色散缓变光纤中初始啁啾对超高斯脉冲传输特性的影响

Influence of Initial Chirp on Propagation Properties of Super-Gaussian Pulses in Fibers with Slowly Decreasing Dispersion

从非线性薛定谔方程出发,采用变分法,导出了色散缓变光纤中超高斯脉冲参数随传输距离的演化方程组及其解,讨论了初始啁啾对色散缓变光纤中超高斯脉冲传输特性的影响。求出了振幅与脉宽、频率与啁啾、脉宽与啁啾之间的三个解析约束关系,得出了脉宽随传输距离演化的解析解,用龙格-库塔法进行数值求解描绘了初始啁啾和脉冲前后沿锐度对呈指数变化的色散缓变光纤中超高斯脉冲的脉宽的影响。结果表明:初始啁啾、色散缓变和脉冲前后沿锐度对超高斯脉冲的振幅、脉宽、啁啾和相位有直接影响,脉冲前后沿锐度对超高斯脉冲中心位置没有影响,超高斯脉冲传输过程中会产生啁啾,但脉冲中心的等效频率保持为常数。

Based on the nonlinear Schroedinger equation, the variational method is used to derive the evolution equations for the parameters of the super-Gaussian pulse in fibers with slowly decreasing dispersion. The effect of initial chirp on the super-Gaussian pulse is discussed. Then three restricted relations between amplitude and width, frequency and chirp, width and chirp are derived. Analytical solution about the evolution of pulse width versus propagation distance is obtained. By using Runge-Kutta algorithm, the influence of the initial chirps and the degree of the pulse＇s edge sharpness on the pulse width is described. The results show that initial chirps, dispersion decreasing and the degree of the pulse＇s edge sharpness have direct influence on amplitude, width, chirp and phase. The degree of the pulse＇s edge sharpness has no effect on pulse central position, and the super-Gaussian pulse in the process of transmission can cause chirps, but the equivalent frequency keeps constant.