时空介质中的折射定律
Refraction laws in spatio-temporal media
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中文总结 AI 辅助
研究时空介质中电磁波传播的时变麦克斯韦方程组，推导广义斯涅尔定律等，以斜入射示例验证，方法不要求光滑场且允许界面外材料参数非恒定。
中文摘要 AI 辅助
我们研究以分布意义表述的时变麦克斯韦方程组，针对在具有时间和空间材料界面的介质中传播的电磁波。在对介电常数和磁导率的显式迹与正则性假设下，我们推导了由时间不连续性及后续空间界面产生的跳跃条件。这些条件用于获得由时间分裂、反射和透射产生的波矢的广义斯涅尔定律。我们还推导了相关的振幅方程，并将其整理为时空 slab 几何下的有限维线性系统。最后，我们提供了一个显式斜入射示例。我们的方法未施加光滑场假设，且允许界面外材料参数不必为常数。
英文摘要
We study the time-dependent Maxwell system, formulated in the sense of distributions, for electromagnetic waves propagating through media with temporal and spatial material interfaces. Under explicit trace and regularity assumptions on the permittivity and permeability, we derive the jump conditions produced by temporal discontinuities and by subsequent spatial interfaces. These conditions are used to obtain generalized Snell laws for the wave vectors generated by temporal splitting, reflection, and transmission. We also derive the associated amplitude equations and organize them as a finite-dimensional linear system for a space-time slab geometry. Finally, we provide an explicit oblique-incidence example. Our approach does not impose a smooth-field ansatz and allows material parameters that need not be constant away from the interfaces.
