于物理学其它领域的光学涡旋现象的研究具有先导意义,并对相关的光学和物理前沿领域中奇异现象的研究有重要应用前景。
本学位论文结合了高斯随机表面散射形成的散斑场及其相位奇异现象的前沿领域最新成果的理论和方法,在连续相干激光光波照明,对方形孔径在夫朗和费面上形成的高斯随机散斑场及其实部和虚部零值线相切和重合情况下形成的相位奇异特性进行了详细研究;对方形环孔径和圆环孔径在夫朗和费面上形成的散斑场及其由实部和虚部零值线复杂相切相交情况下形成的相位奇异特性进行了研究;研究了多孔径径随机散射屏在远场平面上形成的局部区域的散斑场中光强亮斑及其相位奇异点的规则分布;研究了四孔径衍射屏在菲涅尔深区形成光场及其相位奇异等进行了一系列创造性的研究工作;最后,对拉盖尔-高斯光束通过多圆孔径形成的干涉光场的相位和零值线的分布,讨论了入射光束的轨道角动量和多条零值线相交点形成的相位奇异点拓扑荷的关系。本文的结果可以帮助我们更好地了解物理学各领域的相位奇异点周围的相位分布,在光开关、光学数据存储、微观粒子的操纵、保护眼睛的光限幅、散斑涡旋现象在地质冰层探测、医学检查和宇宙探索等领域应用前景等领域都有应用。概括起来,本学位论文取得了以下主要成果:
1.通过对二维高斯相关随机表面在夫朗和费面上产生的随机散斑场及其相位的计算模拟,得到散斑场的实部零值线和虚部零值线,并得出散斑场的相位等值线的分布。通过对散斑实虚部零值线的分析,发现在某一平面上,除了实部零值线与虚部零值线的传统的相交之外,还有相切和重合的情况。研究了零值线相切和重合附近的相位等值线特征,因为零值线切点和重合处光场振幅也等于零,因此,在这些位置也可以形成相位奇异。研究了零值线相切和重合处等值线的闭合特征及其引起的相位奇异点附近独特的相位跃变特征;发现其周围的相位分布与传统的实部零值线与虚部零值线相交形成的奇点周围相位的螺旋变化不同,呈现出对称性和不连续性的特征。随着光波的传播,在不同的观察面上,散斑场复振幅的实部零值线和虚部零值线的相对位置经历了由相切到重合再到相交的演变过程,相位奇异现象也随之发生变化。并且验证了这零值线相切和重合处的相位奇异现象并不是表面粗糙度所造成。最后分析了它们形成的机理。
本文也为不同应用要求下的散射场仿真提供了很好的手段,为准确理解和分析相位涡旋现象形成的原因提供了实验观察的依据,并对散斑相位涡旋的研究有重要意义。
2.在实验过程中,利用参考光和随机散射光相干涉,提取了方形环孔的散斑场复振幅的实部和虚部,同时在理论上通过对方形环孔和圆环孔在远场平面上形成的散斑场及其相位的数值计算得到散斑场相位的分布和零值线分布图,发现在某一平面上实部和虚部零值线的位置关系出现了复杂相切相交的情况,即两条实部零值线(或虚部零值线)本身相切,同时又会与虚部零值线(或实部零值线)与之相交或相切的情况,复杂相切相交点光场振幅为零,因此也形成相位奇异,并且其周围相位分布与传统的实部零值线与虚部零值线相交形成的相位奇异点周围相位的螺旋变化不同,呈现出对称性和不连续性的特征。方形环孔和圆环孔形成的散斑场的散斑颗粒分布与传统方孔的不同:受散射孔径的调制分别排成水平与竖直的条纹状轮廓和类似于圆形的轮廓,有趣的是:在散斑场的局部光强图中出现了很多类似于圆形的黑暗区域,我们称其为“光强暗核”,其中心对应着一个相位分布较均匀的涡旋。
随机散斑场中特殊相位涡旋的性质不仅对散斑相位涡旋的研究有重要意义,对相关的光学和物理前沿领域中奇异现象的研究也有重要应用前景,而且对于光学涡旋现象的研究具有先导意义。
3.通过对多孔径随机散射屏在夫琅和费面上形成的散斑场及其相位的计算模拟,发现在某一观察面上,在双圆孔形成的散斑场的相位分布图中,正负相位涡旋分层排列,相位分布多为条带状区域,并在某些位置有位错现象;在三圆孔和四圆孔形成的局部散斑场强度图中,有很多呈类圆形的亮斑,相邻的两个亮斑之间有一个相位涡旋,在相应的相位分布图中,出现了正负相位涡旋列,相位区域的形状多为不规则的四边形或六边形,调节散射屏前孔径上圆孔的相对位置,亮斑或相位涡旋的相对位置随之改变。
这对研究相位涡旋的本质结构和散斑场的新规律和新的奇异现象具有重要的意义,并且对多圆孔干涉仪有重要应用。本文也为不同应用要求下的散射场仿真提供了很好的手段,为准确理解和分析相位涡旋现象形成的原因提供了实验观察的依据。
4.利用基尔霍夫衍射理论计算了四圆孔径衍射屏在菲涅尔深区形成的光场强度、零值线和相位的分布,发现衍射光场亮斑关于中心呈对称分布,在距离衍射屏较近的观察面上,光强值为零点组成光强零值线段,该线段上光强等值线的离心率都接近或等于1,其两侧的光强值变化非常剧烈。复振幅的实部和虚部零值线多为封闭的曲线,零值线交点的个数为偶数,并且正负奇异点的个数相等。特殊相位奇异点周围的相位不仅呈对称分布,而且该点的拓扑荷出现了奇异现象。随着光波的传播,在不同的观察面上,光强零值线段逐渐变短最终趋于一点。
这对研究相位奇异点的本质结构和新的奇异现象具有重要意义,并且对多圆孔干涉仪的设计有重要作用。本文也为准确理解和分析相位奇异点周围的相位分布提供了实验观察的依据。
5.通过对拉盖尔-高斯光束经多圆孔径衍射屏在远场平面上形成的干涉光场的相位和零值线的计算模拟,发现:当入射光束的轨道角动量量子数为零时,实部零值线与虚部零值线在干涉光场中心点不相交,因而该点上不能形成相位涡旋;当入射光束的轨道角动量量子数为+1和-1时,实部零值线与虚部零值线在干涉光场中心垂直并相交,干涉光场相应位置处的相位涡旋的符号相反;当入射光束的轨道角动量量子数为±2和±3时,有四条零值线相交于干涉光场的中心点上,并且实部零值线和虚部零值线交替分布,该交点处形成的相位涡旋的拓扑荷的值恰好与拉盖尔-高斯光束的轨道角动量量子数相等。
这对利用多孔干涉仪,测量新天体所发光的轨道角动量有最重要的应用,并可用来测具有轨道角动量的涡旋光束。
本论文共分七章,第一章为绪论,简要叙述了相位奇异的发展历史、相位奇异的国内外研究现状、标量波场中相位奇异的基本概念、光场中标量相位奇异的产生方法、相位奇异的应用等内容。第二章通过计算模拟,研究了散斑场复振幅的实部和虚部的零值线相切、相切重合和交叉重合等情况下的相位奇异及其性质,验证了这两类相位奇异现象并不是表面粗糙度所造成,最后计算了它们的演变过程,并分析了它们形成的机理。第三章从理论和实验上详细研究了方形环孔和圆环孔形成的散斑场及其零值线复杂相切相交情况下的相位奇异性,并分析了它们形成的机理,并分析了“光强暗核”的形成、散斑颗粒规则排列的原因。第四章从理论上详细研究了多孔径随机散射屏在夫琅和费面上形成的散斑场中光强及其相位涡旋的分布特性。第五章利用基尔霍夫衍射理论详细研究了四圆孔径衍射屏在菲涅尔深区形成的干涉光场的强度、相位奇异点和零值线的分布特性及演化过程,并计算了光强零值线上光强等值线的离心率的值和拓扑荷的值。第六章从理论上详细研究了拉盖尔-高斯光束通过多圆孔径衍射屏在远场平面上形成的干涉光场的光强、相位和零值线的分布特性。第七章对论文做了总结和展望。
When the coherent light waves are scattered from the random surfaces or the random media, speckles are formed in the diffraction regions. Measurements and computer simulations have shown that the speckle grains and phase singularities have the same density in the random fields, so there are as many phase singularities as speckle grains in speckle field. The zeros of light intensity are the phase singularities at which the phase of is undefined. Around each singularity the current circulates and then the zeros are also called optical vortices. It exists in various linear and nonlinear physical systems, such as the angular momentum eigenstates of the hydrogen atom, the Meissner state of type-II superconductors, vortex states of superfluids, Bose-Einstein condensates, and optical vortex solitons. Phase singularities are very important and widely used in the optical microcontroller, quantum entanglement, information transmission. Phase singularities in optical fields owing to potential applications have driven a surge of interest in recent years. However, the existing literatures on the zero-contour of the real and imaginary parts of speckle field are intersection situation. As we all know, in fact, due to the complexity of the speckle field, the zero-contour of the real and imaginary parts can be in tangential or superposition situation. Study the characters of phase singularities in random speckle field have leading significance, not only a new task for speckle phase singularities but also for the phenomenon of optical vortex in other areas of physics, and have important applications in related frontier areas of optics and physics.
This thesis combining methodologies and the theories in the achievements in such frontier areas of physics as the speckle fields generated by the Gaussian correlation random scattering screen and their phase singularities properties under the illumination of continuous lasers. The phase singularities of speckle fields produced by the scattering from square aperture Gaussian correlation random surfaces in the Fraunhofer plane, the zero-contour of the real and imaginary parts of complex amplitude of speckle fields are tangent and coincidence, at the tangential points and the superposition-lines can also form phase singularities, the speckle fields produced by the square loop aperture and circular ring aperture and their phase singularities, the intensity distribution and phase singularities of speckle fields generated by multi-aperture random scattering screens and the intensity distribution and topological charge singularity of special phase singularities generated by four-pinhole aperture diffraction screens in deep Fresnel diffraction region.
The results presented in this thesis offer us a better understanding of phase singularities which may result in applications in optical switching, optical data storage, manipulation of micro-particles and optical limiting for eye protection, and the results could help researchers in geology, engineering, and medicine learn about the internal makeup of materials and tissues by studying the so-called speckle pattern in waves that pass through them. The major achievements are summarized as follows:
1. The two-dimensional speckle fields and the phase produced by the Gaussian correlation random surfaces on the Fraunhofer plane were simulated. It was found that the zero-contour of the real and imaginary parts can be in the tangent and superposition situations besides the traditional intersection situation. The tangential points and the superposition-lines can also form phase singularities, around which the phase distribution shows the characteristics of discontinuity and symmetry and differs from the spiral distribution around the traditional singular points that formed by the zero crossings of the real and imaginary parts. With the propagation of the optical wave, the relative positions of the zero-contour of the real and imaginary parts change from tangent to superposition, and then to intersection on the different observation plane with the simultaneously changes of the the phase singularities.
This result provides an important means to different application requirements in speckle simulation, and provides experimental observation to accurately understand and analyze the reasons of formation of the phase vortex phenomenon.
2. The speckle fields and their phase singularities produced respectively by the square loop aperture and circular ring aperture are studied. It is found that the zero-contour of the real and imaginary parts can be in the complex tangent and intersection situations. The complex tangent and intersection points can also form phase singularities, around which the phase distribution shows the characteristics of symmetry and discontinuity, it differs from the spiral distribution around the traditional singular points that formed by the zero crossings of the real and imaginary parts. The speckle particles distribution in the speckle fields produced by the square loop aperture and circular ring aperture differ from those by the traditional square aperture: the speckle particles distribution is modulated by the scattering aperture, respectively in stripes of level or vertical outlines and circular outlines. In addition, an interesting phenomenon occurs: a lot of circle-like dark regions appear in the intensity pattern of the speckle fields, it is called“light intensity dark nucleus”, whose center corresponds to a vortex, with homogeneous phase distribution.
We study the properties of particular phase vortices of random speckle field is important not only for research on speckle phase vortices but also plays an important role in the frontier area of singular phenomenon in other physical fields.
3. The intensity distribution and phase vortices of the speckle fields generated by multi-aperture random scattering screens are simulated, and it is found that the vortices exhibit layer-like structures and the dislocation phenomena occur in the local phase patterns produced by the two-pinhole aperture, whose phase distributions appear striped structures. For three- or four-pinhole aperture, there are many circular bright spots appearing in the speckle grains, and there is one vortex between the neighboring circular bright spots. The positive and negative phase vortex lattices appear in the phase distributions, and the regions circled by the isothetic phase lines form irregular quadrilaterals or hexagons. Moreover, the relative positions of the vortices or bright spots can be adjusted by changing those of the pinhole apertures.
This result has an important significance in the studies of the essential structures, the new characteristics and new laws of phase vortices, and the new singularity phenomena in the speckle fields. This might also be used in such field as multi-hole interferometer design.
4. The diffraction theory of Kirchhoff is applied to the four-pinhole aperture diffraction screens, the intensity, the zero-contour of the real and imaginary parts of complex amplitude and the phase distribution in deep Fresnel diffraction region are simulated, and it is found that the bright spots in interference field show central symmetry distribution. When the observation plane close to the diffraction screen, the zero-value points of light intensity can form line segment, on which the eccentricities of the light intensity isoline are close or equal to 1, the intensity changes very fast on both sides of the zero-line of light intensity. The zero-contours of the real and imaginary parts of complex amplitude are closed curves. The number of intersection points of the zero-contour of the real and imaginary parts is even, and positive and negative singularities are equal. Not only the phase around special phase singularities appears symmetry distribution, but also the topological charges of special phase singularities show singularity phenomena. With the propagation of the optical wave, the line segment of zero-value intensity change shorter and shorter, final to a point.
This has an important significance in the studies of the essential structures, the new characteristics and new laws of phase singularities, and the new singularity phenomena. This would be a better understanding of the characteristics of phase singularities in other physical fields.
5. The phase and the zero-contour of the real parts and the imaginary parts of the interference fields on the far-field plane generated by multi-aperture diffraction screens are simulated, and it is found that: when the orbital angular momentum quantum number of incident beam is equal to zero, at the center of interference field zero-lines can not intersect with each other, therefore, where can not form the phase vortices; when the orbital angular momentum quantum number of incident beam are opposite, namely, -1and+1, at the center of interference field zero-lines perpendicular and intersect to each other, the signs of the phase vortices at the corresponding positions in interference fields are opposite too; when the orbital angular momentum quantum number of incident beam is equal to±2 or±3 , there are four zero-lines intersect with alternating distribution at the center of interference fields, where the topological charge values of phase vortices are just equal to the orbital angular momentum quantum number of the Laguerre-Gaussian beams.
This method, based on a multipoint interferometer, has its most important application in measuring the orbital angular momentum of light from astronomical sources and vortex laser beams.
This paper is divided into six chapters. In first chapter, we propose the first time the theory methods of phase singularities of the random speckle field and description of the phase singularity phenomenon. The history, current status and main developments of phase singularities, the basic concept of the phase singularities in scalar wave field, a number of generating methods about scalar phase singularities in optical fields and the application of phase singularities are summarized. At the same time, we give the concept of phase singularities----phase vortices, the computational method of topological charge and the sign principle of phase singularity of wave field, and the eccentricities of intensity-contours. In chapter 2, by computer simulation, we study the properties of phase singularities at the tangential points and the superposition-lines of the zero-contour of the real parts and the imaginary parts of complex amplitude of the speckle fields on the Fraunhofer plane, verify those two types of phase singular phenomenon are not caused by surface roughness, and analyze the mechanism of their formation. In chapter 3, by theory and experiment, we study the properties of phase singularities at the complex tangential intersection situation of the zero-contour of the real parts and the imaginary parts of complex amplitude of the speckle fields produced respectively by square loop aperture and circular ring aperture on the Fraunhofer plane, and analyze the mechanism of their formation. At last, we give the causes of“light intensity dark nucleus”and regular arrays of speckle particles distribution. In Chapter 4, we study distribution characteristics of optical intensity and phase vortices of the speckle fields produced by multi-aperture random scattering screens on Fraunhofer plane in detail. In Chapter 5, Based on the diffraction theory of Kirchhoff, the intensity, the special phase singularities and the zero-contour generated by four-pinhole aperture diffraction screens in deep Fresnel diffraction region are studied in detail, and we find that the bright spots in diffractive field show central symmetry distribution. The eccentricities of the zero-line of light intensity are rather large, showing that the typical phase structure is strongly anisotropic. The phase around special phase singularities is symmetrical distribution, whose topological charges may appear singularity phenomena. In Chapter 6, Based on numerical calculation, we study the distribution properties of phase and the zero-contour of the real parts and the imaginary parts of the interference fields on the far-field plane generated by Laguerre-Gaussian beams through multi-aperture diffraction screens.
本学位论文结合了高斯随机表面散射形成的散斑场及其相位奇异现象的前沿领域最新成果的理论和方法,在连续相干激光光波照明,对方形孔径在夫朗和费面上形成的高斯随机散斑场及其实部和虚部零值线相切和重合情况下形成的相位奇异特性进行了详细研究;对方形环孔径和圆环孔径在夫朗和费面上形成的散斑场及其由实部和虚部零值线复杂相切相交情况下形成的相位奇异特性进行了研究;研究了多孔径径随机散射屏在远场平面上形成的局部区域的散斑场中光强亮斑及其相位奇异点的规则分布;研究了四孔径衍射屏在菲涅尔深区形成光场及其相位奇异等进行了一系列创造性的研究工作;最后,对拉盖尔-高斯光束通过多圆孔径形成的干涉光场的相位和零值线的分布,讨论了入射光束的轨道角动量和多条零值线相交点形成的相位奇异点拓扑荷的关系。本文的结果可以帮助我们更好地了解物理学各领域的相位奇异点周围的相位分布,在光开关、光学数据存储、微观粒子的操纵、保护眼睛的光限幅、散斑涡旋现象在地质冰层探测、医学检查和宇宙探索等领域应用前景等领域都有应用。概括起来,本学位论文取得了以下主要成果:
1.通过对二维高斯相关随机表面在夫朗和费面上产生的随机散斑场及其相位的计算模拟,得到散斑场的实部零值线和虚部零值线,并得出散斑场的相位等值线的分布。通过对散斑实虚部零值线的分析,发现在某一平面上,除了实部零值线与虚部零值线的传统的相交之外,还有相切和重合的情况。研究了零值线相切和重合附近的相位等值线特征,因为零值线切点和重合处光场振幅也等于零,因此,在这些位置也可以形成相位奇异。研究了零值线相切和重合处等值线的闭合特征及其引起的相位奇异点附近独特的相位跃变特征;发现其周围的相位分布与传统的实部零值线与虚部零值线相交形成的奇点周围相位的螺旋变化不同,呈现出对称性和不连续性的特征。随着光波的传播,在不同的观察面上,散斑场复振幅的实部零值线和虚部零值线的相对位置经历了由相切到重合再到相交的演变过程,相位奇异现象也随之发生变化。并且验证了这零值线相切和重合处的相位奇异现象并不是表面粗糙度所造成。最后分析了它们形成的机理。
本文也为不同应用要求下的散射场仿真提供了很好的手段,为准确理解和分析相位涡旋现象形成的原因提供了实验观察的依据,并对散斑相位涡旋的研究有重要意义。
2.在实验过程中,利用参考光和随机散射光相干涉,提取了方形环孔的散斑场复振幅的实部和虚部,同时在理论上通过对方形环孔和圆环孔在远场平面上形成的散斑场及其相位的数值计算得到散斑场相位的分布和零值线分布图,发现在某一平面上实部和虚部零值线的位置关系出现了复杂相切相交的情况,即两条实部零值线(或虚部零值线)本身相切,同时又会与虚部零值线(或实部零值线)与之相交或相切的情况,复杂相切相交点光场振幅为零,因此也形成相位奇异,并且其周围相位分布与传统的实部零值线与虚部零值线相交形成的相位奇异点周围相位的螺旋变化不同,呈现出对称性和不连续性的特征。方形环孔和圆环孔形成的散斑场的散斑颗粒分布与传统方孔的不同:受散射孔径的调制分别排成水平与竖直的条纹状轮廓和类似于圆形的轮廓,有趣的是:在散斑场的局部光强图中出现了很多类似于圆形的黑暗区域,我们称其为“光强暗核”,其中心对应着一个相位分布较均匀的涡旋。
随机散斑场中特殊相位涡旋的性质不仅对散斑相位涡旋的研究有重要意义,对相关的光学和物理前沿领域中奇异现象的研究也有重要应用前景,而且对于光学涡旋现象的研究具有先导意义。
3.通过对多孔径随机散射屏在夫琅和费面上形成的散斑场及其相位的计算模拟,发现在某一观察面上,在双圆孔形成的散斑场的相位分布图中,正负相位涡旋分层排列,相位分布多为条带状区域,并在某些位置有位错现象;在三圆孔和四圆孔形成的局部散斑场强度图中,有很多呈类圆形的亮斑,相邻的两个亮斑之间有一个相位涡旋,在相应的相位分布图中,出现了正负相位涡旋列,相位区域的形状多为不规则的四边形或六边形,调节散射屏前孔径上圆孔的相对位置,亮斑或相位涡旋的相对位置随之改变。
这对研究相位涡旋的本质结构和散斑场的新规律和新的奇异现象具有重要的意义,并且对多圆孔干涉仪有重要应用。本文也为不同应用要求下的散射场仿真提供了很好的手段,为准确理解和分析相位涡旋现象形成的原因提供了实验观察的依据。
4.利用基尔霍夫衍射理论计算了四圆孔径衍射屏在菲涅尔深区形成的光场强度、零值线和相位的分布,发现衍射光场亮斑关于中心呈对称分布,在距离衍射屏较近的观察面上,光强值为零点组成光强零值线段,该线段上光强等值线的离心率都接近或等于1,其两侧的光强值变化非常剧烈。复振幅的实部和虚部零值线多为封闭的曲线,零值线交点的个数为偶数,并且正负奇异点的个数相等。特殊相位奇异点周围的相位不仅呈对称分布,而且该点的拓扑荷出现了奇异现象。随着光波的传播,在不同的观察面上,光强零值线段逐渐变短最终趋于一点。
这对研究相位奇异点的本质结构和新的奇异现象具有重要意义,并且对多圆孔干涉仪的设计有重要作用。本文也为准确理解和分析相位奇异点周围的相位分布提供了实验观察的依据。
5.通过对拉盖尔-高斯光束经多圆孔径衍射屏在远场平面上形成的干涉光场的相位和零值线的计算模拟,发现:当入射光束的轨道角动量量子数为零时,实部零值线与虚部零值线在干涉光场中心点不相交,因而该点上不能形成相位涡旋;当入射光束的轨道角动量量子数为+1和-1时,实部零值线与虚部零值线在干涉光场中心垂直并相交,干涉光场相应位置处的相位涡旋的符号相反;当入射光束的轨道角动量量子数为±2和±3时,有四条零值线相交于干涉光场的中心点上,并且实部零值线和虚部零值线交替分布,该交点处形成的相位涡旋的拓扑荷的值恰好与拉盖尔-高斯光束的轨道角动量量子数相等。
这对利用多孔干涉仪,测量新天体所发光的轨道角动量有最重要的应用,并可用来测具有轨道角动量的涡旋光束。
本论文共分七章,第一章为绪论,简要叙述了相位奇异的发展历史、相位奇异的国内外研究现状、标量波场中相位奇异的基本概念、光场中标量相位奇异的产生方法、相位奇异的应用等内容。第二章通过计算模拟,研究了散斑场复振幅的实部和虚部的零值线相切、相切重合和交叉重合等情况下的相位奇异及其性质,验证了这两类相位奇异现象并不是表面粗糙度所造成,最后计算了它们的演变过程,并分析了它们形成的机理。第三章从理论和实验上详细研究了方形环孔和圆环孔形成的散斑场及其零值线复杂相切相交情况下的相位奇异性,并分析了它们形成的机理,并分析了“光强暗核”的形成、散斑颗粒规则排列的原因。第四章从理论上详细研究了多孔径随机散射屏在夫琅和费面上形成的散斑场中光强及其相位涡旋的分布特性。第五章利用基尔霍夫衍射理论详细研究了四圆孔径衍射屏在菲涅尔深区形成的干涉光场的强度、相位奇异点和零值线的分布特性及演化过程,并计算了光强零值线上光强等值线的离心率的值和拓扑荷的值。第六章从理论上详细研究了拉盖尔-高斯光束通过多圆孔径衍射屏在远场平面上形成的干涉光场的光强、相位和零值线的分布特性。第七章对论文做了总结和展望。
When the coherent light waves are scattered from the random surfaces or the random media, speckles are formed in the diffraction regions. Measurements and computer simulations have shown that the speckle grains and phase singularities have the same density in the random fields, so there are as many phase singularities as speckle grains in speckle field. The zeros of light intensity are the phase singularities at which the phase of is undefined. Around each singularity the current circulates and then the zeros are also called optical vortices. It exists in various linear and nonlinear physical systems, such as the angular momentum eigenstates of the hydrogen atom, the Meissner state of type-II superconductors, vortex states of superfluids, Bose-Einstein condensates, and optical vortex solitons. Phase singularities are very important and widely used in the optical microcontroller, quantum entanglement, information transmission. Phase singularities in optical fields owing to potential applications have driven a surge of interest in recent years. However, the existing literatures on the zero-contour of the real and imaginary parts of speckle field are intersection situation. As we all know, in fact, due to the complexity of the speckle field, the zero-contour of the real and imaginary parts can be in tangential or superposition situation. Study the characters of phase singularities in random speckle field have leading significance, not only a new task for speckle phase singularities but also for the phenomenon of optical vortex in other areas of physics, and have important applications in related frontier areas of optics and physics.
This thesis combining methodologies and the theories in the achievements in such frontier areas of physics as the speckle fields generated by the Gaussian correlation random scattering screen and their phase singularities properties under the illumination of continuous lasers. The phase singularities of speckle fields produced by the scattering from square aperture Gaussian correlation random surfaces in the Fraunhofer plane, the zero-contour of the real and imaginary parts of complex amplitude of speckle fields are tangent and coincidence, at the tangential points and the superposition-lines can also form phase singularities, the speckle fields produced by the square loop aperture and circular ring aperture and their phase singularities, the intensity distribution and phase singularities of speckle fields generated by multi-aperture random scattering screens and the intensity distribution and topological charge singularity of special phase singularities generated by four-pinhole aperture diffraction screens in deep Fresnel diffraction region.
The results presented in this thesis offer us a better understanding of phase singularities which may result in applications in optical switching, optical data storage, manipulation of micro-particles and optical limiting for eye protection, and the results could help researchers in geology, engineering, and medicine learn about the internal makeup of materials and tissues by studying the so-called speckle pattern in waves that pass through them. The major achievements are summarized as follows:
1. The two-dimensional speckle fields and the phase produced by the Gaussian correlation random surfaces on the Fraunhofer plane were simulated. It was found that the zero-contour of the real and imaginary parts can be in the tangent and superposition situations besides the traditional intersection situation. The tangential points and the superposition-lines can also form phase singularities, around which the phase distribution shows the characteristics of discontinuity and symmetry and differs from the spiral distribution around the traditional singular points that formed by the zero crossings of the real and imaginary parts. With the propagation of the optical wave, the relative positions of the zero-contour of the real and imaginary parts change from tangent to superposition, and then to intersection on the different observation plane with the simultaneously changes of the the phase singularities.
This result provides an important means to different application requirements in speckle simulation, and provides experimental observation to accurately understand and analyze the reasons of formation of the phase vortex phenomenon.
2. The speckle fields and their phase singularities produced respectively by the square loop aperture and circular ring aperture are studied. It is found that the zero-contour of the real and imaginary parts can be in the complex tangent and intersection situations. The complex tangent and intersection points can also form phase singularities, around which the phase distribution shows the characteristics of symmetry and discontinuity, it differs from the spiral distribution around the traditional singular points that formed by the zero crossings of the real and imaginary parts. The speckle particles distribution in the speckle fields produced by the square loop aperture and circular ring aperture differ from those by the traditional square aperture: the speckle particles distribution is modulated by the scattering aperture, respectively in stripes of level or vertical outlines and circular outlines. In addition, an interesting phenomenon occurs: a lot of circle-like dark regions appear in the intensity pattern of the speckle fields, it is called“light intensity dark nucleus”, whose center corresponds to a vortex, with homogeneous phase distribution.
We study the properties of particular phase vortices of random speckle field is important not only for research on speckle phase vortices but also plays an important role in the frontier area of singular phenomenon in other physical fields.
3. The intensity distribution and phase vortices of the speckle fields generated by multi-aperture random scattering screens are simulated, and it is found that the vortices exhibit layer-like structures and the dislocation phenomena occur in the local phase patterns produced by the two-pinhole aperture, whose phase distributions appear striped structures. For three- or four-pinhole aperture, there are many circular bright spots appearing in the speckle grains, and there is one vortex between the neighboring circular bright spots. The positive and negative phase vortex lattices appear in the phase distributions, and the regions circled by the isothetic phase lines form irregular quadrilaterals or hexagons. Moreover, the relative positions of the vortices or bright spots can be adjusted by changing those of the pinhole apertures.
This result has an important significance in the studies of the essential structures, the new characteristics and new laws of phase vortices, and the new singularity phenomena in the speckle fields. This might also be used in such field as multi-hole interferometer design.
4. The diffraction theory of Kirchhoff is applied to the four-pinhole aperture diffraction screens, the intensity, the zero-contour of the real and imaginary parts of complex amplitude and the phase distribution in deep Fresnel diffraction region are simulated, and it is found that the bright spots in interference field show central symmetry distribution. When the observation plane close to the diffraction screen, the zero-value points of light intensity can form line segment, on which the eccentricities of the light intensity isoline are close or equal to 1, the intensity changes very fast on both sides of the zero-line of light intensity. The zero-contours of the real and imaginary parts of complex amplitude are closed curves. The number of intersection points of the zero-contour of the real and imaginary parts is even, and positive and negative singularities are equal. Not only the phase around special phase singularities appears symmetry distribution, but also the topological charges of special phase singularities show singularity phenomena. With the propagation of the optical wave, the line segment of zero-value intensity change shorter and shorter, final to a point.
This has an important significance in the studies of the essential structures, the new characteristics and new laws of phase singularities, and the new singularity phenomena. This would be a better understanding of the characteristics of phase singularities in other physical fields.
5. The phase and the zero-contour of the real parts and the imaginary parts of the interference fields on the far-field plane generated by multi-aperture diffraction screens are simulated, and it is found that: when the orbital angular momentum quantum number of incident beam is equal to zero, at the center of interference field zero-lines can not intersect with each other, therefore, where can not form the phase vortices; when the orbital angular momentum quantum number of incident beam are opposite, namely, -1and+1, at the center of interference field zero-lines perpendicular and intersect to each other, the signs of the phase vortices at the corresponding positions in interference fields are opposite too; when the orbital angular momentum quantum number of incident beam is equal to±2 or±3 , there are four zero-lines intersect with alternating distribution at the center of interference fields, where the topological charge values of phase vortices are just equal to the orbital angular momentum quantum number of the Laguerre-Gaussian beams.
This method, based on a multipoint interferometer, has its most important application in measuring the orbital angular momentum of light from astronomical sources and vortex laser beams.
This paper is divided into six chapters. In first chapter, we propose the first time the theory methods of phase singularities of the random speckle field and description of the phase singularity phenomenon. The history, current status and main developments of phase singularities, the basic concept of the phase singularities in scalar wave field, a number of generating methods about scalar phase singularities in optical fields and the application of phase singularities are summarized. At the same time, we give the concept of phase singularities----phase vortices, the computational method of topological charge and the sign principle of phase singularity of wave field, and the eccentricities of intensity-contours. In chapter 2, by computer simulation, we study the properties of phase singularities at the tangential points and the superposition-lines of the zero-contour of the real parts and the imaginary parts of complex amplitude of the speckle fields on the Fraunhofer plane, verify those two types of phase singular phenomenon are not caused by surface roughness, and analyze the mechanism of their formation. In chapter 3, by theory and experiment, we study the properties of phase singularities at the complex tangential intersection situation of the zero-contour of the real parts and the imaginary parts of complex amplitude of the speckle fields produced respectively by square loop aperture and circular ring aperture on the Fraunhofer plane, and analyze the mechanism of their formation. At last, we give the causes of“light intensity dark nucleus”and regular arrays of speckle particles distribution. In Chapter 4, we study distribution characteristics of optical intensity and phase vortices of the speckle fields produced by multi-aperture random scattering screens on Fraunhofer plane in detail. In Chapter 5, Based on the diffraction theory of Kirchhoff, the intensity, the special phase singularities and the zero-contour generated by four-pinhole aperture diffraction screens in deep Fresnel diffraction region are studied in detail, and we find that the bright spots in diffractive field show central symmetry distribution. The eccentricities of the zero-line of light intensity are rather large, showing that the typical phase structure is strongly anisotropic. The phase around special phase singularities is symmetrical distribution, whose topological charges may appear singularity phenomena. In Chapter 6, Based on numerical calculation, we study the distribution properties of phase and the zero-contour of the real parts and the imaginary parts of the interference fields on the far-field plane generated by Laguerre-Gaussian beams through multi-aperture diffraction screens.
引文
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