It is shown that focal shifts of apertured FGBs not only depend on the beam order N, Fresnel number F w associated with the beam, but also depend on the Fresnel number F a associated with the aperture.

Based on the generalized Huygens Fresnel diffraction integral, the propagation of the Bessel modulated Gaussian beams with quadratic radial dependence ( QBG beams) through a circle apertured ABCD optical system has been studied.

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。

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It is shown that intensity distribution of apertured off-axes Gaussian beam depends on the Fresnel number, truncation parameter, relative propagation distance, relative excursion and obliquity of the beam.

研究表明：受光阑限制离轴高斯光束的光强分布与菲涅耳数、截断参数、相对传输距离、光束的相对偏移和倾角有关。

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Propagation of Apertured Off-axial Hermite-Cosine-Gaussian Beams

受光阑约束的离轴厄米余弦高斯光束的传输

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The analytical propagation equations of flattened Gaussian beams through a paraxial ABCD optical system with linear gain ( absorption), unapertured and apertured ABCD systems are derived.

推导出了平顶高斯光束通过有线性增益（损耗）的近轴ABCD光学系统、无光阑和有光阑ABCD光学系统后解析形式的传输方程。

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Based on the Collins formula and Sylvester theorem, the propagation equation of Gaussian beams passing through a multi-Gaussian apertured paraxial optical ABCD system is derived.

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。

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Our calculations show that the Bessel-Gauss beam can be produced in the focused plane of the ring apertured Gaussian beam, this method is efficient and simple.

本文通过计算指出环状分布的光束经透镜后可在焦平面产生适用于激光打孔的贝塞尔－高斯光束，这是一种高效、简单实用的方法。

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There-fore, the beam propagation through hard-edged apertured optical systems is of practical importance, and a variety of simulation methods have been developed.

因此，光束通过有硬边光阑限制光学系统传输问题的研究有重要实际意义。

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In a similar way, the corresponding analytical expressions of off-axial Cosine-Gaussian beams through apertured ABCD matrix were also given.

用同样方法分析得到了离轴余弦高斯光束通过受光阑约束的傍轴ABCD轴对称光学系统传输后的解析式。

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Focusing Property of Apertured Hermite-Gaussian Beams

受光阑限制厄米-高斯光束的聚焦特性

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For the apertured case we have performed detailed numerical calculations, showing the focusing field characteristics of Hermite-Gaussion beams.

对有光阑限制下的H&G光束的聚焦场特性做了详细的数值计算和讨论。

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Detailed numerical caculationshave been Performed to illustrate the focusing properties of apertured Laguerre-Gaussian beams.

对有光阑限制的拉盖尔-高斯光束作了详细的数值计算以说明其聚焦特性。

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Two ABCD matrices for describing hard apertured Gaussian beams weakly diffracted in the far field are defined.

定义两种描述高斯光束被硬边光阑弱衍射的远场下的光阑ABCD矩阵。

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Starting from the Collins formula, the focusing property of apertured Hermite-Gaussian beams is studied.

该文从Collins公式出发，对受光阑限制厄米-高斯光束的聚焦特性进行了研究。

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Analytical Propagation Expressions for Apertured Off-Axis Gaussian Beams

受光阑限制离轴高斯光束的解析传输

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Propagation of Gaussian beams through a multi-Gaussian apertured ABCD system

高斯光束通过多高斯光阑ABCD系统的传输

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Propagation expressions for apertured Hermite-cosine-Gaussian beams

受光阑限制厄米-余弦-高斯光束的解析传输公式

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Therefore, it is very significant to study the propagation properties of apertured polychromatic partially coherent beams.

因此，研究受光阑限制的多色部分相干光束通过湍流大气的传输特性具有重要意义。

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The Frequency Property of the Apertured Bessel Beams

Bessel光束的频率特性

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Propagation Properties of Bessel Beams Through a Hard-edged Annular Apertured ABCD Optical System

贝塞尔光束通过环形硬边光阑的ABCD光学系统传输

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Space Spectrum and Filtering of Apertured Bessel Beam

加光阑的贝塞尔光束的空间频谱和滤波

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