存在色散时的时变材料：具有时间不连续性的洛伦兹介质中的平面波传播
Time-Varying Materials in Presence of Dispersion: Plane-Wave Propagation in a Lorentzian Medium with Temporal Discontinuity
AI总结：
本文研究洛伦兹色散介质中等离子体频率发生时间突变时单色平面波的散射问题，揭示二阶介电函数导致两个频移频率，并需两个额外时间边界条件来确定瞬时产生的两列前向波和两列后向波，同时给出集总电路传输线等效模型。
摘要：
我们研究了一个具有洛伦兹色散的无界介质中介电常数发生时间不连续性的问题。更具体地说，我们处理的情况是：一列在（一般有损的）类洛伦兹介质中前向传播的单色平面波，因等离子体频率发生突然的时间变化（同时保持其共振频率不变）而形成的“时间半空间界面”上发生散射。为了实现跨越时间不连续性的动量守恒，我们展示了与众所周知的非色散不连续性问题不同，介电函数的二阶特性现在会产生两个频移频率。因此，在非色散情形中，电位移D和磁感应强度B的连续性足以确定新的前向和后向波的振幅，而现在我们需要两个额外的时间边界条件。也就是说，响应于一列仅前向传播的平面波，现在会瞬时产生两列前向波和两列后向波。我们还给出了一个包含集总电路元件的传输线等效模型，用以描述所考虑的色散时间不连续情形。
英文摘要：
We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-travelling in a (generally lossy) Lorentzian-like medium scatters from the temporal "half-space interface" that results from an abrupt temporal change in its plasma frequency (while keeping its resonance frequency constant). In order to achieve momentum preservation across the temporal discontinuity, we show how, unlike in the well-known problem of a nondispersive discontinuity, the second-order nature of the dielectric function now gives rise to two shifted frequencies. As a consequence, whereas in the nondispersive scenario the continuity of the electric displacement D and the magnetic induction B suffice to find the amplitude of the new forward and backward wave, we now need two extra temporal boundary conditions. That is, two forward and two backward plane waves are now instantaneously generated in response to a forward-only plane wave. We also include a transmission-line equivalent with lumped circuit elements that describes the dispersive time-discontinuous scenario under consideration.
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