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-traveling in a (generally lossy) Lorentzian-like medium scatters from the temporal interface that results from an instantaneous and homogeneous 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 $\mathbf{D}$ and the magnetic induction $\mathbf{B}$ suffices 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.

中文翻译：

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存在色散的时变材料：平面波在具有时间不连续性的洛伦兹介质中的传播

我们研究了具有洛伦兹色散的无界介质的介电常数的时间不连续性问题。更具体地说，我们解决了在（通常是有损的）类洛伦兹介质中向前传播的单色平面波从时间界面散射的情况，这是由于其等离子体频率的瞬时均匀突然时间变化（同时保持其共振）频率常数）。为了在时间不连续性上实现动量保持，我们展示了与众所周知的非色散不连续性问题不同，介电函数的二阶性质现在如何产生两个移位的频率。因此，而在非分散情况下，电位移的连续性$\mathbf{D}$ 和磁感应 $\mathbf{乙}$足以找到新的前向和后向波的幅度，我们现在需要两个额外的时间边界条件。即，现在响应仅向前的平面波，瞬时产生两个前向和两个后向平面波。我们还包括一个传输线等效的集总电路元件，描述了正在考虑的色散时间不连续场景。