光束

It was illuminated that the width of the centre bright fringe decreased along with the increasing width of the rectangular aperture when the effect of the aperture on the beam couldn't be ignored,however,the width of centre bright fringe step changed with increase of the size of the aperture when the effect could be ignorable,the width of the half maximum intensity of the centre bright fringe decreased along with the accretion of the width of the aperture and then it tends to a constant.

结果表明，当光阑对光束的衍射影响明显时，光束衍射场的中央亮条纹的宽度随着光阑边长的增大而减小；当光阑对光束的衍射影响极小时，中央亮条纹的宽度随着光阑边长的增加而阶跃变化，中央亮条纹强度的半最大值宽度随着光阑边长的增大而减小；当光阑对光束衍射影响极小时，中央亮条纹半最大值宽度趋近于一定值。

Chapter 2、When treat propagate problem of high power laser beams, ordinary assume beam to be ideal plane wave or Gaussian. Actually, beams is not ideal Gaussian or plane wave. The reason is that is phase aberraed and intensity nonuniform. In this chapter, we have developed a method on frequency conversion of aberrated beam. Based on statistical optics method and within the limits of thin crystal, we have studies on second harmonic generation of the phase aberrted beam. And the phase aberration is assumed to be a Gaussian random variable.

第二部分：在处理高功率光束传输问题中，通常假设光束为理想平面波或高斯型，而实际光束都不可能是理想的高斯光束或平面波，均会有一定的位相畸变及光强不均匀，本部分从统计光学的观点出发，在薄晶体近似下，建立了具有高斯型随机相位畸变光束倍频转换的一种统计描述方法，并对倍频转换光束的横向空间特性进行了分析。

By using Zernike polynomials to describe the wavefront distortion of beams, the propagation properties of the flattened Gaussian beams, super Gaussian beams, Gaussian beams and plane waves passing through an aberrated lens or an aberrated annular lens are studied based on the generalized Huygens-Fresnel diffraction integral.

以广义惠更斯—菲涅尔衍射理论为基础，采用Zernike多项式描述像差光束畸变波前相位，研究了平顶高斯光束、超高斯光束、高斯光束以及平面波通过像差透镜和环状像差透镜的传输。

In chapter 4, the influence of the wave-front curvature of Raman pulses on the measurement precision of gravitational acceleration in atom interferometers is analyzed with the method of a transmission matrix. It is shown that the measurement precision of gravitational acceleration is highly dependent on the spot size of the Raman pulse, the temporal interval between Raman pulses and the optical path difference of the two counter-propagating Raman pulses.

第四章运用高斯光束传输矩阵的方法计算了原子干涉仪实验中拉曼光束波前弯曲对重力加速度测量精度的影响，得出了精度与拉曼光束光斑大小，拉曼脉冲作用的间隔时间，以及拉曼光束光程差之间的关系。

These pulses include a Gaussian pulse, a hyperbolic secant pulse, a Lorentzian pulse, a Poisson spectrum pulse, a asymmetrical hyperbolic secant pulse, a rectangular pulse, a chirped Gaussian pulse and a chirped super-Gaussian pulse.

本论文基于上述提及的基本概念、分析方法和衍射积分理论，以描述超短脉冲光束的数学物理模型(包括超短脉冲高斯光束、超短脉冲贝塞耳—高斯光束、超短脉冲拉盖尔—高斯光束和超短啁啾脉冲光束等)为主要研究对象，研究超短脉冲光束在自由空间、色散介质和通过光阑的传输特性和位相奇点附近的光谱异常行为。

The general analytical expression of the deformed high-order Bessel beam and its propagation properties of in self-focusing lens self-imaging process in free space wer.

从产生高阶贝塞尔光束的典型光路着手，通过将高阶贝塞尔光束分解为高阶贝塞尔余弦光束和高阶贝塞尔正弦光束，利用柱坐标下的Collins公式，分析了变形高阶贝塞尔光束的解析表达式和在自聚焦透镜中的传播。

Secondly, three kinds of mathematics model of optical vortex beams were introduced here. Then the propagation dynamics of optical vortex beams through the non-axis symmetry system is studied, this chapter includes the introduction of the symmetry vortex beam and the non- symmetry vortex beam, the deduction of the Collins diffract integral formula for the non-axis symmetry system, and the transformation of the vortex beam passing through the non-axis symmetry system has been described by using the numerical simulation. Then the general calculation for the orbit momentum of vortex beams, the matrix form for the orbit momentum of vortex beams, and the photon method to describe the orbit momentum of vortex beams are also introduced here. Finally, the interference about optical vortex beams was studied.

本文对涡旋光束进行了较为全面的介绍和研究，主要内容包括：（1）光学涡旋光束的基本理论，主要是介绍了单个光学涡旋光束在柱坐标中的一些表征，涡旋光束的奇异相位和光学涡旋的相位结构；（2）光学涡旋光束的三种数学模型；（3）光学涡旋光束在非轴对称光学系统中的传播动力学，其中介绍了对称涡旋光束与非对称涡旋光束，推导了非轴对称光学系统的 Collins 衍射积分公式，并利用计算机模拟图描述了对称涡旋光束经过非轴对称光学系统后涡旋形态的改变；（4）涡旋光束轨道角动量的一般计算，涡旋光束轨道角动量的矩阵形式，光子法描述涡旋的轨道角动量；（5）涡旋光束的干涉。

The mutual connection that analyses Bessel beam of light and Bessel-Gauss beam of light theoretically reachs distinction, beam of light of Bessel of numeric imitate ideal and Bessel-Gauss beam of light are in the radial light intensity of aleatoric plane distributings, and the influence that smooth waist radius and syntonic antrum antrum grow pair of output Bessel-Gauss beam of light.

梗概： 理论分析Bessel光束和Bessel-Gauss光束的相互联系及区别，数值模拟理想Bessel光束和Bessel-Gauss光束在任意平面的径向光强分布，以及光腰半径和谐振腔腔长对输出Bessel-Gauss光束的影响。

It is composed of above two mircoprisms dislocated and closely arranged, each microprism has three all-reflecting surfaces, N microprisms change the light beam into N vertical closely-arranged light beam groups, the distance between the light beam groups can be controlled by the difference of optical distance of the light beam between the first and second reflecting surfaces of the two adjacent microprisms and after shaped, the light beam does not change the advancing direction.

本整形器是由两片以上棱镜错位紧密排列构成，每片微棱镜有三个全反射面，N片棱镜使得光束变成N个垂直紧密排列的光束组，光束间的距离可由相邻两棱镜的第一反射面和第二反射面间光束光程差控制，并且整形后光束不改变前进方向。

It is shown that the M×N ChG beams in turbulent undergo three stages of evolution with increasing propagation distance,and turbulence accelerates the evolution of three stages.The turbulence results in a spreading and degradation of the maximum intensity in the far field.But β-parameter decreases with increasing beam numbers M,separate distances xd and beam parameter δ.And there exists optimal values of xd and δ,and SR of the corresponding M×N ChG beams reaches its maximum.

研究表明：在湍流大气中，双曲余弦高斯列阵光束的传输将经历三个阶段的变化，并且湍流使得光束传输经历三阶段的进程加快；湍流导致双曲余弦高斯列阵光束扩展、最大峰值光强下降，但是，β参量随光束数目M、相邻子光束间距xd和光束参量δ的增加而减少，即光束扩展受湍流的影响减小；并且，存在最佳xd和δ值使得Strehl比取得极大值。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。