基于格林函数法研究分数阶Bessel-Gaussian光束近场传输  

Near field propagation of fractional-order Bessel-Gauss beams based on Green function

作　　者：施继忠[1] 任志君[2] 董永胜[3] SHI Jizhong;REN Zhijun;DONG Yongsheng(Key Laboratory of Urban Rail Transit Intelligent Operation and Maintenance Technology and Equipment of Zhejiang Province,Zhejiang Normal University,Jinhua 321004,China;Key Laboratory of Optical Information Detecting and Display Technology,Zhejiang Normal University,Jinhua 321004,China;College of Physics and Electronic Information Engineering,Jining Normal University,Wulanchabu 012000,China)

机构地区：[1]浙江师范大学,浙江省城市轨道交通智能运维技术与装备重点实验室,浙江金华321004 [2]浙江师范大学,浙江省光信息检测与显示技术研究重点实验室,浙江金华321004 [3]集宁师范学院,物理与电子信息工程学院,内蒙古乌兰察布012000

出　　处：《浙江师范大学学报（自然科学版）》2023年第2期139-145,共7页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(11974314)。

摘　　要：为揭示FBG(fractional-order Bessel-Gaussian)光束在近场传输时的光强和相位演化情况,基于光传播的独立性和叠加性原理,通过引入虚光源点,并结合格林函数法,严格推导了FBG光束的非傍轴积分表达式,并进一步利用非傍轴下的各阶修正解,精确计算了FBG光束轴上的光强分布.计算结果表明:对于分数阶Bessel-Gaussian光束的远场传输,利用经典的傍轴近似理论可以得到准确的计算结果,但在近场传输时,傍轴近似理论的计算结果误差很大,只有利用非傍轴修正解才能精确研究FBG光束的近场光学传输.研究结果为将FBG光束更好地应用于近场光学奠定必要的理论基础.In order to reveal the light intensity and phase evolution of FBG beam in near field,based on the principle of independent transmission and superposition of light,the Green function method combined with a series of virtual sources was introduced to analytically study the far field propagation characteristics of FBG beam in free space.First,the nonparaxial integral expression of FBG beams during propagation was rigorously derived.Then,the analytic expression of the important axial optical field amplitude of FBG beams was ob-tained.Finally,the on-axis intensity and phase of FBG beams were calculated on the basis of the analytic ex-pression.Calculated results quantitatively revealed some important intensity information regarding the near field propagation characteristic of FBG beams.It was concluded that the intensity and phase difference under different corrected expressions was relatively small.Only when the propagating distance was sufficiently large,the nonparaxial correction solution was necessary to study the propagation properties of FBG beams in near field optics.

关 键 词：格林函数法 分数阶Bessel-Gaussian(FBG)光束 虚点源 近场传输 

分 类 号：O436[机械工程—光学工程]