含参艾里光束在变系数分数系统中的传输  

Propagation of Airy Beams with Parameters in Fractional Systems with Variable Coefficients

作　　者：辛旺 王艳[2] 李禄[1] XIN Wang;WANG Yan;LI Lu(Institute of Theoretical Physics,State Key Laboratory of Quantum Optics and Quantum Optics Devices,Shanxi University,Taiyuan 030006,China;College of Physics and Electronic Engineering,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学理论物理研究所,量子光学与量子光学器件国家重点实验室,山西太原030006 [2]山西大学物理电子工程学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2023年第5期1129-1137,共9页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(61475198)。

摘　　要：基于变系数分数薛定谔系统,采用分步傅里叶方法研究了含参艾里光束的传输特性。首先,展示了含参艾里函数中各系数对有限能量艾里函数光场分布的影响。随后,详细地研究含参艾里函数中的系数,啁啾参量以及系统的纵向调制和Lévy指数对艾里光束演化的影响。结果表明:在无啁啾的情况下,含参艾里函数中的立方系数和线性系数正负符号的改变会导致艾里光束在传输过程中发生倒逆行为,二次系数正负号的变化会使传输光束产生半波损失现象。同时发现,通过改变这些系数的大小可控制传输光束的强度。当啁啾存在时,啁啾会对一侧的劈裂光束产生抑制作用,而另一侧分裂光束增强。因此,光束会劈裂为两束强度不相同的光波。当啁啾为负值时,对光束的抑制和增强作用刚好相反。在纵向周期调制下,艾里光束表现出周期性的振荡行为。另外,存在啁啾的情况下,Lévy指数对光束演化的影响也被研究,结果发现:Lévy指数的增大会增强光束在传输中的衍射,同时光束的振荡振幅会增大。Based on the fractional Schrodinger system with variable coefficients,the propagation characteristics of Airy beams with parameters are studied by using the split step Fourier method.Firstly,the influence of the coefficients of the Airy function with pa-rameters on the intensity distribution of the finite energy Airy function is shown.Then,the effects of the coefficients,chirp parame-ters,longitudinal modulation and Levy index of the system on the evolution of the Airy beams are studied in detail.The results show that in the case of no chirp,the change of the sign of the cubic coefficient and the linear coefficient in the Airy function with parameters cause the inverse behavior of the Airy beam in the process of propagation,and the change of the positive and negative sign of the quadratic coefficient causes the half-wave loss of the transmitted beam.It is also found that the intensity of the transmit-ted beam can be manipulated by changing the size of these coefficients.When the chirp exists,the chirp suppresses the splitting beam on one side,while the spliting beam on the other side is enhanced.Therefore,the beam splits into two wave packets with un-equal intensities.When the chirp is negative,the suppression and enhancement of the beam are just opposite.Under the longitudinal periodic modulation,the Airy beam exhibits periodic oscillation behavior.Meanwhile,when chirp exists,the influence of Levy index on the beam evolution is also studied.The results show that the increase of Levy index enhances the diffraction of the beam in transmission,and the oscillation amplitude of the beam increases at the same time.

关 键 词：含参艾里光束 线性啁啾 Lévy指数 光束翻转 

分 类 号：O436[机械工程—光学工程]