横向电磁场在相邻障碍物中的数学分析：非局部边界条件下的准静态情形
Mathematical analysis of transverse EM field concentration for adjacent obstacles with nonlocal boundary conditions in the quasistatic regime
AI总结：
本文研究了相邻障碍物间横向电磁场集中问题，分析了非局部边界条件对经典梯度估计的影响，并推导了梯度爆炸的最优速率，揭示了波频率对场集中程度的缓解作用。
摘要：
本文对准静态近似下相邻障碍物间横向电磁场集中现象进行了严谨的数学分析。我们研究了三种退化导体模型，其中两种引入了非局部边界条件以捕捉表面非局部性和薄层相互作用等基本物理现象。主要结果建立了梯度爆炸的精确条件并推导了对应的最优爆炸速率。这些发现阐明了非局部边界条件如何修改经典梯度估计。此外，我们分析了波频率的影响，证明即使在间隙距离趋于零的极限情况下，波频率也能减轻场集中程度。因此，本文将经典等离子体和超材料系统中的场增强理论扩展到包含非局部表面效应，得到精确的渐近公式，这对纳米光子器件的定量设计至关重要。
英文摘要：
This paper presents a rigorous mathematical analysis of transverse electromagnetic (EM) field concentration between two adjacent obstacles within the framework of the quasi-static approximation. We investigate three degenerate conductivity models recently introduced in [22], two of these incorporating nonlocal boundary conditions to capture fundamental physical phenomena, such as surface nonlocality and thin-layer interactions. Our primary results establish sharp conditions for gradient blowup and derive the corresponding optimal blowup rates. These findings elucidate how nonlocal boundary conditions modify classical gradient estimates. Furthermore, we analyze the influence of wave frequency, demonstrating that it mitigates the severity of field concentration even in the limit of a vanishing gap distance. Consequently, this work extends the classical theory of field enhancement in plasmonic and metamaterial systems to incorporate nonlocal surface effects, yielding precise asymptotic formulas that are essential for the quantitative design of nanophotonic devices.
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