基于高阶准离散汉克尔变换的光束整形算法  

Beam Shaping Algorithm Based on High-Order Quasi-Discrete Hankel Transform

作　　者：余惠 丁新辉 李大为[1] 周琼[1] 吕凤年[1] 卢兴强[1] Yu Hui;Ding Xinhui;Li Dawei;Zhou Qiong;LüFengnian;Lu Xingqiang(Key Laboratory of High Power Laser and Physics,Shanghai Institute of Optics and Fine Mechanics,Chinese Academy of Sciences,Shanghai 201800,China;Center of Materials Science and Optoelectronics Engineering,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院上海光学精密机械研究所高功率激光物理联合实验室,上海201800 [2]中国科学院大学材料与光电研究中心,北京100049

出　　处：《光学学报》2024年第7期196-204,共9页Acta Optica Sinica

基　　金：国家自然科学基金(62175245)。

摘　　要：针对具有圆对称结构特征的光束,提出了一种基于高阶准离散汉克尔变换的光束整形算法。与传统Gerchberg-Saxton算法相比,相同条件下,该算法能够在较少的迭代次数内实现快速收敛,并大幅节省计算时间(约100倍),利用该算法设计的衍射光学元件呈圆对称分布,结构简单、更易于加工;此外,设计实验对目标光束整形,验证了该算法的可行性,实验结果光强分布较好,为衍射光学元件的设计和加工提供了重要的指导意义。Objective In the realm of beam shaping,diffractive optical elements(DOEs)can manipulate the laser intensity distribution by altering the laser phase through microstructures.Beam shaping algorithms play a significant role in the design of diffractive optical elements.Specifically,the most representative is the Gerchberg-Saxton(GS)algorithm proposed by R.W.Gerchberg and W.O.Saxton.It involves an iterative process of performing a Fourier transform between the input plane and output plane,while simultaneously imposing known constraints on both planes.To enhance the convergence effect of the algorithm,an input-output algorithm and the phase-mixture algorithm have been developed based on the GS algorithm.In recent years,there have been advancements in mixed-region amplitude freedom algorithms,particularly those demonstrating superior convergence effects in the signal region,as well as offset mixed-region amplitudefreedom algorithms.Global optimization algorithms,such as the feedback GSGA(Gerchberg-Saxton genetic algorithm)and the last place elimination GSGA,have also gained attraction.These algorithms are derived from the GS algorithm.However,the phase complexity of these designs is high,presenting significant challenges to the physical processing of DOEs.Furthermore,as the number of limiting conditions increases,the computational time required also escalates,especially for the feedback GSGA and last place elimination GSGA.Methods To optimize time efficiency and reduce phase complexity,we discover that in conventional laser applications,the use of the Hankel transform is more effective than the Fourier transform in numerical calculations when both the incident beam and target beam exhibit circular symmetry.We introduce a beam shaping algorithm,the pQDHT-GS algorithm,for a circularly symmetric beam system based on the GS algorithm.The implementation process is based on the characteristic that the Hankel transform is solely related to the radial coordinate.This is achieved by iteratively alternating between the input pla

关 键 词：物理光学 汉克尔变换 光束整形算法 Gerchberg-Saxton算法 衍射光学元件 

分 类 号：O436[机械工程—光学工程]