We theoretically and numerically investigate the dynamics of a time truncated finite energy Airy pulse (FEAP) under longitudinally varying group velocity dispersion (GVD), which significantly influences the Airy dynamics. Realistic waveguide geometries are proposed that offer linear and oscillating GVD profiles through which one can efficiently control the ballistic Airy trajectory. We observe that a linear spatial variation of GVD may lead to a quasi-linear trajectory of the accelerating Airy pulse with modulated peak power. The impact of the periodic GVD on Airy dynamics is found to be interesting, where FEAP exhibits an oscillatory trajectory with a periodic modulation of peak power. Exploiting the transcendental relation between the modulation strength and period of GVD, we theoretically estimate an optimized length of the waveguide that delivers maximum power at the output. The effect of oscillatory third-order dispersion is dramatic for an Airy pulse, where it experiences successive singularities during its propagation. At singularity, the Airy pulse undergoes a temporal inversion after reaching a focal point. The rich dynamics of FEAP near the singularity point is theoretically investigated by solving the propagation equation. We provide detailed theoretical analyses to achieve selective temporal focusing of FEAP, which may be useful for practical applications. Theoretical results derived in this paper are verified numerically with satisfactory agreements.

中文翻译：

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时变截断艾里脉冲在变化色散介质中的动力学和选择性时间聚焦

我们在理论上和数值上研究了在纵向变化的群速度色散（GVD）下，时间截断的有限能量艾里脉冲（FEAP）的动力学，这极大地影响了艾里动力学。提出了现实的波导几何形状，该几何形状提供了线性和振荡的GVD轮廓，通过它们可以有效地控制弹道艾里弹道。我们观察到，GVD的线性空间变化可能导致具有调制峰值功率的加速艾里脉冲的准线性轨迹。发现周期性GVD对Airy动力学的影响很有趣，其中FEAP表现出具有周期性调制峰值功率的振荡轨迹。利用GVD的调制强度和周期之间的超越关系，我们从理论上估算出在输出端提供最大功率的波导的最佳长度。对于艾里脉冲，振荡三阶色散的影响是巨大的，在传播过程中，艾里脉冲经历了连续的奇点。在奇异点上，艾里脉冲在到达焦点后经历时间反转。通过求解传播方程，从理论上研究了奇点附近FEAP的丰富动力学。我们提供详细的理论分析以实现FEAP的选择性时间聚焦，这可能对实际应用有用。本文得出的理论结果在数值上得到了满意的验证。它在传播过程中经历连续的奇点。在奇异点上，艾里脉冲在到达焦点后经历时间反转。通过求解传播方程，从理论上研究了奇点附近FEAP的丰富动力学。我们提供详细的理论分析以实现FEAP的选择性时间聚焦，这可能对实际应用有用。本文得出的理论结果在数值上得到了满意的验证。它在传播过程中经历连续的奇点。在奇异点上，艾里脉冲在到达焦点后经历时间反转。通过求解传播方程，从理论上研究了奇点附近FEAP的丰富动力学。我们提供详细的理论分析以实现FEAP的选择性时间聚焦，这可能对实际应用有用。本文得出的理论结果在数值上得到了满意的验证。这对于实际应用可能很有用。本文得出的理论结果在数值上得到了满意的验证。这对于实际应用可能很有用。本文得出的理论结果在数值上得到了满意的验证。