截断系数对皮尔斯光束聚焦行为的影响  

The Influence of Truncation Coefficient on the Propagation Dynamics of the Pearcey Beams

作　　者：臧峰 刘利锋 邓富胜[1,2] 刘艳红 董丽娟[1,2] 石云龙 ZANG Feng;LIU Li-feng;DENG Fu-sheng;LIU Yan-hong;DONG Li-juan;SHI Yun-long(Institute of Solid State Physics,Shanxi Datong University,Datong 037009,China;Shanxi Provincial Key Laboratory of Micro structure Electromagnetic Functional Materials,Shanxi Datong University,Datong 037009,China)

机构地区：[1]山西大同大学固体物理研究所,山西大同037009 [2]微结构电磁功能材料山西省重点实验室,山西大同037009

出　　处：《量子光学学报》2021年第4期312-318,共7页Journal of Quantum Optics

基　　金：国家自然科学基金(11874245);大同市重点研发计划项目(2019030)。

摘　　要：基于无势阱的薛定谔方程,通过解析方法推导出了描述皮尔斯-高斯光束演化的动力学解。结果显示:皮尔斯光束的各个瓣在横向上做加速运动,离主瓣越远,加速度越大,这就导致了这些旁瓣和主瓣在同时到达了同一位置,呈现出聚焦行为。当越过这一位置,加速度方向变为沿x轴负方向,这时光束在横向上做减速运动,越靠外的旁瓣做减速运动的加速度越大,这样就导致了主瓣和旁瓣的分离,强度分布发生倒逆,最终形成了聚焦翻转的演化图样。根据解析结果,给出了小截断系数的情况下皮尔斯-高斯光束聚焦距离的数学表达式z=2,并得到了数值模拟的验证。此外,数值研究了截断系数对皮尔斯-高斯光束动力学行为的影响。研究结果表明:随截断系数的增加,皮尔斯-高斯光束的聚焦行为会逐渐减弱。当截断系数较大时,皮尔斯-高斯光束的聚焦行为完全消失,取而代之的是扩散行为。最后,进一步给出了皮尔斯光束聚焦位置以及聚焦处的峰值功率对截断系数的依赖关系,结果显示:随截断系数的增加,聚焦距离在逐渐减小,而聚焦处的峰值功率则会快速减小。In this paper,based on the potential-free Schr?dinger equation,the dynamic solution describing the evolution of the Pearcey-Gaussian beam is obtained.It is found that each lobe of the Pearcey-Gaussian beam is accelerated in the transverse direction,and the farther away from the main lobe,the greater the acceleration of these side lobes.Eventually,the side lobes and the main lobe reach the same position at the same time.When passing this position,the direction of acceleration changes,so they slow down in the transverse direction.The difference in acceleration of the lobes leads to the separation of the lobes and the invertion of the profile of the Pearcey-Gaussian beam.Thus a focusing and inverting behavior forms.According to the analytical result,the analytical expression governing the focusing distance of the Pearcey-Gaussian beam with a small truncation coefficient is given and verified by numerical simulation.Moreover,the effect of the truncation coefficient on the dynamic behavior of the Pearcey-Gaussian beam is studied numerically by means of a symmetrized split-step Fourier scheme.The results show that the focusing behavior of the Pearcey-Gaussian beam weakens with the increasing of the truncation coefficient.When the truncation coefficient is large,the focusing behavior of the Pearcey-Gaussian beam disappears completely and is replaced by the diffusion behavior.Finally,the dependences of the focusing distance and the peak power at the focusing position on the truncation coefficient are investigated in detail.The results show that with the increasing of the truncation coefficient,the focusing distance decreases gradually,while the peak power at the focusing position decreases rapidly.The results have an important application value for generating an optical beam with high peak power by adjusting the truncation coefficient.

关 键 词：无势阱薛定谔方程 皮尔斯光束 截断系数 自聚焦行为 

分 类 号：O436[机械工程—光学工程]