部分空间相干光经准均匀介质的散射

基于一阶波恩近似,研究了部分空间相干平面光经准均匀介质的散射特性,得到了远场散射光谱强度和光谱相干度的解析表达式。讨论了入射光的空间相干性和介质特性对散射场光谱强度和光谱相干度的影响。比较了入射光是完全相干光和部分相干光时,散射场光谱强度和相干度的区别。研究结果表明:入射光的空间相干性对散射场光谱强度的分布有重要影响;随着入射光空间相干长度的增大,光谱宽度减小;光谱相干度随着入射光束腰宽度或介质有效半径的增大而减小。当准均匀介质的有效半径和相干长度、入射光的空间相干长度满足一定条件时,散射光是完全相干光。     

A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory

We derive the spectral dispersion law for the virtually imaged phased array (VIPA) based on paraxial wave theory using the Fresnel diffraction analysis. The validity of the dispersion law is verified by comparison with experiments. This spectral dispersion law is compared to a previous law based on plane wave theory. At small incident angles where the VIPA provides its largest spectral dispersion, the paraxial wave law provides a much better fit to the data than the plane wave law does.     

湍流对部分相干光光谱移动的影响

Wolf效应，即部分相干光除满足定标律之外，即使在自由空间中传输时其光谱一般也会发生变化，是一类著名的相关诱导光谱变化现象。以高斯-谢尔模型(GSM)光束作为部分相干光的典型例子，研究湍流对高斯-谢尔模型光束光谱移动的影响。基于部分相干光的传输定理，并考虑湍流的存在，推导出了高斯-谢尔模型光束通过湍流介质的光谱公式，并作了数值计算。研究表明，无论定标律是否满足，湍流都会影响高斯-谢尔模型光束的光谱。湍流越强，与无湍流情况比较光谱移动越大。特别是，若不满足定标律时轴外光谱还会出现分裂。高斯-谢尔模型光束在湍流介质中的光谱移动由光束的空问相干性、折射率结构常数Cn^2和位置等参量决定。     

矢量涡旋光束经光阑-透镜系统的OAM与偏振特性

与标量涡旋光束不同,矢量涡旋光束同时具有各项异性的空间偏振分布和螺旋相位分布,并携带与相位分布有关的轨道角动量(Orbital angular momentum,OAM)。根据柯林斯衍射积分理论,得到了傍轴近似条件下矢量涡旋光束的OAM密度,实验采集了矢量涡旋光束通过光阑-透镜系统后的光场,详细讨论了光阑截断参数以及光阑-透镜间距等参数对矢量涡旋光场及其OAM密度的影响。结果表明:相比标量涡旋光束,矢量涡旋光束OAM通过光阑系统后随传输距离的衰减更慢,受光阑截断参数影响更小。矢量涡旋光束偏振态不受光阑-透镜系统影响,截断参数大于4.2时,轨道角动量密度和光强不受截断参数影响。在透镜焦点位置处,OAM密度达到最大值。研究结果为矢量涡旋光束OAM特性的应用提供理论依据。     

Evaluation of beam fields reflected at a plane interface

The complex ray method is employed to calculate the fields of a Gaussian beam reflected at a plane interface between two different media. A lateral wave is included in the region of total reflection. To simplify the calculation, a paraxial approximation is employed when the observer is located near the beam axis. These calculations all fail when the beam axis and observer simultaneously approach the critical angle, the criterion of failure being a parameter called the numerical distance. The correct solution in the transition region is generated by a parabolic cylinder transition function. Detailed numerical comparisons with a reference solution generated by numerical integration of the exact spectral integral representation provide an assessment of the validity of the various formulations and approximations.     

光在纤维介质中传播的研究

利用光线追踪方法在近轴近似下模拟了高斯光束在不同折射率分布纤维状介质中的传播。针对等离子体对激光的导引和离焦现象 ,以及应用激光操纵粒子的空心环状光束产生进行了模型化分析和讨论。     

A General Spectral-Domain Formulation of the Electromagnetic Scattering by a Perfectly Conducting Circular Cylinder

A full-wave method for the two-dimensional scattering problem by a perfectly conducting circular cylinder is presented, providing an exact solution for the Helmholtz equation in very general cases. The method is based on the Fourier series expression of the boundary conditions (Dirichlet and Neumann) generated by an arbitrary, finite-power, incident beam, and the analysis is performed in the complex plane of the analytic continuation of a space spectral variable. This approach allows us to define an analytic continuation for cylindrical wave expansions, working with lossy propagation media and with a full incident spectrum, including inhomogeneous waves, both in E and in H polarization. Convergence of the modal expansion is investigated, to verify that very weak hypotheses are needed, and no geometrical or paraxial approximation is required. Extact expressions for the expansion coefficients are given, in terms of complex intergrations involving the Fourier spectrum of the incident beam.     

Coherence-Based 3-D and Spectral Imaging and Laser-Scanning Microscopy

The basics of three-dimensional (3-D) and spectral imaging techniques that are based on the detection of coherence functions and other related techniques are reviewed. The principle of the 3-D source retrieval is based on understanding the propagation law of optical random field through the free space. The 3-D and spectral information are retrieved from the cross-spectral density function of optical random field or numerical calculation of the inverse propagation of the cross-spectral density. We will first introduce the coherence-based spectral tomography techniques with low-coherence light sources. These techniques limit their scheme of coherence detection only along the optical axis and some of them achieve simultaneously the high resolution and high speed of detection taking advantage of an imaging lens. We then provided explanations of the principle of 3-D source retrieval that is based on the propagation law of optical random field through the free space along with the introduction of the numerical holography and computed tomography techniques. We will lastly show 3-D spectral imaging schemes with the concurrent laser-scanning cross-sectioning techniques: one is the confocal laser scanning microscopy and the other is the two-photon laser-scanning fluorescence microscopy.     

非傍轴厄米-高斯光束及其高阶修正

使用级数修正公式研究了非傍轴厄米高斯光束的传输。用数值计算例子说明了修正公式的适用范围。结果表明,在束宽可与波长相比时,修正公式是发散的,并分析了发散的原因。     

湍流大气中传输光波的波相位结构解析函数

在湍流大气对传输光波调制的双尺度湍涡(大尺度湍涡和小尺度湍涡)近似下,研究了用于计算描述湍流大气中传输光波相干长度变化的核心函数(互相干函数)的关键因子波结构函数(WSF),通过建立包含不同尺度湍流因子的折射率起伏谱密度函数,导出了可以用于精确理论分析平面波与球面波在湍流大气中传播时所产生的诸如到达角起伏和相干性变化等效应的波相位结构函数的精确解析式,同时给出了便于数值计算的近似误差在2%范围以内的波相位结构函数的精确渐近表达式。     

Rate of Convergence in Approximating the Spectral Factor of Regular Stochastic Sequences

Common methods for the calculation of the spectral factorization rely on an approximation of the given spectral density by a polynomial and a subsequent factorization of this polynomial. It is known that the regularity of the stochastic sequence determines the achievable approximation rate of its spectrum. However, since the approximative polynomial should be factorized, it has to be positive. It is shown that this restriction on the approximation polynomial implies a limitation on the approximation rate for linear methods whereas for nonlinear methods the optimal approximation rate can still be achieved. This has also consequences for the rate of convergence of the spectral factor, which is investigated in the second part. There, a lower and an upper bound for the error in the spectral factor is derived, which shows the dependency on the approximation degree and on the regularity of the stochastic sequence. Finally, if the spectral density is given only on a finite set of sampling points, no linear approximation method exists such that the error in the spectral factor can be controlled by the approximation degree.      

ABCD定律的推广

高斯光束的传输可用ABCD定律来描述。本文利用光束传输流体模型理论讨论了任意傍轴光束的传输,从而获得推广了的ABCD定律。     

A 2D Gaussian-Beam-Based Method for Modeling the Dichroic Surfaces of Quasi-Optical Systems

In this article, we propose an approach in the spectral domain to treat the interaction of a field with a dichroic surface in two dimensions. For a Gaussian beam illumination of the surface, the reflected and transmitted fields are approximated by one reflected and one transmitted Gaussian beams. Their characteristics are determined by means of a matching in the spectral domain, which requires a second-order approximation of the dichroic surface response when excited by plane waves. This approximation is of the same order as the one used in Gaussian beam shooting algorithm to model curved interfaces associated with lenses, reflector, etc. The method uses general analytical formulations for the GBs that depend either on a paraxial or far-field approximation. Numerical experiments are led to test the efficiency of the method in terms of accuracy and computation time. They include a parametric study and a case for which the illumination is provided by a horn antenna. For the latter, the incident field is firstly expressed as a sum of Gaussian beams by means of Gabor frames.     

锥形发散梯度折射率介质的激光束传播特性

本文从近轴波动方程出发,导出在锥形发散梯度折射率介质中传播的高斯光束光斑半径、波面曲率半径及光强分布的解析式,讨论了激光束的发散传播特性。     

光漂白法制备聚合物PMMA/DR1啁啾光栅波导透镜

本文分析了一种平面波导啁啾光栅的透镜性质。并在旁轴近似条件下求出了这种光栅透镜的焦距。首次采用了光漂白方法在PMMA／DR1平面波导上制备出了啁啾光栅，从实验上观测了这种啁啾光栅对衍射光的透镜效应。     

光阑约束超几何激光束的传输特性

基于广义惠更斯-菲涅耳衍射积分和圆孔光阑函数展开为有限复高斯函数之和的方法,导出了超几何激光束通过有圆孔光阑约束的近轴ABCD光学系统传输的近似解析表达式,并对其传输特征进行了数值计算和分析。研究结果表明,超几何激光束光强的分布及其衍射效应与光阑的孔径大小、传输的距离以及光束参数等因素密切相关。此外,文中采用的近似解析方法与直接利用衍射积分计算相比,具有更高的计算效率,可以大大节省计算机时。     

纵向场能量与光束的傍轴标量近似判据

对于一个傍轴标量光场ε＝［εｘ，０，０］，考虑其一阶纵向场修正项的影响时，光场的纵向场能量Ｅｚ是一个不随光束截面位置ｚ变化的守恒量，其值完全决定于傍轴场（εｘ）的分布情况。纵向场能量Ｅｚ的大小反映了光束的傍轴标量近似程度，定义一个近似因子η用来作为衡量光束的这一特征的量化判据；其值越小，近似程度就越好。以超高斯光束为例，讨论了其一阶纵向场能量及傍轴标量近似等问题     

非傍轴部分相干修正贝塞尔-高斯光束的传输

利用广义瑞利衍射积分公式和部分相干光理论,推导了任意阶非傍轴部分相干修正贝塞尔-高斯光束在自由空间传输的解析表达式.作为特例,给出了非傍轴部分相干修正贝塞尔-高斯光束的远场公式和傍轴部分相干修正贝塞尔-高斯光束的传输方程.数值计算和分析表明,f参数对光束的非傍轴特性有重要影响,此外,相干度也影响部分相于修正贝塞尔-高斯光束的非傍轴行为.     

线性偏振和方位偏振Bessel-Gauss光束的传输特性比较

利用Collins衍射积分公式,给出了线性偏振Bessel-Gauss和方位偏振Bessel-Gauss光束通过ABCD轴对称光学系统的解析表选式。作为应用,对该两类光束通过单透镜系统的传输特性作了数值计算比较,并对结果作了分析和讨论.     

Focusing of a light beam of Gaussian field distribution in continuous and periodic lens-like media

The behavior of a light beam traveling in continuous or periodic lens-like media is considered. The light beam is assumed to be launched with a Hermite-Gaussian or Laguerre-Gaussian field distribution. Under suitable conditions and for most focusing media we find that the beam center follows a paraxial ray, and an independent equation determines the motion of the beam radius. The form of the field distribution does not change. In a continuous inhomogeneous focusing medium, the beam cross section varies periodically in distance with a period half of that of the oscillatory motion of the beam center. In periodic media, a particular solution is found for the case when the beam propagates with a nearly constant cross section. Discussions include an acoustic lens-guide and a lens-guide using heat diffusion in a gas.