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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 Schrödinger equation, the variational method is used to derive the evolution equation and the solution of the parameters of the super-Gaussian pulse with respect to the transmission distance in the fiber with slowly decreasing dispersion. The influence of the initial chirp on the transmission characteristics of the super-Gaussian pulse in the fiber with slowly- . The three analytic constraints between amplitude and pulse width, frequency and chirp, pulse width and chirp are obtained, and the analytic solution of pulse width with the evolution of transmission distance is obtained. The numerical solution is obtained by Runge-Kutta method The effect of initial chirp and sharpness along the pulse front and back on the pulse width of a super-Gaussian pulse in an exponentially varying dispersion-slowing fiber is depicted. The results show that the initial chirp, the chromatic dispersion and the sharpness of the anterior and posterior edge of the pulse have a direct effect on the amplitude, pulse width, chirp and phase of the super-Gaussian pulse. The sharpness of the anterior and posterior pulse has no influence on the center position of the super- Chirp occurs during pulse transmission, but the equivalent frequency of the pulse center remains constant.