高斯光束通过有硬边光阑ABCD光学系统的近似解析传输公式

对高斯光束通过有硬边光阑近轴ABCD光学系统的传输进行了研究,采用将矩形函数展开为复高斯函数的技巧,推导出了近似的解析传输公式。以高斯光束在有光阑情况下自由空间的传输为例进行了数值计算,对所用方法能节约大量机时的优点和计算误差作了讨论,并进一步推广用于平面波和平顶高斯光束,证实了这一方法具有广泛的应用意义。     

双曲余弦高斯光束通过有光阑限制的ABCD光学系统的传输

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究,采用将矩形域函数表示为复高斯函数叠加的技巧,推导出了解析的传输公式,在特殊情况下,该公式简化为在无光阑情况下的传输公式,对双曲余弦高斯光束通过有光阑限制的薄膜镜聚焦进行了数值计算,计算结果与直接由柯林斯（Collins)公式所得结果一致,且此解析方法便于进行物理分析,可节约大量机时。     

通过有光阑近轴ABCD光学系统激光束的近似解析传输公式

 用傅立叶级数展开法研究光束通过有光阑限制的近轴ABCD光学系统的传输特性，导出了光阑透射率函数不同时的传输公式。硬边光阑的情况可作为其它光阑的特例得到，其它光阑也可视作硬边光阑来处理。数值计算表明了该方法快速的优点，并得到与用Collins公式直接积分一致结果。     

通过有光阑近轴ABCD光学系统激光束的近似解析传输公式

用傅立叶级数展开法研究光束通过有光阑限制的近轴ABCD光学系统的传输特性,导出了光阑透射率函数不同时的传输公式。硬边光阑的情况可作为其它光阑的特例得到,其它光阑也可视作硬边光阑来处理。数值计算表明了该方法快速的优点,并得到与用Collins公式直接积分一致结果。     

贝塞耳函数调制的高斯光束通过有光阑ABCD光学系统的传输

基于惠更斯菲涅尔广义衍射积分,对变量为径向平方的贝塞耳函数调制的高斯光束(QBG光束)通过有圆孔光阑限制的一阶ABCD光学系统的传输进行了研究.采用将圆域函数可表示为复高斯函数叠加的方法,推导出了普适的场分布解析公式,以QBG光束通过有圆孔光阑限制的薄透镜系统为例进行了分析与讨论,数值计算结果证明了本文所用方法的优点,所得结果与直接用广义衍射积分公式进行复杂的数值计算结果完全一致 关键词： QBG光束 光阑 ABCD光学系统 传输特性     

厄米-余弦-高斯光束通过具有光阑光学系统时的传输特性

当厄米_余弦_高斯光束通过带有矩形光阑的一阶ABCD近轴光学系统时,可由Collins公式给出其场分布的积分形式。将其中硬边光阑的窗口函数写成矩形函数,并将矩形函数用高斯函数展开,通过积分可得到由光阑限制的厄米_余弦_高斯光束传输的解析式。分析和讨论了厄米_余弦_高斯光束通过具有圆孔光阑限制的薄透镜系统时的情况,其结果与直接用广义衍射积分公式进行复杂数值计算时的结果完全一致。这样不仅便于进行物理分析,而且也节省了计算机的计算时间。     

部分相干光束通过硬边光阑的推广光束传输M2因子

给出部分相干光通过硬边光阑后的强度二阶矩的计算公式，由此可得到部分相干光通过硬边光阑后的推广光束传输M^2因子。以部分相干高斯－谢尔模型光束为例，推导出相应的M^2因子，并作了数值计算和分析讨论。     

厄米-高斯光束在内含硬边光阑光学系统中的传输

把硬边光阑从复杂光学系统中“移”出来,即把任意一个含有硬边光阑的复杂光学系统体现到含有入射光瞳和出射光瞳的光学系统中，使硬边光阑的作用转化为出射光瞳的作用，以便求出观察面上的解析解。对入射面上的二维厄米 高斯光束，利用柯林斯公式和入射光瞳与出射光瞳的物像关系，可得到所要求观察面的场分布和解析结果，通过数值模拟验证了其正确性。通过分析计算得到如下结论：对于任意一个含有硬边光阑的复杂光学系统，都可以把光阑的作用从系统中“移”出来，把其看作是出射光瞳的作用，从而可以较为简便地求出观察面上的场分布。     

厄米-高斯光束通过多个硬边光阑复杂光学系统变换的计算模拟

用Wen的方法研究了厄米－高斯光束通过含有多个硬边光阑复杂光学系统的传输,推导出了具有快速计算优点的传输公式,使计算时间大为减少。高斯光束传输可作为理论模型的特例得出。数值计算例表明使用该解析公式所得结果和直接对Collins公式作数值积分的结果符合较好。对所用方法和所得结果的进一步推广作了讨论。     

厄米-高斯光束通过多个硬边光阑复杂光学系统变换的计算模拟

 用Wen的方法研究了厄米－高斯光束通过含有多个硬边光阑复杂光学系统的传输,推导出了具有快速计算优点的传输公式，使计算时间大为减少。高斯光束传输可作为理论模型的特例得出。数值计算例表明使用该解析公式所得结果和直接对Collins公式作数值积分的结果符合较好。对所用方法和所得结果的进一步推广作了讨论。     

Propagation of Bessel-modulated Gaussian beams through a paraxial ABCD optical system with an annular aperture

Based on the generalized Collins diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expressions of Bessel-Gaussian beams and QBG beams passing through a paraxial ABCD optical system with an annual aperture are derived. As special cases, the corresponding closed-forms for the unaperture or circular aperture or circular black screen cases are also given. The results provide more convenience for studying their propagation and transformation than the usual way by using diffraction integral formula directly. Numerical examples are given to illustrate the propagation properties of Bessel-Gaussian and QBG beams.     

Recurrence propagation equation of Hermite-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture

Based on the generalized Huygens-Fresnel diffraction integral, a recurrence propagation equation of Hermite-Gaussian (H-G) beams through a paraxial optical ABCD system with hard-edge aperture is derived, which permits us to obtain the analytical propagation expression for H-G beams of any order. The advantages of our analytical results are analyzed, and the application is illustrated with numerical examples.     

Propagation of elegant Laguerre–Gaussian beams through an annular apertured paraxial ABCD optical system

Based on the generalized Huygens–Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression of elegant Laguerre–Gaussian beams passing through a paraxial ABCD optical system with an annular aperture is derived. Meanwhile, the corresponding closed-forms for the unapertured, circular apertured or circular black screen cases are also given. The obtained results provide more convenience for studying their propagation and transformation than the usual way by using diffraction integral formula directly. Some numerical examples are given to illustrate the propagation properties of elegant Laguerre–Gaussian beams.     

Propagation characteristics of flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture

The approximate analytical formula for flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture was derived by the extended Huygens–Fresnel principle. Some numerical simulations are illustrated to the effects on the propagation of flattened Gaussian beams by the misaligned annular aperture. To compare the difference between annular apertured system and circular apertured system, the circular apertured system is also studied. The results show that angle misalignments and lateral displacements of aperture create asymmetrical average intensity distribution at receiving plane z = 500. The effects on intensity distribution by angle misalignments of annular aperture were small. In annular aperture case, the smooth of intensity distribution was worse with escalating obscure ratio ? in near-field; the side-lobes increased and the central lobe decreased with escalating obscure ratio ? in far-field. At receiving plane z = 500: for circular aperture, the side-lobes decreased, even to be neglected, with the increasing of truncation parameter δ; for annular aperture, the side-lobes increased with the increasing of truncation parameter δ. In addition, it is found that the aligned thin lens can fix asymmetry of intensity distribution which was caused by the misaligned annular aperture.