相位光栅衍射和随机表面等离子体激元散斑研究
摘要
对于相位光栅的研究是一个古老而新颖的课题，根据散射理论研究了其衍射级次的数目变化。通过时域有限差分法数值模拟了正弦相位光栅的透射场分布，将其分为近场、菲涅尔深区以及远场分析了干涉条纹产生的原因，通过全反射理论证明了倏逝波的存在。
表面等离子体激元散斑的研究对研究表面等离子体激元传播具有重要的意义。而散斑由相干光照明粗糙表面，该表面上不同面元透射或反射的光振动在空间相遇而发生干涉，形成具有无规则分布颗粒状结构的衍射图样。按照光的传播方式，把散斑分成远场散斑，近场散斑和象面散斑。由于散斑场的随机性，对它的统计特性的研究是一个多年来倍受关注的课题，对其统计特性的研究主要根据强度自相关，强度-强度相关进行统计计算随机界面散斑与表面等离子体激元散斑的参数。另外，散斑场强度的实部强度与虚部强度相等时其周围将形成相位涡旋，由于其中含有丰富的光波复振幅和相位信息，对相位涡旋的研究也引起了人们的广泛关注并成为一个新的研究热点。目前主要利用散斑场与参考光的干涉技术和傅里叶变换法实现随机光场的实验提取来研究散斑场的相位涡旋。菲涅尔深区以及极深区内的散斑含有更加丰富的信息，因此对其研究具有更加重要的意义。
本学位论文首先利用制备了随机玻璃样品和随机银膜样品，然后搭建具有高倍显微物镜的实验系统对样品在菲涅耳深区与极深区的随机介质与随机银膜产生的表面等离子体激元的散斑图样进行了采集，研究了样品随银膜厚度的散斑特性的演化以及散斑颗粒的尺度变化，并定性分析了表面等离子体激元在散斑场的演化中的作用，同时根据基尔霍夫近似理论进行数值模拟计算，实现了菲涅耳极深区散斑场的强度分布，并与原子力显微镜扫描的表面高度分布进行比较。本论文通过强度-强度相关曲线拟合计算了散斑颗粒的大小、分形指数随着银膜厚度的演化。另外在原有光路的基础上加上参考光利用散斑场和参考光的干涉技术和傅里叶变换法成功地实现了各种散斑场的实验提取，研究了散斑的强度、复振幅、相位和相位涡旋等的统计特性和传播规律。论文共分八章。
第一章是对本课题的研究历史和现状以及论文相关的一些概念进行了综合性描述。内容包括随机表面的描述方法、主要的统计参量及其高度、强度的统计函数；分形理论、散斑场的形成以及其在随机表面标定中的应用；相位涡旋的定义和一般性质，给出相位涡旋符号的定义方法和相关函数。
第二章首先基于麦克斯韦方程组将负折射材料的介电常数离散得到，通过表面等离子体激元的色散关系，得出了其共振条件与共振频率。对于表面等离子体激元的产生条件进行了详细的介绍。介绍了几种激发耦合方式，本文中主要通过表面随机界面结构补偿波矢使其能够耦合到空间中进行传播，这为我们后面讨论随机银膜界面的散斑结构演化、表面等离子体激元散斑涡旋随着银膜厚度的演化奠定了基础。
第三章讨论了正弦光栅的衍射级次随着光栅周期、入射光的入射角的变化情况。发现当入射光线与栅线垂直入射时，光栅的衍射级次会发生畸变，不再在同一条直线上。光栅周期越大，衍射级次的数目越少；入射光的入射角越大，衍射级次的数目也越少。
第四章我们通过时域有限差分法数值模拟了正弦光栅的透射场分布，计算了不同的光栅周期的透射场分布，发现光栅周期不同，其透射场近场的分布完全不同，将其透射场分为近场、菲涅尔深区、远场。其透射场分布呈现周期性变化，根据其透射场干涉条纹的分布分析了其近场光场分布的机理，通过全反射证明了倏逝波的存在，并简单计算了其干涉条纹的间距。光栅周期是影响其透射场分布的重要参数，光栅周期越小，其周期性干涉条纹出现的越快。在不同的区域，其干涉条纹产生的机理不同，并进行了相信的分析。并且其凹凸槽对应的凹透镜和凸透镜的效果越明显，这对于设计光学器件具有重要的指导意义。
第五章我们通过含有高倍成像显微物镜的光学实验系统采集了随机玻璃样品的散斑图样，观察发现菲涅尔深区的散斑结构中含有棱脊状结构,大的平台颗粒结构,破碎状颗粒结构等多种散斑结构，这些结构与传统的远场散斑结构非常不同，这些散斑结构具有明显的分形特征。在传统的光学实验中，分形结构需要通过照明孔径来实现，而本实验中基于高倍成像显微物镜对散射光的收集能力以及样品的特点可以直接实现分形散斑的获取。我们根据基尔霍夫近似和格林定理，利用原子力扫描显微镜扫描的表面高度数据模拟了在象面上散斑场的分布，通过比较AFM扫描的表面形貌与模拟的散斑场结构发现这些结构来自于随机样品的凸起和凹陷部分。通过高度自相关、高度-高度相关计算了该随机玻璃样品的表面粗糙度、横向相关长度、分形指数等参数。并通过计算随机样品的散斑场的强度-强度相关函数和强度自相关函数，并拟合强度-强度相关曲线获得了散斑场的散斑颗粒的尺度大小、以及分形指数。经过分析发现这些结构与自相关函数曲线的中心峰、过渡区、长尾区三部分相对应。
第六章我们通过含有高倍成像显微物镜的光学实验系统采集了随机玻璃样品和镀有银膜的随机玻璃样品的散斑图样，分析了其散斑结构随着银膜厚度的演化，发现随着银膜厚度的增加，在随机玻璃样品的散斑同样中发现的棱脊状结构,大的平台颗粒,破碎状颗粒等多尺度结构逐渐消失，散斑场的颗粒尺度越来越小，并趋向于一个极限值。对表面等离子体激元散斑的演化特性进行了定性的分析，解释了这些多尺度结构消失的原因。其形成机理由两方面因素决定，随机玻璃的散射与随机银膜的散射共同作用引起了散斑颗粒尺度逐渐减小。计算了其概率密度函数与对比度，并通过拟合概率密度曲线计算了其对比度，并将两者进行了比较。计算了样品的强度自相关函数的全局自相关与局部自相关，通过拟合自相关曲线得出了散斑颗粒的尺度大小以及分形指数。通过拟合数据证明了直观观察的散斑颗粒尺度变小的特性。
第七章我们通过含有显微物镜成像的物光系统与含有空间滤波器来放大和虑波的参考光系统干涉获取随机玻璃样品和镀有银膜的随机玻璃样品表面的散斑干涉图样。通过干涉相位提取技术，通过一次傅里叶变换得到了散斑场的空间正一级频谱分布，通过两次傅里叶变换恢复了散斑场的光强的复振幅、相位分布、光强实部零值线与虚部零值线的分布。分析了随着银膜厚度的增加，表面等离子体激元散斑的相位分布中的涡旋个数越来越多，这主要是由于随机玻璃界面与随机银膜界面的散射作用以及散射波与表面等离子体激元波相互干涉的结果引起的。表面等离子体激元散斑的涡旋分为完整涡旋与非完整涡旋，并对涡旋符号进行了分析。另外随着银膜厚度的增加，散斑涡旋密度增加，对相关函数相关的值在短相关长度范围内较大，一定的相关长度趋于一个定值；电荷相关函数相关的值在短相关长度范围内比对相关函数值小，由于正负电荷相反的贡献，一定的相关长度趋于零。等光强曲线的离心率偏离高斯散斑场的离心率，表明等离子体激元散斑场偏离高斯散斑场。
第八章总结了本学位论文所取得的主要成果和创新点，并简单地介绍了下一步要深入开展的研究工作。
The study of phase grating is an ancient and new topic, According to scattering theory, westudy numbers of the diffraction orders with different grating periods and incident angles. Noblemetal grating can excite surface plasmon polariton by compensation of wave vector. Basing onthe rule structure characteristics of the grating, it has great importance to study transmissionenhancement features of surface plasmon. In order to study the transmission enhancement ofnoble mental grating, we simulate the distribution of transmission field of sine grating.
Random silver film interface can excite surface plasmon, and produce speckle in deep Fresneland the extremely deep Fresnel region. The study of the surface plasmon speckle has greatimportance for the propagation of surface plasmon. When laser light beam illuminate the roughsurface, the transmission or reflection light of different facet interfere, forming diffraction patternwith the grain structure of random distribution. According to the way of propagation, thespeckles can be divided into the far field speckle, near field speckle, and image speckle. Due tothe randomness of the speckle, the study of its statistical properties is a subject widely concernedfor many years, and the study of the statistical characteristics is statistically calculating theparameters of speckle of random surface and surface plasmon, according to the intensityautocorrelation, intensity correlation. In addition, when the real is equal to the image partintensity of speckle, will form phase vortices surroundings. There is abundant information ofcomplex amplitude and phase in the phase vortices, so more and more papers pay attention to theinvestigation of phase vortices and has become a new research hotspot. The study of phasevortices is mainly through the way of experimental extraction by combining the interferencetechnique of speckle fields and reference beam with the digital Fourier transform arithmetic. Sothe speckle in the deep and extremely deep Fresnel diffraction region contain more abundantinformation, thus has more important significance to research.
We manufacture random glass and silver film sample, and then design experimental system toacquire surface plasmon speckles generated by random surface Ag film. We study thecharacteristic evolution and the variation of the scales of the speckle particles accompanythickness of Ag film, qualitatively analyzing the effect of surface plasmon in evolution ofspeckle field, simultaneously carrying on numerical simulation according to the Kirchhoffapproximation theory, obtaining intensity distribution of speckle in extremely deep Fresnelregion, compared with surface height distribution scanned by atomic force microscopy. In this paper, through fitting the intensity-intensity curve, we calculate the size of the particles, thefractal index along with the evolution of the silver film thickness. In addition, through addingreference light in original light path, we have successfully finished the experimental extraction ofspeckle fields, combining the interference technique of speckle fields and reference beam withthe digital Fourier transform arithmetic, and studied the amplitude, phase, intensity and phasevortices of speckle and their properties of statistical and the propagation etc. The whole paper isdivided into seven chapters.
Chapter1: Introduction. In this part, we give a summary and an overall review of thebackground and the current situation of the research on speckles as well as some conceptionsabout speckles. First, we introduce the characterization, the measurement, the primary statisticalparameters and high statistical functions of random surfaces. Then we recite the fractal theories,and the formation of speckles; the definition and the characteristic of the phase vortices.
Chapter2: Based on Maxwell’s equations, we deduce the dielectric constant of negativerefraction materials, and obtain the resonance condition and frequency through the dispersionrelation of surface plasmon. We detailed discuss the excitation of surface plasmon and introduceseveral way of coupling, this lay the theoretical foundation of following study.
Chapter3: we analyze theoretically the diffraction of a one-dimensional reflective grating onthe basis of the scattering theory, and discuss in detail the distribution of the diffraction ordersand the number of the visible diffraction orders. The relationship of the diffraction order and thegrating period and the incident angle is presented in the form of the inequality, and the number ofthe visible diffraction orders can be determined by the incident angle and the grating period.
Chapter4: we numerically simulate the distribution of transmission field by Finite differencetime domain (FDTD), calculate the distribution of transmission field of different grating, andfind that distribution is completely different. The distribution of transmission field varyperiodically, we discuss the mechanism of near field according to the distribution of interferencefringe, verify the existence of evanescent wave, and calculate the distance between interferencefringes.
Chapter5: with a microscopic imaging system composed of microscopic objective, lens andCCD, we observe the complicated structures in the speckle fields on the surface of rough screen.We find that such structures contain ridge stripes, large platform like grains, and shivy grains,exhibiting multiple scales in size and multiple fractalities, which have not been observed in theconventional far field speckles. Simulations based on the Green’s integral and the Kirchhoffapproximation of wave diffractions shows these structures are formed by the different parts ofthe rough surface. The experimental curve of the autocorrelation function of the speckle intensity includes the three parts of the central peak, the transition part and the long tail part. Using thesum of self-affine fractal models with different scales and fractalities, we propose theoretically atriple-scale autocorrelation function to describe the speckle field. Fit of this autocorrelationfunction to the experimental curve gives the values of such parameters as average speckle sizesand fractalities in different scales of the speckle structures.
Chapter6: we experimental studies on speckles produced by the rough silver films. Thespeckles on the rough glass and silver surfaces are measured with a microscopic imaging system.The structures of speckle patterns have the characteristics of fractals and multi scaled sizes. Wefind that with the increase of the silver film thickness, the contrast of the speckles increases, andthe intensity probability density functions gradually transit to exponential decay. We calculate theglobal and the local correlation functions of the speckle patterns, and find that both the fractalexponent and correlation length of the small sized speckles decrease with the thickness of thesilver films. We use the mechanisms of rough dielectric interface scattering and random surfaceplasmon waves to give the preliminary explanations for the evolutions of the speckles.
In chapter7, we acquire the interference speckle patterns of the random glass and the randomsilver film samples by the experiment systems with the one used as object light with amicroscopic objective MO for collecting and imaging the speckles on the surface of samples andthe other one used as reference light wave which is expanded and filtered by spatial pinhole filter.By the Fourier transform method, the first order spatial frequency spectrum, the amplitude of theintensity including the real and the image and the phase of speckles can be experimentallyextracted. With the phase vortices distribution, we can see that the number of the vorticesbecomes larger with the increasing of the thickness of the silver film. Surface plasmon polaritonscan be excited and scattered, and then may be coupled by the rough silver and air interfaceradiate into the air-side space in silver films. Surface plasmon polaritons can interfere with thewaves scattered by the rough glass to form the speckles. The vortices produced by theinterference of the surface plasmon waves and the waves scattered by the random screen can bedivided into holonomic and nonholonomic, and their symbols are also studied. The specklevortices densities are increasing with the thickness of the silver films. The pair correlationfunction is larger in smaller correlation length with the increasing of the silver film, and thevalues of the pair correlation functions approach to one constant value. The charge correlationfunctions are smaller than the pair correlation functions, and the values of the charge correlationfunctions are near to0with the opposite effects of the positive and negative charges. The averageeccentricities for different thickness of the silver film deviate from the Gaussian speckles.
In chapter8, we sum up the main conclusions and the innovations of the dissertation, and briefly introduce the in-depth researches we will conduct.
表面等离子体激元散斑的研究对研究表面等离子体激元传播具有重要的意义。而散斑由相干光照明粗糙表面，该表面上不同面元透射或反射的光振动在空间相遇而发生干涉，形成具有无规则分布颗粒状结构的衍射图样。按照光的传播方式，把散斑分成远场散斑，近场散斑和象面散斑。由于散斑场的随机性，对它的统计特性的研究是一个多年来倍受关注的课题，对其统计特性的研究主要根据强度自相关，强度-强度相关进行统计计算随机界面散斑与表面等离子体激元散斑的参数。另外，散斑场强度的实部强度与虚部强度相等时其周围将形成相位涡旋，由于其中含有丰富的光波复振幅和相位信息，对相位涡旋的研究也引起了人们的广泛关注并成为一个新的研究热点。目前主要利用散斑场与参考光的干涉技术和傅里叶变换法实现随机光场的实验提取来研究散斑场的相位涡旋。菲涅尔深区以及极深区内的散斑含有更加丰富的信息，因此对其研究具有更加重要的意义。
本学位论文首先利用制备了随机玻璃样品和随机银膜样品，然后搭建具有高倍显微物镜的实验系统对样品在菲涅耳深区与极深区的随机介质与随机银膜产生的表面等离子体激元的散斑图样进行了采集，研究了样品随银膜厚度的散斑特性的演化以及散斑颗粒的尺度变化，并定性分析了表面等离子体激元在散斑场的演化中的作用，同时根据基尔霍夫近似理论进行数值模拟计算，实现了菲涅耳极深区散斑场的强度分布，并与原子力显微镜扫描的表面高度分布进行比较。本论文通过强度-强度相关曲线拟合计算了散斑颗粒的大小、分形指数随着银膜厚度的演化。另外在原有光路的基础上加上参考光利用散斑场和参考光的干涉技术和傅里叶变换法成功地实现了各种散斑场的实验提取，研究了散斑的强度、复振幅、相位和相位涡旋等的统计特性和传播规律。论文共分八章。
第一章是对本课题的研究历史和现状以及论文相关的一些概念进行了综合性描述。内容包括随机表面的描述方法、主要的统计参量及其高度、强度的统计函数；分形理论、散斑场的形成以及其在随机表面标定中的应用；相位涡旋的定义和一般性质，给出相位涡旋符号的定义方法和相关函数。
第二章首先基于麦克斯韦方程组将负折射材料的介电常数离散得到，通过表面等离子体激元的色散关系，得出了其共振条件与共振频率。对于表面等离子体激元的产生条件进行了详细的介绍。介绍了几种激发耦合方式，本文中主要通过表面随机界面结构补偿波矢使其能够耦合到空间中进行传播，这为我们后面讨论随机银膜界面的散斑结构演化、表面等离子体激元散斑涡旋随着银膜厚度的演化奠定了基础。
第三章讨论了正弦光栅的衍射级次随着光栅周期、入射光的入射角的变化情况。发现当入射光线与栅线垂直入射时，光栅的衍射级次会发生畸变，不再在同一条直线上。光栅周期越大，衍射级次的数目越少；入射光的入射角越大，衍射级次的数目也越少。
第四章我们通过时域有限差分法数值模拟了正弦光栅的透射场分布，计算了不同的光栅周期的透射场分布，发现光栅周期不同，其透射场近场的分布完全不同，将其透射场分为近场、菲涅尔深区、远场。其透射场分布呈现周期性变化，根据其透射场干涉条纹的分布分析了其近场光场分布的机理，通过全反射证明了倏逝波的存在，并简单计算了其干涉条纹的间距。光栅周期是影响其透射场分布的重要参数，光栅周期越小，其周期性干涉条纹出现的越快。在不同的区域，其干涉条纹产生的机理不同，并进行了相信的分析。并且其凹凸槽对应的凹透镜和凸透镜的效果越明显，这对于设计光学器件具有重要的指导意义。
第五章我们通过含有高倍成像显微物镜的光学实验系统采集了随机玻璃样品的散斑图样，观察发现菲涅尔深区的散斑结构中含有棱脊状结构,大的平台颗粒结构,破碎状颗粒结构等多种散斑结构，这些结构与传统的远场散斑结构非常不同，这些散斑结构具有明显的分形特征。在传统的光学实验中，分形结构需要通过照明孔径来实现，而本实验中基于高倍成像显微物镜对散射光的收集能力以及样品的特点可以直接实现分形散斑的获取。我们根据基尔霍夫近似和格林定理，利用原子力扫描显微镜扫描的表面高度数据模拟了在象面上散斑场的分布，通过比较AFM扫描的表面形貌与模拟的散斑场结构发现这些结构来自于随机样品的凸起和凹陷部分。通过高度自相关、高度-高度相关计算了该随机玻璃样品的表面粗糙度、横向相关长度、分形指数等参数。并通过计算随机样品的散斑场的强度-强度相关函数和强度自相关函数，并拟合强度-强度相关曲线获得了散斑场的散斑颗粒的尺度大小、以及分形指数。经过分析发现这些结构与自相关函数曲线的中心峰、过渡区、长尾区三部分相对应。
第六章我们通过含有高倍成像显微物镜的光学实验系统采集了随机玻璃样品和镀有银膜的随机玻璃样品的散斑图样，分析了其散斑结构随着银膜厚度的演化，发现随着银膜厚度的增加，在随机玻璃样品的散斑同样中发现的棱脊状结构,大的平台颗粒,破碎状颗粒等多尺度结构逐渐消失，散斑场的颗粒尺度越来越小，并趋向于一个极限值。对表面等离子体激元散斑的演化特性进行了定性的分析，解释了这些多尺度结构消失的原因。其形成机理由两方面因素决定，随机玻璃的散射与随机银膜的散射共同作用引起了散斑颗粒尺度逐渐减小。计算了其概率密度函数与对比度，并通过拟合概率密度曲线计算了其对比度，并将两者进行了比较。计算了样品的强度自相关函数的全局自相关与局部自相关，通过拟合自相关曲线得出了散斑颗粒的尺度大小以及分形指数。通过拟合数据证明了直观观察的散斑颗粒尺度变小的特性。
第七章我们通过含有显微物镜成像的物光系统与含有空间滤波器来放大和虑波的参考光系统干涉获取随机玻璃样品和镀有银膜的随机玻璃样品表面的散斑干涉图样。通过干涉相位提取技术，通过一次傅里叶变换得到了散斑场的空间正一级频谱分布，通过两次傅里叶变换恢复了散斑场的光强的复振幅、相位分布、光强实部零值线与虚部零值线的分布。分析了随着银膜厚度的增加，表面等离子体激元散斑的相位分布中的涡旋个数越来越多，这主要是由于随机玻璃界面与随机银膜界面的散射作用以及散射波与表面等离子体激元波相互干涉的结果引起的。表面等离子体激元散斑的涡旋分为完整涡旋与非完整涡旋，并对涡旋符号进行了分析。另外随着银膜厚度的增加，散斑涡旋密度增加，对相关函数相关的值在短相关长度范围内较大，一定的相关长度趋于一个定值；电荷相关函数相关的值在短相关长度范围内比对相关函数值小，由于正负电荷相反的贡献，一定的相关长度趋于零。等光强曲线的离心率偏离高斯散斑场的离心率，表明等离子体激元散斑场偏离高斯散斑场。
第八章总结了本学位论文所取得的主要成果和创新点，并简单地介绍了下一步要深入开展的研究工作。
The study of phase grating is an ancient and new topic, According to scattering theory, westudy numbers of the diffraction orders with different grating periods and incident angles. Noblemetal grating can excite surface plasmon polariton by compensation of wave vector. Basing onthe rule structure characteristics of the grating, it has great importance to study transmissionenhancement features of surface plasmon. In order to study the transmission enhancement ofnoble mental grating, we simulate the distribution of transmission field of sine grating.
Random silver film interface can excite surface plasmon, and produce speckle in deep Fresneland the extremely deep Fresnel region. The study of the surface plasmon speckle has greatimportance for the propagation of surface plasmon. When laser light beam illuminate the roughsurface, the transmission or reflection light of different facet interfere, forming diffraction patternwith the grain structure of random distribution. According to the way of propagation, thespeckles can be divided into the far field speckle, near field speckle, and image speckle. Due tothe randomness of the speckle, the study of its statistical properties is a subject widely concernedfor many years, and the study of the statistical characteristics is statistically calculating theparameters of speckle of random surface and surface plasmon, according to the intensityautocorrelation, intensity correlation. In addition, when the real is equal to the image partintensity of speckle, will form phase vortices surroundings. There is abundant information ofcomplex amplitude and phase in the phase vortices, so more and more papers pay attention to theinvestigation of phase vortices and has become a new research hotspot. The study of phasevortices is mainly through the way of experimental extraction by combining the interferencetechnique of speckle fields and reference beam with the digital Fourier transform arithmetic. Sothe speckle in the deep and extremely deep Fresnel diffraction region contain more abundantinformation, thus has more important significance to research.
We manufacture random glass and silver film sample, and then design experimental system toacquire surface plasmon speckles generated by random surface Ag film. We study thecharacteristic evolution and the variation of the scales of the speckle particles accompanythickness of Ag film, qualitatively analyzing the effect of surface plasmon in evolution ofspeckle field, simultaneously carrying on numerical simulation according to the Kirchhoffapproximation theory, obtaining intensity distribution of speckle in extremely deep Fresnelregion, compared with surface height distribution scanned by atomic force microscopy. In this paper, through fitting the intensity-intensity curve, we calculate the size of the particles, thefractal index along with the evolution of the silver film thickness. In addition, through addingreference light in original light path, we have successfully finished the experimental extraction ofspeckle fields, combining the interference technique of speckle fields and reference beam withthe digital Fourier transform arithmetic, and studied the amplitude, phase, intensity and phasevortices of speckle and their properties of statistical and the propagation etc. The whole paper isdivided into seven chapters.
Chapter1: Introduction. In this part, we give a summary and an overall review of thebackground and the current situation of the research on speckles as well as some conceptionsabout speckles. First, we introduce the characterization, the measurement, the primary statisticalparameters and high statistical functions of random surfaces. Then we recite the fractal theories,and the formation of speckles; the definition and the characteristic of the phase vortices.
Chapter2: Based on Maxwell’s equations, we deduce the dielectric constant of negativerefraction materials, and obtain the resonance condition and frequency through the dispersionrelation of surface plasmon. We detailed discuss the excitation of surface plasmon and introduceseveral way of coupling, this lay the theoretical foundation of following study.
Chapter3: we analyze theoretically the diffraction of a one-dimensional reflective grating onthe basis of the scattering theory, and discuss in detail the distribution of the diffraction ordersand the number of the visible diffraction orders. The relationship of the diffraction order and thegrating period and the incident angle is presented in the form of the inequality, and the number ofthe visible diffraction orders can be determined by the incident angle and the grating period.
Chapter4: we numerically simulate the distribution of transmission field by Finite differencetime domain (FDTD), calculate the distribution of transmission field of different grating, andfind that distribution is completely different. The distribution of transmission field varyperiodically, we discuss the mechanism of near field according to the distribution of interferencefringe, verify the existence of evanescent wave, and calculate the distance between interferencefringes.
Chapter5: with a microscopic imaging system composed of microscopic objective, lens andCCD, we observe the complicated structures in the speckle fields on the surface of rough screen.We find that such structures contain ridge stripes, large platform like grains, and shivy grains,exhibiting multiple scales in size and multiple fractalities, which have not been observed in theconventional far field speckles. Simulations based on the Green’s integral and the Kirchhoffapproximation of wave diffractions shows these structures are formed by the different parts ofthe rough surface. The experimental curve of the autocorrelation function of the speckle intensity includes the three parts of the central peak, the transition part and the long tail part. Using thesum of self-affine fractal models with different scales and fractalities, we propose theoretically atriple-scale autocorrelation function to describe the speckle field. Fit of this autocorrelationfunction to the experimental curve gives the values of such parameters as average speckle sizesand fractalities in different scales of the speckle structures.
Chapter6: we experimental studies on speckles produced by the rough silver films. Thespeckles on the rough glass and silver surfaces are measured with a microscopic imaging system.The structures of speckle patterns have the characteristics of fractals and multi scaled sizes. Wefind that with the increase of the silver film thickness, the contrast of the speckles increases, andthe intensity probability density functions gradually transit to exponential decay. We calculate theglobal and the local correlation functions of the speckle patterns, and find that both the fractalexponent and correlation length of the small sized speckles decrease with the thickness of thesilver films. We use the mechanisms of rough dielectric interface scattering and random surfaceplasmon waves to give the preliminary explanations for the evolutions of the speckles.
In chapter7, we acquire the interference speckle patterns of the random glass and the randomsilver film samples by the experiment systems with the one used as object light with amicroscopic objective MO for collecting and imaging the speckles on the surface of samples andthe other one used as reference light wave which is expanded and filtered by spatial pinhole filter.By the Fourier transform method, the first order spatial frequency spectrum, the amplitude of theintensity including the real and the image and the phase of speckles can be experimentallyextracted. With the phase vortices distribution, we can see that the number of the vorticesbecomes larger with the increasing of the thickness of the silver film. Surface plasmon polaritonscan be excited and scattered, and then may be coupled by the rough silver and air interfaceradiate into the air-side space in silver films. Surface plasmon polaritons can interfere with thewaves scattered by the rough glass to form the speckles. The vortices produced by theinterference of the surface plasmon waves and the waves scattered by the random screen can bedivided into holonomic and nonholonomic, and their symbols are also studied. The specklevortices densities are increasing with the thickness of the silver films. The pair correlationfunction is larger in smaller correlation length with the increasing of the silver film, and thevalues of the pair correlation functions approach to one constant value. The charge correlationfunctions are smaller than the pair correlation functions, and the values of the charge correlationfunctions are near to0with the opposite effects of the positive and negative charges. The averageeccentricities for different thickness of the silver film deviate from the Gaussian speckles.
In chapter8, we sum up the main conclusions and the innovations of the dissertation, and briefly introduce the in-depth researches we will conduct.
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