Recently, the temporal control of graphene carrier density has emerged as a viable means to create various frequency shifting, modulation, and sensing photonic devices. Here we describe a general theoretical approach to calculate the graphene plasmon transformation after rapid changes of the Fermi level and carrier density. The approach is based on solving the Maxwell equations supplemented by the microscopic current equation. We derive formulas for the amplitudes of the transmitted and reflected plasmons after a rapid carrier density drop. The relation of these amplitudes and the Fourier transformed finite-difference time-domain (FDTD) fields is also established by introducing the concept of differential spectral transformation of wavepackets. The results of the analytical and FDTD approaches refute the claims of plasmon amplification under rapid carrier changes that appeared in recent theoretical studies. The presented theoretical and computational approaches form a basis of time-varying electromagnetics of graphene plasmonics.

中文翻译：

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载流子密度的快速降低导致石墨烯等离子体激元的时间散射

最近，石墨烯载流子密度的时间控制已成为创建各种移频，调制和感测光子器件的可行手段。在这里，我们描述了在费米能级和载流子密度快速变化后计算石墨烯等离子体激元转变的一般理论方法。该方法基于求解由微观电流方程补充的麦克斯韦方程。我们推导了在载流子密度快速下降之后透射和反射等离子体激元振幅的公式。通过引入波包的差分频谱变换的概念，还建立了这些振幅与傅立叶变换的有限差分时域（FDTD）场之间的关系。分析和FDTD方法的结果驳斥了最近理论研究中出现的在快速载流子变化下等离激元扩增的主张。所提出的理论和计算方法构成了石墨烯等离子体激元的时变电磁学的基础。