The equation for the quasi - continuous atom laser beam wave - function is given by schrodinger equation , the beam width , divergence curvature radius and quality factor were introduced to represent the atom laser beam whose transverse potential could be separated . for the conservative quality factor system in some direction , we can ge t the propagator of abcd formulation 本文在含时量子系统传播子的abcd形式理论的基础上，引入某一方向的束宽、发散角、曲率半径和品质因子等光束传输参数来表征横向势能满足x和y分量相互独立的原子激光的传输。
This article discussed ar modeling method , capon method , music method and mn method four kinds of high resolution algorithms principle and has separately made the computer simulation in the ideal situation to the above four algorithms . through the comparison , the beam width of high resolution algorithm is much narrower than conventional beamforming method . then unifies the actual utilization , discussed the influence of time delay unbalance , time domain sampling , plane wave supposition and array element with scope and phase not identically to the beamforming and made the computer simulation 本文首先讨论了ar模型法、 capon法、 music法和mn法四种高分辨率算法的原理,在理想的情况下分别对上述四种算法作了计算机仿真,通过比较,高分辨率算法的束宽比常规波束形成法窄得多;然后结合实际运用时的情况,重点探讨了延时失配、时域抽样、平面波假设和基阵的幅相不一致对波束形成的影响并做了计算机仿真。
The condition under which higher - order dispersive effects can be neglected is also discussed with numerical examples . 6 . based on the fourier optics , the focusing of ultrashort pulses by a silica lens in both cases of constant beam waist and constant diffraction length is studied considering dispersion of first , second and higher order , respectively 6 ，使用傅立叶积分变换法，在考虑透镜色差和高阶色散效应的较为一般情况下，分别研究了等束宽超短脉冲高斯光束和等衍射长度超短脉冲高斯光束通过硅玻璃透镜的聚焦特性。
In chapter 3 , the elegant hermite - cosh - gaussian beams as another special case in hermite - sinusodiol - gaussian family is introduced and its propagation properties through a first - order optical abcd system are investigated . an analytical solution of the elegant herimite - cosh - gaussian beam propagating through a first - order abcd system is derived , and correspondingly , the closed - form m2 - factor , the beam width , the curvature radius and the power in bucket are presented analytically . the numerical investigations are carried out and show that the m2 - factor of elegant hermite - cosh - gaussian beam is greater than that of elegant hermite - gaussian beams and less than that of hermite - gaussian beams approximately 本文得到的主要结果可归纳为：首次用强度矩的方法研究了hermite - cosh - gaussia ( hchg )光束，得到了hchg光束的束宽、曲率半径、 m ~ 2因子、瑞利距离等的解析表达式；用陡峭度和pib参数去衡量hchg光束的光束质量，找到了hchg光束在传输过程中影响光束质量的因素并得到了变化规律；证明了hchg光束在传输过程中的重心和对称性都会得到保持。
