The propagation properties and kurtosis parametric characteristics of Hermite-cosh-Gaussian beams passing through fractional Fourier transformation systems
The propagation properties and kurtosis parametric characteristics of Hermite-cosh-Gaussian beams passing through fractional Fourier transformation systems
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DOI：
10.1016/j.ijleo.2005.03.002
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发表时间：
2005-09
期刊：
影响因子：
3.1
通讯作者：
Daomu Zhao;H. Mao;Chong-wei Zheng;Shaomin Wang;F. Jing;Xiaofeng Wei;Q. Zhu;Hongjie Liu
中科院分区：
文献类型：
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作者：
Daomu Zhao;H. Mao;Chong-wei Zheng;Shaomin Wang;F. Jing;Xiaofeng Wei;Q. Zhu;Hongjie Liu
基于柯林斯衍射积分公式和辐照度矩，详细分析了厄米-余弦-高斯(HCHG)光束通过球差透镜分数傅里叶变换系统后的传输特性和峰度参数特性。给出了高次谐波光束通过理想分数阶傅里叶变换系统的传输方程和峰度参数的闭合表达式。利用一种有效的算法，本文还进行了一些数值计算。结果表明，球差透镜对高次谐波光束通过分数傅里叶变换系统后的光强分布和峰度参数有很大影响。即使在相同的分数阶和相同的球差系数的情况下，HCHG光束通过两种具有球差透镜的罗曼系统的光强分布和峰度参数也不再相等。具有球差透镜的两种罗曼系统的基波周期是不同的，I型有4个，II型有2个。因此，在有球差透镜的情况下，实现分数傅立叶变换的两种光学装置不再是等价的。
Based on the Collins diffraction integral formula and irradiance moments, the propagation properties and kurtosis parametric characteristics of Hermite-cosh-Gaussian (HChG) beams passing through fractional Fourier transformation systems with spherically aberrated lenses are analyzed in detail. The closed-form expressions for the propagation equation and kurtosis parameter of HChG beams passing ideal fractional Fourier transformation systems are also obtained. By using an efficient algorithm some numerical calculations are also performed in this paper. The results show that the spherically aberrated lenses greatly influence on the intensity distribution and kurtosis parameter of HChG beams passage through fractional Fourier transformation systems. The intensity distribution and kurtosis parameter of HChG beams passage through two types of Lohmann's systems with spherically aberrated lenses, respectively, are no longer equal even in the case of the same fractional order and the same spherical aberration coefficients. The fundamental periods of the two types of Lohmann's systems with spherically aberrated lenses are different, 4 for the type I and 2 for the type II. Therefore, the two optical setups for implementing the fractional Fourier transformation are no longer equivalent in the presence of spherically aberrated lenses.