Dorrah Ahmed H, Ramakrishnan Abhinav, Mojahedi Mo
Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario M5S 3G4, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Mar;91(3):033206. doi: 10.1103/PhysRevE.91.033206. Epub 2015 Mar 24.
Spectral reshaping and nonuniform phase delay associated with an electromagnetic pulse propagating in a temporally dispersive medium may lead to interesting observations in which the group velocity becomes superluminal or even negative. In such cases, the finite bandwidth of the superluminal region implies the inevitable existence of a cutoff distance beyond which a superluminal pulse becomes subluminal. In this paper, we derive a closed-form analytic expression to estimate this cutoff distance in abnormal dispersive media with gain. Moreover, the method of steepest descent is used to track the time-frequency dynamics associated with the evolution of the center of mass of a superluminal pulse to the subluminal regime. This evolution takes place at longer propagation depths as a result of the subluminal components affecting the behavior of the pulse. Finally, the analysis presents the fundamental limitations of superluminal propagation in light of factors such as the medium depth, pulse width, and the medium dispersion strength.
与在时间色散介质中传播的电磁脉冲相关的频谱重塑和非均匀相位延迟可能会导致一些有趣的现象，其中群速度可能会变得超光速甚至为负。在这种情况下，超光速区域的有限带宽意味着必然存在一个截止距离，超过这个距离，超光速脉冲就会变成亚光速脉冲。在本文中，我们推导了一个封闭形式的解析表达式，用于估计具有增益的反常色散介质中的这个截止距离。此外，最速下降法被用于追踪与超光速脉冲质心演化为亚光速状态相关的时频动态。由于亚光速分量影响脉冲的行为，这种演化发生在更长的传播深度处。最后，根据介质深度、脉冲宽度和介质色散强度等因素，分析给出了超光速传播的基本限制。
