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本文中采用人们熟知的单模光纤负色散区中光脉冲的传输演化模型[20]:
$ {\rm i}{U_Z} + {U_{\tau \tau }}/2 + {N^2}\left| {{U^2}} \right|U = 0 $
(1) 式中, U是光场复幅度,Z和τ分别是归一化传输距离和归一化的时间; UZ表示U对Z的1阶导数,Uττ则表示U对τ的2阶导数; 孤子阶数N=1。1阶相位调制下的光脉冲形式如下:
$ U(0, \tau ) = {\rm{exp}}\left( { - {\tau ^{2{m}}}/2} \right){\rm{exp}}( - {\rm{i}}b\tau ) $
(2) 式中,b是相位调制参量,m是脉冲平顶程度的参量,m=2和m>2分别代表高斯和平顶光脉冲。U, Z, τ, m和b都是无量纲的量。
光纤中光脉冲的直线平移及幅度衰减振荡特性
Straight line shifts and damping amplitude oscillation of optical pulses in optical fibers
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摘要: 为了探索初始1阶相位调制对高斯光脉冲光纤中长距离传输特性的影响规律,从光纤中的非线性光演化方程出发,采用分步傅里叶算法,数值研究了初始1阶相位调制的高斯光脉冲在光纤中传输时的形状、幅度、时间轨道的演化特性。结果表明,高斯脉冲在长距离传输中,一方面其幅度呈现出衰减的振荡行为,另一方面其时间轨道则因为1阶相位调制的存在而发生直线平移;直线平移的大小和方向分别取决于相位调制参量的绝对值和正负号。该工作可扩展非孤子脉冲的长距离传输特性研究,并可用于脉冲时间轨道的直线调控。Abstract: In order to explore the effects of the initial first-order phase modulation on the long distance propagation properties of Gaussian optical pulses in optical fibers, evolutions of initially first-order phase modulated Gaussian optical pulses in terms of their shapes, amplitudes, and temporal trajectories, were numerically investigated by starting from the nonlinear evolution equation governing the optical pulse propagation and using the split-step Fourier algorithm. The results show that, the Gaussian pulses exhibit damped oscillation behavior in terms of their amplitudes on the one hand and shift towards the leading or trailing edges of the pulses along straight lines in terms of their temporal trajectories on the other hand due to the first-order phase modulation. The shifting magnitude and direction respectively depend on the absolute value and sign of the phase modulation parameters. This work can extend study on long distance propagation properties of non-soliton pulses. Moreover, it can also be applied in straight-line manipulating of temporal trajectories.
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