高斯光束在分数阶非均匀介质中的传输特性  

Propagation Characteristics of the Gaussian Beam in the Fractional Inhomogeneous Media

作　　者：宋丽军[1] 刘晓琪 刘树杰 SONG Li-jun;LIU Xiao-qi;LIU Shu-jie(College of Physics and Electronic Engineering,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学物理电子工程学院,山西太原030006

出　　处：《量子光学学报》2022年第2期149-157,共9页Journal of Quantum Optics

摘　　要：基于非线性分数薛定谔方程,采用分步傅里叶方法研究了非线性增益和线性损耗对高斯光束传输特性的影响。结果表明:在非线性分数薛定谔方程中,可以通过调控系统参数来改变高斯光束演化得到的呼吸孤子的传输行为,其中系统Lévy指数对呼吸孤子的脉宽、振幅和周期有很好的控制作用;当线性损耗为零时,非线性增益越大,光束衍射越弱,在传输过程中的脉宽越窄,周期减小地越快,振幅增大也越快;当线性损耗不为零时,线性损耗系数越大,呼吸孤子的呼吸周期沿传输方向增大越快,振幅衰减也越快;当线性损耗为常数或者余弦形式时,通过合理选择参数和非线性增益的大小,可以使呼吸孤子的传输趋于稳定,但指数形式的线性损耗并不能平衡非线性增益对呼吸孤子的影响。Based on the nonlinear fractional Schr?dinger equation, the effects of nonlinear gain and linear loss on the propagation characteristics of Gaussian beams are numerically studied. The results show that: the gaussian beam quickly evolved into the breathing soliton and we can control breathing soliton transmission behavior by changing system parameters. The changes in Lévy index have a good control effect on the pulse width, amplitude and period of the breathing solion. A larger Lévy index makes the pulse width larger, the amplitude smaller, and the soliton period larger. When there is no linear loss, the nonlinear gain weakened the beam diffraction, the pulse width is smaller in the transmission process, the soliton period decreases and the amplitude increases faster. Constant linear loss enhanced the diffraction of breathing soliton, the soliton period increases faster along the transmission direction, and the amplitude decreases faster at the same time. Therefore, the peak intensity of breathing soliton at the maximum compression can be kept unchanged by selecting the constant linear loss and the nonlinear gain reasonably. Cosine linear loss coefficient τ;makes the soliton period increase faster along the transmission distance, but the frequency parameter β of the cosine function makes the soliton period increase slower along the transmission distance. So we can obtain the breathing soliton stability transmission by adjusting two parameters of the cosine function. When the nonlinear gain is not zero, comprehensively adjust various parameters, and the breathing soliton can be transmitted more stably. Exponential linear loss make the breathing soliton skew to left and the peak intensity attenuates exponentially along the transmission direction. The coefficient τ;is larger, the attenuation rate is larger and the soliton period increases faster. The index β make the soliton skew to left further and the soliton period change slower. However, the nonlinear gain cannot balance the effect of exponential linear los

关 键 词：分数薛定谔方程 非线性增益 线性损耗 

分 类 号：O413.1[理学—理论物理]