截断非傍轴标量高斯光束的传输特性

基于精确光强定义下非傍轴标量光束的二阶矩理论,计算了不同束腰及光阑孔径条件下截断非傍轴标量高斯光束的束腰半径、远场发散角以及质量因子等光束传输特性,并将截断非傍轴标量高斯光束与自由高斯光束和平面波圆孔衍射光束进行了比较.数值计算表明截断参量的不同对截断高斯光束的传输特性影响很大.当R2ω0时,截断高斯光束与高斯光束在自由空间传输特性趋于一致,因此在精确光强定义下,对于非傍轴标量光束来说,当光阑孔径大于2倍束腰时,可以不考虑光阑对高斯光束的衍射作用.当R0.3ω0时,截断高斯光束传输特性趋于平面波通过圆孔的衍射曲线.因此,在这种情况下,可以将高斯光束作为平面波处理.只有当光阑孔径介于0.3倍束腰和2倍束腰之间时,需要同时考虑光阑孔径和高斯束腰对衍射的影响.     

平顶高斯光束经含失调圆孔光阑的失调光学系统的传输特性

为分析平顶高斯光束通过光学系统传输时圆孔光阑失调和光学元件失调对平顶高斯光束传输特性的影响,利用失调圆孔光阑的近似展开式和适用于失调光学系统的广义衍射公式,得出了平顶高斯光束经含失调圆孔光阑的失调光学系统传输的近似解析式,给出了输出光束场分布与光束参量、光阑孔径尺寸、光阑和光学元件失调量等的定量关系.针对特定光学系统定量分析了各失调量对输出光束场分布的影响,结果表明各元件失调都对输出光束强度分布产生较大影响.但在各失调量较小的情况下,透镜失调对输出光束传输特性的影响比光阑失调对输出光束传输特性的影响更明显.     

平顶高斯光束经含失调圆孔光阑的失调光学系统的传输特性

为分析平顶高斯光束通过光学系统传输时圆孔光阑失调和光学元件失调对平顶高斯光束传输特性的影响,利用失调圆孔光阑的近似展开式和适用于失调光学系统的广义衍射公式,得出了平顶高斯光束经含失调圆孔光阑的失调光学系统传输的近似解析式,给出了输出光束场分布与光束参量、光阑孔径尺寸、光阑和光学元件失调量等的定量关系.针对特定光学系统定量分析了各失调量对输出光束场分布的影响,结果表明各元件失调都对输出光束强度分布产生较大影响.但在各失调量较小的情况下,透镜失调对输出光束传输特性的影响比光阑失调对输出光束传输特性的影响更明显.     

椭圆孔径与轴棱锥系统产生带状近似无衍射光束

基于菲涅耳衍射理论,硬边孔径的复高斯函数展开法及稳相法研究了椭圆孔径与轴棱锥系统的光束传输特性,推导出了高斯平面波经轴棱锥衍射后产生的无衍射光场的表达式,数值模拟了不同传播距离处的截面光强分布,并设计了实验进行验证。用电荷耦合器件(CCD)拍摄得到不同传播距离处的光强分布。实验和模拟结果均表明平面波经椭圆孔径和轴棱锥系统后可获得具有马丢光束特征的带状无衍射光束。研究结果对无衍射光束在光学无损检测、条码扫描等应用上具有重要的指导作用。     

方形光阑限制高斯光束的传输变换

对基模高斯光束经方形光阑限制光学系统的光斑传输变换规律进行了论述．对于任一共轴光学系统,在不考虑有效光阑前面元件的衍射和变换时,考察入射光经有效光阑和其后面的元件发生衍射,根据柯林斯公式,对于非成像光学系统,采用稳相法得到出射光场的振幅分布;对于成像光学系统,根据像传递原理得到出射光场的振幅分布,最后得出出射光斑大小由有效光阑边长与光阑处高斯光束腰斑大小比较决定的结论．     

高光束质量高斯非稳腔固体激光器研究

为了获得高光束质量的脉冲固体激光输出,研究了高斯非稳腔固体激光器的模式分布。运用边界有限元法将谐振腔内光场衍射积分方程转化成矩阵方程组,模拟分析了平凸高斯非稳腔内光阑位置、孔径大小以及高斯镜参数对输出光束模式的影响。基于理论模拟结果对激光器结构参数进行了优化,分别测量了腔内不同光阑位置和孔径下的激光器输出光束振幅及模式分布情况。在光阑半径为1 mm、光阑距高斯镜为150 mm、泵浦电压为900 V的实验条件下,光束质量M_x~2=1. 9、M_y~2=2. 3,激光最大输出能量为280 mJ的高光束质量激光输出。实验结果表明,在腔内加入选模光阑以及优化高斯镜参数可以进一步改善腔内模式分布,获得高光束质量激光输出,这与理论模拟结果基本相符。     

光阑对高斯谢尔模型光束偏振特性的影响

根据光束的相干-偏振矩阵理论,应用柯林公式对部分相干光经光阑衍射后的轴向、横向偏振特性从近场区到远场区的演化规律进行了详细的数值计算。经研究表明,由于光阑的衍射效应,使得高斯谢尔模型光束的偏振出现非均匀分布,光束偏振度沿轴向、横向分布出现多峰振荡现象,并且随着光阑截断参数的减小、光束空间相干长度的增大和传输距离的增大,多峰振荡逐渐增强。光束在自由空间沿轴向传输时,在近场区偏振度分布均匀,与源平面相同,随着传输距离的增大和空间相干长度的减小,偏振度沿轴向分布逐渐增大,无振荡现象。     

圆孔受限波差高斯光束的远场近似及发散度分析

引入复高斯函数对衍射受限的圆孔进行了复高斯分解,得到了波差高斯光束远场衍射的近似解析式。在各种参量条件下,近似解析式所表示的衍射图样与严格的夫琅和费衍射积分的衍射图样完全一致,这表明用此解析式表征远场衍射是正确的。它的形式相对简单,为计算带来极大的方便。基于此,对有波差的高斯光束的远场发散度进行了深入的研究,检验了确定参量的光束随距离的改变而发散度不被改变的特性;同时,探讨了在圆孔限制下,发散度随高斯光束的束腰及波差的改变而变化的关系曲线,结果表明,这两个参量是影响发散度的主要因素。     

椭圆高斯光束产生近似无衍射Bessel-Gauss光

研究了轴棱锥聚焦像散椭圆高斯光束的光场分布特性,根据菲涅耳衍射积分理论导出了椭圆高斯光束经轴棱锥衍射后的光场分布,通过数值积分给出椭圆高斯光束经轴棱锥聚焦后的近轴光场强度分布情况,将其与圆高斯光束产生的近似Bessel-Gauss场进行比较,发现椭圆高斯光束经轴棱锥聚焦后的光束在一定的传播距离内也具有无衍射特性,且轴上光强分布与圆高斯光束产生的Bessel-Gauss光束的轴上光强分布具有相似的形式,而这种无衍射光场的强度在垂直于光轴的平面上不再是柱对称分布。根据近轴球面波产生近似Bessel光束的最大无衍射距离公式计算了椭圆Bessel-Gauss光束在子午面和弧矢面上的最大无衍射距离,整个光束的无衍射距离由入射到轴棱锥上的椭圆光斑短轴方向的尺寸决定。     

部分相干平顶光束经光阑衍射的偏振特性

根据光束的相干-偏振矩阵和传输理论,对部分相干平顶光束经正多边形光阑衍射的偏振特性进行了系统的研究.给出了部分相干平顶光束偏振度传输公式,并将高斯-谢尔模型光束以及部分相干平顶光束在自由空间传输的偏振度作为特例统一于一般表达式中.研究表明：部分相干平顶光束经光阑衍射的偏振特性与光阑截断参数、光束的空间相干性、衍射角、传输距离、平顶光束的阶数有关. 关键词： 部分相干平顶光束 偏振特性 相干-偏振矩阵 正多边形光阑 光阑衍射     

高斯光束经环形光栅的衍射特性分析

基于傅里叶-贝塞尔变换计算高斯光束垂直入射环形光栅时的衍射远场分布,分析了其衍射远场光强分布的一般规律,并与平面波入射时的情况进行了比较.计算结果表明：当光栅半径为1.5倍高斯光束束腰半径时, 随着光栅环数的增加,中央亮斑半值全宽先减小后增大、中央亮斑所包含的功率占总功率的比值减小、中央主极大光强值减小,三者的变化趋势与平面波入射时的趋势一致;中央亮斑半径、次极大光强值变化趋势与平面波入射时的变化趋势不同.当环数小于5时,高斯光束经过环形光栅的衍射场光强变化无规律;当环数大于10后两种情况下衍射场光强变化都不明显;当环数趋于无穷时中央亮斑半径、中央亮斑半值全宽、次极大光强值趋于圆孔衍射(环数等于1)时的值,中央亮斑所包含的功率占总功率的比值约等于圆孔衍射时的1/2,中央主极大光强值约等于圆孔衍射时的1/4.     

Bessel光束经椭圆环形孔径后的衍射光场

基于菲涅耳衍射积分理论及硬边孔径的复高斯函数展开法导出了Bessel光束经椭圆环形孔径后的光场表达式, 数值模拟了其光场的强度分布. 研究了Bessel光束经椭圆环形孔径后的光场变化及其传播过程; 在实验上利用轴棱锥输出的近似无衍射Bessel光, 通过椭圆环形孔径, 使用电荷耦合器件拍摄得到不同传播距离处的光强分布. 理论结果和实验结果均表明无衍射光束经椭圆环形孔径后会产生空心光束.     

Propagation characteristics of linearly polarized Bessel-Gaussian beams through an annular apertured paraxial ABCD optical system

By means of Collins diffraction integral formula in the paraxial approximation and based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical expression for linearly polarized Bessel-Gaussian beams passing through a paraxial ABCD optical system with an annular aperture has been derived. The results provide more convenient for studying their propagation and transformation than the usual way by using diffraction integral directly. By using the analytical expression and the diffraction integral formula some numerical simulations are done to illustrate for the propagation characteristics of a linearly polarized Bessel-Gaussian beam through an optical system with an annular aperture.     

Axial distribution of Gaussian beam limited by a hard-edged aperture

In this letter, the axial distribution of Gaussian beam limited by a hard-edged aperture is studied. We theoretically analyze the axial diffraction of Gaussian beam limited by a hard-edged aperture, and give the simpler formulas of the axial diffraction intensities of Gaussian beam in Fresnel diffraction field and Fraunhofer diffraction field. The corresponding numerical calculation of axial diffraction intensity distribution of Gaussian beam with different wave waist is provided and the evolution of the diffraction distribution with the wave waist of Gaussian beam is explained. As the especial cases of the truncated Gaussian beam,the Gaussian beam in free space and the parallel light limited by the aperture are discussed too, and the system parameters of the truncated Gaussian beam which can cause it to equal to these cases are given.The theoretical results conform to the numerical analysis.     

Analytical formula for a circular flattened Gaussian beam propagating through a misaligned paraxial ABCD optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a misaligned paraxial ABCD optical system in the cylindrical coordinate system, analytical formula for a circular flattened Gaussian beam propagating through such optical system is derived. Furthermore, an approximate analytical formula is derived for a circular flattened Gaussian beam propagating through an apertured misaligned ABCD optical system by expanding the hard aperture function as a finite sum of complex Gaussian functions. Numerical examples are given.     

基于畸变透镜孔衍射的激光束型转变

为了研究用畸变透镜孔产生的不同束型的精细激光束,先由基尔霍夫衍射公式得到高斯光束微圆孔衍射积分式,然后再经适当推理得到高斯光束通过畸变透镜孔的菲涅耳衍射的计算式,进而探讨了畸变透镜孔菲涅耳衍射对高斯光束进行束型转变的原理。用Matlab软件进行计算机模拟实验,表明了这种方法和技术是可行的。这种激光束整形技术可产生用于微细加工的不同束型的精细激光束。     

Propagation of a hollow Gaussian beam through a paraxial misaligned optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a paraxial misaligned optical system in the cylindrical coordinate system, we obtain an analytical formula for a hollow Gaussian beam passing through a paraxial misaligned optical system. Furthermore, we also obtain the approximate analytical formula for a hollow Gaussian beam passing through a paraxial circularly apertured misaligned optical system by expanding the hard aperture function into a finite sum of complex Gaussian functions. As a numerical example, the propagation properties a hollow Gaussian beam through a misaligned thin lens are studied numerically.     

Propagation of a Laguerre–Gaussian beam through a slightly misaligned paraxial optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a slightly misaligned optical system in a cylindrical coordinate system, an analytical formula for a Laguerre–Gaussian beam passing through such an optical system is derived. Furthermore, an approximate analytical formula is derived for a Laguerre–Gaussian beam passing through an apertured slightly misaligned optical system by expanding the hard aperture function as a finite sum of complex Gaussian functions. Some analytical formulas are also given for a flattened Gaussian beam by expanding its field as a superposition of a finite series of Laguerre–Gaussian beams. PACS 42.25.Bs; 41.85.Ew; 41.85.Ct     

Propagation properties of the beam generated by Gaussian mirror resonator passing through a paraxial ABCD optical system

By expanding a hard aperture function into a finite sum of complex Gaussian functions, approximate propagation formula is derived in the situation that the beam generated by Gaussian mirror resonator passes through a paraxial ABCD optical system with an annular aperture. The corresponding forms for a circular aperture and a circular black screen are also given. Some numerical simulations are shown to illustrate propagation properties and focusing properties of the beam passing through a paraxial ABCD optical system with the three different kinds of aperture.