Zhao Chengliang, Cai Yangjian
School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
J Opt Soc Am A Opt Image Sci Vis. 2010 Mar 1;27(3):637-47. doi: 10.1364/JOSAA.27.000637.
Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.
研究了一般类型光束通过截断分数傅里叶变换（FRT）光学系统的傍轴传播。基于柯林斯公式推导了FRT平面中一般类型光束的电场和有效光束宽度的解析公式。我们的公式可用于研究各种激光束（如高斯光束、余弦高斯光束、双曲余弦高斯光束、正弦高斯光束、双曲正弦高斯光束、平顶光束、厄米特双曲余弦高斯光束、厄米特正弦高斯光束、高阶环形高斯光束、厄米特双曲正弦高斯光束和厄米特余弦高斯光束）通过有或没有截断的FRT光学系统的传播。作为数值示例，研究了厄米特余弦高斯光束通过矩形截断FRT光学系统的传播特性。我们的结果清楚地表明，截断FRT光学系统为激光束整形提供了一种便捷的方法。
