为研究飞秒脉冲在共振二能级原子介质中传播较长距离时的演化规律,用时域有限差分的方法数值模拟了5 fs脉冲载波与共振介质相互作用的麦克斯韦布洛赫方程。结果表明,5 fs脉冲的包络与载波的形状基本吻合,变化趋势大体一致,慢变振幅近似和旋转波近似不影响基本结论。在脉冲的谱宽远大于原子介质跃迁线形增宽的条件下,3.2π脉冲演化成2π双曲正割脉冲所经历的过程非常复杂,达到稳态所通过的空间长度大约是面积演化成稳态值所需要的长度的5×104倍。因此,在短距离的面积演化过程中,飞秒脉冲无法保持双曲正割的脉冲形状,只有经过很长的传播距离才能最终到达稳态,形成孤子解。同时,通过比较5 fs和50 fs脉冲的演化情况,得出结论,脉宽越短的脉冲达到稳态所经历的过程越复杂,需要通过的空间距离越长。

To study the evolution of femtosecond (fs) laser pulse in a long-distance two-level medium, the Maxwell-Bloch equations of 5 fs carrier interaeting with two-level medium are numerically solved with use of finite-difference time domain procedure. It is found that the 5 fs pulse envelope, obtained within the slowly varying envelope approximation and rotating-wave approximation, agrees nicely with the carrier field. It is also found that it takes 50000 times longer distance for a pulse with an area of 3.2π to evolve into a stable symmetric hyperbolic-secant pulse than its area varying into a stable value. The evolution process is complicated, for the pulse's spectral width much larger than the atomic linewidth. As a result, an injected pulse with an area of 3.2π could not maintain a shape of symmetric hyperbolic-secant during its area evolving into stable, and must propagate a very long distance to transform into a stable solitary wave. In addition, comparison of the results of the 5 fs and 50 fs pulse has demonstrated that the shorter the pulse is, the more intricate process, the longer distance it needs.