Lorentzian-type media support optical phonons that oscillate with longitudinal polarization parallel to the wave direction, at a wave-vector-independent frequency at which the permittivity becomes zero. Here, we study the interactions between the longitudinal optical phonons and Lorentzian medium-based dispersive photonic time crystals (PTCs). We demonstrate that a stationary charge embedded in the PTCs can excite these longitudinal modes through the conversion of the static polarization field induced by the charge. Furthermore, the PTCs can develop a momentum band gap across the entire wave vector space to amplify the longitudinal modes. Remarkably, this infinite momentum band gap can be established with minimal temporal modulation of the refractive index when creating the PTCs. Our approach expands the range of waves that can be manipulated in PTCs and shows potential for observing the momentum band gap phenomenon in realistic optical experiments, where the modulation depth of the refractive index is severely constrained.

中文翻译：

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含有固定电荷的光子时间晶体中的纵向光学声子


洛伦兹型介质支持光学声子，该光学声子以平行于波方向的纵向偏振以与波矢量无关的频率振荡，在该频率下介电常数变为零。在这里，我们研究纵向光学声子和洛伦兹介质色散光子时间晶体（PTC）之间的相互作用。我们证明，嵌入 PTC 中的固定电荷可以通过电荷感应的静态极化场的转换来激发这些纵向模式。此外，PTC 可以在整个波矢量空间上形成动量带隙，以放大纵模。值得注意的是，在创建 PTC 时，可以通过折射率的最小时间调制来建立这种无限动量带隙。我们的方法扩大了 PTC 中可操纵的波范围，并显示出在现实光学实验中观察动量带隙现象的潜力，其中折射率的调制深度受到严重限制。