Bessel-Gaussian光束在分数傅里叶变换面上的光强分布

利用广义衍射积分方法,研究了Bessel-Gaussian(BG)光束的分数傅里叶变换特性,推导出了BG光束通过分数傅里叶变换光学系统后,光场分布的解析公式,利用该公式对BG光束经分数傅里叶变换后光强的分布规律进行了数值分析。研究结果表明,分数傅里叶变换阶数p对BG光束的光强分布有明显影响,光强分布随分数傅里叶变换阶数p呈周期性变化。     

利用分数傅里叶变换设计衍射光学元件

本文讨论了分数傅里叶变换与菲涅耳衍射的关系,提出球面衍射过程就是一种具有尺度因子的分数傅里叶变换,并应用分数傅里叶变换进行衍射光学元件的设计。     

光腔的分数付里叶变换描述

运用矩阵光学技巧,球面镜光腔的往返一周光束变换矩阵可分解为两矩阵之积,它们各对应于一分数付里叶变换,因而光腔的振荡本质就是不断作用分数付里叶变换的过程。其稳定条件和束腰位置可用分数阶次描述,分数阶次可为复数。同时,给出了可能的拓展。     

基于角谱分析的分数傅里叶变换数值模拟算法

从分数傅里叶变换的表达式入手，分析了分数傅里叶变换与菲涅尔衍射积分之间的关系，针对采用衍射积分的方法计算分数傅里叶变换的局限性，提出了基于角谱分析的数值模拟方法。文中给出了计算方法的理论描述和计算实例。     

菲涅耳衍射系统的分数级传递函数

基于分数傅里叶变换与菲涅耳衍射的等效性和线性系统理论,给出了菲涅耳衍射系统在分数傅里叶变换下光学传递函数的数学表达式,分析了其基本特征,阐述了其物理意义,证明了常规傅里叶变换下的光学传递函数为分数传递函数的特例,对光学分数傅里叶变换在光学测量、信息处理和像质评价等的应用具有实用价值。计算机模拟文验验证了结论的正确与可行。     

菲涅耳衍射的分数傅里叶变换分析

基于菲涅耳衍射与分数傅里叶变换的关系，得出了描述菲涅耳近似下光波传播的光学分数傅里叶变换基本公式，并用分数傅里叶变换相加性证明了球面波的传播过程。进一步完善了分数傅里叶光学理论及分数傅里叶变换在物理上表示光波的传播。     

板条激光器用光腔的模式计算:快速傅里叶变换法

本文使用快速傅里叶变换法对三维光腔衍射积分方程作了数值解,用以说明板条固体激光器用新型棱镜腔的模式特性.     

会聚球面波照明下由菲涅耳衍射实现分数傅里叶变换

提出了在会聚球面波照明下,用菲涅耳衍射实现分数傅里叶变换的光学装置。定量得出了为实现分数傅里叶变换系统结构参数应满足的条件。分析表明,利用该系统可实现任意阶分数傅里叶变换。     

分数傅里叶变换与菲涅耳衍射的等效性

用波前相因子判断法,分析了分数傅里叶变换频变分布与球面波照明物体的自由空间菲涅耳衍射光场分布的等效性,给出了分数傅里叶变换与菲涅耳衍射相互转化的约束条件。结果表明：分数傅里叶变换是适应于菲涅耳衍射的数学工具。计算机模拟实验证明了结论的可靠与可行。     

单透镜成象的分数傅里里叶变换分析

利用描述光波傍轴传输的光学分数傅里叶变换基本关系式,对单透镜系统进行分析,结果表明,单透镜系统可实现任意阶分数傅里叶变换,Lohmann第一类光学分数傅里叶变换装置是其特例,单透镜成像过程是进行阶次为π的分数傅里叶变换,进一步表明光学分数傅里叶变换的物理实质是光波的菲涅耳衍射。     

A canonical formulation for analyzing multielement unstable resonators

A simple but general formulation for the unified analysis of many different varieties of unstable optical resonators is obtained by expressing the round-trip Huygens' integral for the resonator in terms of the round-trip paraxial ray matrix. Complicated multielement resonators, ring resonators, and unstable resonators with variable-reflectivity output mirrors are thereby all reduced to a single equivalent collimated-beam diffraction problem. Essential assumptions in the analysis are that all elements in the resonator obey paraxial ray theory and that there is only one significant output coupler or limiting aperture per round trip inside the resonator. The only parameters needed to describe an arbitrary unstable resonator in this formulation are the round-trip magnificationMand either the equivalent Fresnel number Neqor else an equivalent collimated Fresnel numberN_{c} = [2M^{2}/(M^{2} - 1)] N_{eq}, plus for variable-reflectivity mirrors a specification of the mirror reflectivity profile.     

分析光学谐振腔的矩阵方法(1)

本文总结了将矩阵方法用于研究光腔问题的一些新的进展情况。证明了在普遍情况下描述光腔主要特征的光束参数、失调灵敏度等都能表示为ABCD矩阵元或光腔g参数的形式。对一些典型的光腔,例如含热透镜的望远镜腔(TRTL)、交叉棱镜腔(CPR)、相位共轭腔(PCR)和共焦型多元件非稳腔(CMUR)等作了详细的分析和讨论。     

包含光阑的激光谐振腔模式

用光线矩阵方法研究了两类带有光阑的谐振腔。对包含软边光阑的腔,从衍射积分方程出发,求出了本征模式的普遍解析解。对包含硬边光阑的腔,用适当孔径的高斯光阑代替实际小孔,得到模式的近似解。用于分析常见的小孔选模腔、自孔径选模腔及包含光阑的热稳腔等,所得结果和实验测量值良好地相符。     

非轴对称光腔的矩阵光学分析

用矩阵光学理论对一般非轴对称光学谐振腔进行了研究,得出基模本征解。讨论了约束稳定、非约束稳定及准约束稳定的条件。指出这种腔在一般情况下存在双解。所得结果适用于多元件非轴对称光腔,具有普遍性。     

Design and Cold Tests of Asymmetric Quasioptical Resonators

This paper presents the design and test of asymmetric quasioptical resonators for gyrotron applications, where most of the diffraction output coupling comes from the smaller of two mirrors. A computer code based on scalar diffraction theory is used to calculate the resonator losses and the electric field near the mirrors. Resonators with mirror separations approaching confocal have reduced side lobes in the diffraction patterns, which should allow for better power transmission and focusing. Cold tests have been performed at 94 and 141 GHz to measure the quality factor of the asymmetric resonators as a function of mirror separation and mirror misalignment. Typical resonator parameters include 65 cm mirror separation, 1-3% output coupling and 85% of the losses from the small mirror. A half-symmetric resonator with one flat and one curved mirror has also been investigated. The calculated values of Q are in reasonably good agreement with the cold test measurements.     

Unstable optical resonators for laser applications

A simple geometrical analysis has been developed which describes the lowest-order transverse mode of any large-Fresnel-number optical resonator located in the unstable or high-loss region of the resonator mode chart. Such resonators include, for example, resonators in which one or both of the mirrors are divergent spherical surfaces. The lowest mode in such a resonator is assumed to consist of two oppositely traveling divergent spherical waves which uniformly illuminate the end mirrors. The centers of curvature of these spherical waves do not, in general, coincide with the mirror centers of curvature, but are found by requiring that each center be the image of the other upon reflection from the appropriate mirror. The resonator losses are found from purely geometrical considerations, and are given by simple analytical expressions. These losses turn out to be independent of the mirror sizes, so that hyperbolic universal equiloss contours can be drawn on the resonator mode chart. The losses agree well with more exact results obtained by Fox and Li for a few specific cases. Experimental results in good agreement with the analysis have been obtained using a ruby laser rod having a divergent spherical surface ground directly onto one end of the laser rod. Unstable resonators, particularly the "Cassegrainian" unstable configuration used in the experiments, appear potentially useful for diffraction output coupling applications, and possibly also for transverse mode control, in ruby and other high-gain lasers.     

关于等价共焦腔方法的讨论

一、概述稳定球面两镜腔的模式理论是建立在其与共焦腔等价的基础上的.在许多文献中,为了证明等价共焦腔存在的唯一性,都假设稳定球面两镜腔本征模式的等相位面曲率半径ρ_(Gi),在腔镜处等于腔镜的曲率半径ρ_i:ρ_(Gi)=ρ_i (1)由于上式并不普遍成立,因此文献[1]的作者对等价共焦腔方法提出质疑.鉴于这个问题的重要性,有     

高斯反射率方形平凹腔激光模场的有限元分析

利用柯林斯公式和边界有限元方法，将方形球面镜腔的衍射积分方程转化为矩阵方程，并对高斯反射率方形平凹腔的模场分布进行了数值计算。研究结果表明，高斯反射率方形平凹腔具有较好的选模性能，可以应用于高功率激光器以获得高质量的激光光束。     

高斯反射平凹二维腔横模选择特性的有限阶矩阵分析

本文利用自再现理论,将高斯反射二维腔的衍射积分析方程转化为有限阶国方程,对高斯反射平凹二维腔的横模选择特性进行数值分析,研究结果表明,高斯反射平凹二维腔选横模的性能优越,可应用于大功率激光器,从而为激光材料表面处理提供优质的激光光束。     

高斯镜平凸非稳腔本征模场的有限元数值计算

为了研究激光在高斯镜平凸非稳腔中的模式和相位特征,在SIEGMAN分析多元件非稳腔的理论基础上,采用有限元数值方法计算耦合输出镜镜面反射率为高斯分布的圆镜平凸非稳腔本征模场分布。将光场在腔内一次往返的ABCD系数代入惠更斯-基尔霍夫衍射积分方程,可以写出光场往返一次的衍射积分方程。将镜面分割成若干个等宽圆环,把衍射积分方程转化成矩阵相乘形式,经过数值计算,得到理想空腔和非共轴空腔优先起振的光场本征模式分布结果与相位特性。计算结果表明,当合适选择输出镜半径与高斯反射率分布,可以得到光斑半径为0.3cm的基模高斯光束输出,此计算结果与实验结果相符。同时也讨论了耦合输出镜对光束质量的影响。