Algorithms for flattened Gaussian beams passing through apertured and unapertured paraxial ABCD optical systems

The propagation property of flattened Gaussian beams (FGBs) is studied based on the Collins formula, and analytical propagation equations for FGBs with and without an aperture are derived. It is shown that the closed-form expressions for the FGB of order N passing through paraxial ABCD optical systems without an aperture can be written as the combinations of Confluent Hyper-geometric Functions, and that the analytical equations for the FGB of order N passing through apertured paraxial ABCD optical systems may involve Error Functions. The proposed algorithms for the considered beams can save computing time, provide intuitive physical insights, and help to design optical systems. Our results are confirmed and illustrated with numerical examples.     

光阑对偏振高斯-谢尔模型光束偏振特性的影响（英文）

根据广义惠更斯-菲涅尔原理和Collins公式,基于复高斯函数展开法,推导出椭圆偏振的高斯-谢尔模型光束经过矩形光阑衍射后的交叉谱密度公式,结合斯托克斯矢量理论推导了椭圆偏振高斯-谢尔模型光束在接收平面的光强、偏振度、方位角和椭圆度的表达式,数值分析了光阑的孔径遮拦比对光强、偏振度及方位角和椭圆度的影响.结果表明,光阑的孔径遮拦比在近场区对经过光阑后椭圆偏振高斯-谢尔模型光束的光强和偏振特性有显著影响;随着传输距离的增大,光强和偏振特性受孔径遮拦比的影响减小,光强和偏振特性变化平稳.     

高斯-谢尔模型光束通过光阑像散透镜传输轴上光谱变化

从部分相干光的传输理论出发,研究了高斯-谢尔模型(GSM)光束通过光阑像散透镜传输轴上的光谱变化规律.结果表明,与光源光谱相比,高斯-谢尔模型(GSM)光束通过光阑像散透镜传输轴上光谱发生了中心频率的移动,这种现象被称为光谱位移.详细分析了透镜的像散、光束的空间相关性和光阑的截断参量对光谱变化的影响.数值计算表明,这些参量会对光谱移动产生比较大的作用.     

A detailed study of Mathieu-Gauss beams propagation through an apertured ABCD optical system

Using Collins formula and the expansion of Mathieu beams in terms of Bessel beams we derive the exact propagation equations of Mathieu-Gauss beams through an apertured paraxial ABCD optical system. A comparison between the exact propagation equations and the approximated ones, which are derived by expanding the circ function into a finite sum of Gaussian functions, is presented. The propagation characteristics of zeroth-order Mathieu-Gauss beams in (y-z) and (x-z) planes are analyzed with detailed numerical calculations. It is found that the profile of the propagated Mathieu-Gauss beam is similar to that of Bessel-Gauss beam. Furthermore, the focalization of the Mathieu-Gauss beams through a thin lens is illustrated and analyzed with numerical results.     

Approximate analytical representation of Wigner distribution function for Gaussian beams passing through ABCD optical systems with hard aperture

Based on the treatment that a rectangular function can be expanded as an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of the Wigner distribution function for a Gaussian beam passing through a paraxial ABCD optical system with hard-edged aperture is obtained. By numerical simulation, it is shown that the effect of the aperture on the Wigner distribution function is prominent. By comparing the analytical results with the numerical integral results, it is shown that this method of expanding hard-edged aperture into Gaussian functions with finite numbers is proper and ascendant. This method could be extended to study the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with hard-edged aperture.     

Composition of Fourier Integral Operators with Fold and Blowdown Singularities

ABSTRACT

The purpose of this work is to present results about the composition of Fourier integral operators with certain singularities, for which the composition is not again a Fourier integral operator. The singularities considered here are folds and blowdowns. We prove that for such operators, the Schwartz kernel of F*F belongs to a class of distributions associated to two cleanly intersection Lagrangians. Such Fourier integral operators appear in integral geometry, inverse acoustic scattering theory and Synthetic Aperture Radar imaging, where the composition calculus can be used as a tool for finding approximate inversion formulas and for recovering images.     

装有电路板孔阵矩形腔对快上升前沿电磁脉冲的屏蔽效能

 介绍了快上升前沿电磁脉冲的特性,用传输线法分析了孔阵矩形腔屏蔽效能的基本原理。将基本公式作进一步修正,使其能计算矩形腔内装有印刷电路板（PCB）的情形。对修正的传输线模型计算公式进行了扩展,使之能计算任意极化方向时的情况。计算和仿真结果表明: 当频率低于主谐振频率时,测量点离孔阵越近,屏蔽效能越差,同时低频段的屏蔽效能比高频段的要好;孔阵的屏蔽效能比相同面积单孔的要好;装有PCB腔体的屏蔽效能比空腔的要好,这在谐振区域内尤为突出;PCB板尺寸越大,屏蔽效能越好;屏蔽效能随极化角度的递增而增加;屏蔽体越小,屏蔽效果越好。     

正方形自聚焦透镜光线理论研究

针对正方形自聚焦透镜折射率分布特点,引入方向角概念,以平方律表征其折射率分布.从理论上研究了平方律折射率分布下正方形自聚焦透镜的光线轨迹方程,得到了子午光线表达式.结果表明,与传统径向自聚焦透镜相比,正方形自聚焦透镜的光线轨迹受光线入射方向角影响,会产生较大像差.得到了正方形自聚焦透镜数值孔径表达式,表明数值孔径并非常量,且与方向角密切相关.计算了中心轴上的最大数值孔径,方向角为0°时最小为0.405,方向角为45°时最大值0.5以上.     

相位翻转厄米-高斯光束的传输特性

将相位翻转高斯光束的概念推广到相位翻转高阶模光束.以相位翻转厄米-高斯光束为例,推导出相位翻转高斯光束通过近轴理想(无光阑)ABCD光学系统,以及带刀口和光阑的ABCD光学系统传输的递推方程,并用以研究相位翻转高斯光束的传输特性.特别是,得出对TEM1、TEM2和TEM3模相位翻转高斯光束,光阑效应可以忽略的条件分别是截断参量δ≥2.1,2.5和 3.0.