基于不同变系数和势场的分数系统中二次相位调控厄米-高斯光束动力学  

Dynamics of quadratic phase controlled Hermite-Gaussian beams in fractional systems based on different variable coefficients and potentials

作　　者：谭超[1] 梁勇 邹敏 雷同 陈龙 唐平华 刘明伟 Tan Chao;Liang Yong;Zou Min;Lei Tong;Chen Long;Tang Ping-Hua;Liu Ming-Wei(School of Information and Electrical Engineering,Hunan University of Science and Technology,Xiangtan 411201,China;School of Chemistry and Chemical Engineering,Hunan University of Science and Technology,Xiangtan 411201,China;School of Physics and Optoelectronics,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]湖南科技大学信息与电气工程学院,湘潭411201 [2]湖南科技大学化学化工学院,湘潭411201 [3]湘潭大学物理与光电工程学院,湘潭411105

出　　处：《物理学报》2024年第13期148-163,共16页Acta Physica Sinica

基　　金：湖南省自然科学基金(批准号:2022JJ30264);湖南省教育厅科学研究项目(批准号:21B0476,21B0136,22B0479)资助的课题。

摘　　要：本文基于带有不同变系数和势的分数薛定谔方程,研究了二次相位调制(QPM)下厄米-高斯光束的演化特性.在自由空间中,光束聚焦位置随着正QPM系数的增加或莱维指数的减小而变大.QPM为负时,光束聚焦消失.在余弦调制和QPM共同作用下,光束的传输不再遵循余弦规律振荡,而是表现出一大一小的呼吸结构,其演化周期会随调制频率的增加而降低.引入线性调制时,分裂光束的运动轨迹呈现抛物线状.在线性调制和QPM共同影响下,光束呈现出聚焦或聚焦消失的特性.当考虑幂函数调制和正QPM共同影响时,在莱维指数较小时,光束在一定传输距离内保持不失真的直线传输.当线性势作用时,光束的分裂随着线性系数的增加而逐渐消失,最终呈现周期性演化.在加入QPM后,光束会得到明显放大.另外,光束演化周期与线性系数成反比,横向振幅随着莱维指数的增加而变大.当抛物势和QPM共同作用时,光束会呈现出自动聚焦,散焦效应,聚焦频率会随着莱维指数和抛物系数的增加而变大.这些特性在光学操纵,光学聚焦等领域具有潜在的应用价值.The Hermite-Gaussian(HG)beam has many potential advanced applications in optical communications,electron acceleration,nonlinear optics and bio-optical disease detection,owing to its distinctive mode and intensity distribution.The research on HG beam are significant in the development of optics,medicine and quantum technology.However,the controlling of the evolutions of HG beam with quadratic phase modulation(QPM)in fractional systems under variable coefficients and potentials has been rarely studied.In this work,the propagation dynamic behaviors of the HG beam with QPM are investigated based on the fractional Schrodinger equation(FSE)under different variable coefficients and potentials by using a split-step Fourier algorithm.In the free space,the focusing spot of the beam becomes larger as the positive QPM coefficient increases or the Levy index decreases.The QPM coefficient has little effect on the focusing amplitude when the Levy index is 2.When the QPM coefficient is negative,the focusing of the beam disappears.Under the joint action of cosine modulations and QPM,the transmission of the beam oscillates not by the cosine law,but presents a large and a small breathing structure.The positive and the negative coefficient of QPM only alter the breathing sequence.The evolution period and width of the beam decrease as the modulation frequency increases.The trajectory of split beams turns into a parabolic shape under the linear modulation.In the joint influence of linear modulations and QPM,the HG beam exhibits either focusing or not focusing.Furthermore,the focusing position and focal plane of the beam decrease as the Levy index increases.When the Levy index is small,the beam keeps a straight-line transmission without distortion at a longer distance under the joint effect of the power function modulation and a positive QPM.The transmission of the beam also stabilizes and the beam width becomes larger with a negative QPM.Under a linear potential,the splitting of the HG beam disappears with the increase of the linear c

关 键 词：分数薛定谔方程 厄米-高斯光束 二次相位调制 变系数和势 

分 类 号：O43[机械工程—光学工程]