In the paper, based on the linear Schrodinger equation, we analytically investigate the effect of initial chirp on the dynamics of the optical beam in a medium with the parabolic potential. For the linear chirp, the results show that the linear chirp of beam can induce a periodically oscillating behavior, where the oscillating amplitude is proportional to the linear chirp parameter, and the beam’s peak and width are related to the depth of parabolic potential. For the quadratic chirp, the results show that the quadratic chirp of beam can induce a periodically breathing behavior and affect the evolution of beam’s peak and width.

中文翻译：

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初始啁啾对抛物线势介质中光束动力学的影响

在本文中，我们基于线性薛定谔方程，分析研究了初始啁啾对具有抛物线势的介质中光束动力学的影响。对于线性chirp，结果表明光束的线性chirp会引起周期性振荡行为，其中振荡幅度与线性chirp参数成正比，光束的峰值和宽度与抛物线势的深度有关。对于二次啁啾，结果表明光束的二次啁啾会引起周期性呼吸行为，并影响光束的峰值和宽度的演变。