Based on the framework of the Huygens–Fresnel diffraction, we investigate theoretically the propagation properties of a new vortex beam, which is referred to as vortex-cosh-Gaussian beam (vChGB), through a paraxial ABCD optical system. A closed-form formula of vChGB passing through the above system is derived. We show by analytical and numerical calculations that the decentered parameter and the topological vortex charge affect strongly the characteristics of the considered beam upon propagating in free space. In a fractional Fourier transform system (FrFT), it is found that the intensity and the phase distributions of the propagating vChGB evolves gradually and periodically versus the order of the FrFT. The shape of the vChGB depends on the parameters of the beam and the fractional order of the FrFT system. The results obtained may be beneficial to applications in optical trapping, optical micromanipulation and beam shaping.

中文翻译：

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一种新型涡旋余弦双曲高斯光束的引入及其在分数阶傅里叶变换光学系统中的传播特性研究

基于惠更斯-菲涅耳衍射的框架，我们从理论上研究了一种新的涡旋光束通过近轴 ABCD 光学系统的传播特性，该光束称为涡旋-柯什-高斯光束 (vChGB)。推导出通过上述系统的vChGB的闭式公式。我们通过分析和数值计算表明，偏心参数和拓扑涡流电荷在自由空间中传播时会强烈影响所考虑光束的特性。在分数阶傅里叶变换系统 (FrFT) 中，发现传播中的 vChGB 的强度和相位分布相对于 FrFT 的阶数逐渐且周期性地演变。vChGB 的形状取决于光束的参数和 FrFT 系统的分数阶数。