发表机构
Johns Hopkins University（约翰斯·霍普金斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出近似计算方法，从麦克斯韦方程组推导出偏积分微分方程，利用正则摄动展开和FFT数值求解器，模拟石墨烯上具有时空依赖属性的等离激元传播，展示行波、驻波及指数增长等波动现象。
AI 中文摘要
本文提出了用于模拟具有时间和空间依赖性材料属性的石墨烯薄片上表面等离激元传播的近似计算方法。从麦克斯韦方程组出发，在空间和时间调制的德鲁德权重下，电流密度的演化被表述为偏积分微分方程（PIDE）。假设德鲁德权重的小振幅扰动，发展了一种正则摄动展开。在适当的Sobolev空间中，建立了所得逐阶积分方程的可解性和傅里叶可逆性。引入了一种结合沃尔泰拉积分方程公式和快速傅里叶变换（FFT）的数值求解器，并给出了逐点误差估计和计算复杂度分析。此外，针对行波德鲁德权重调制，推导了一种基于解析变换的求解方法，该方法使用围道积分和拉普拉斯逆变换。数值模拟展示了多种波动现象，包括行波、驻波和指数增长的等离激元电流密度。
英文摘要
This paper presents approximate computational methods for modeling surface plasmon propagation on a graphene sheet with time- and space-dependent material properties. Starting from Maxwell's equations, the evolution of current density under a spatially and temporally modulated Drude weight is formulated as a partial integro-differential equation (PIDE). Assuming small-amplitude perturbations of the Drude weight, a regular perturbation expansion is developed. The solvability and Fourier invertibility of the resulting order-by-order integral equations are established in appropriate Sobolev spaces. A numerical solver combining a Volterra integral equation formulation with the fast Fourier transform (FFT) is introduced, along with pointwise error estimates and computational complexity analysis. Additionally, an analytical transform-based solution using contour integration and Laplace inversion is derived for traveling-wave Drude weight modulations. Numerical simulations demonstrate diverse wave phenomena, including traveling, standing, and exponentially growing plasmonic current densities.
