AI 中文总结
研究中间各向异性电磁层中嵌入有界各向异性电磁散射体时的时谐电磁散射，通过构造入射波使指定点邻域内电磁场梯度任意大，基于辅助邻域及麦克斯韦 - 赫尔格洛茨波函数逼近等方法实现局部高梯度集中。
AI 中文摘要
本文研究了在中间各向异性电磁层中嵌入有界各向异性电磁散射体时，由麦克斯韦方程组控制的时谐电磁散射问题。我们关注在周围层外界面上有限多个指定点的小边界邻域内总电场和总磁场梯度的局部增强。通过适当构造入射电磁波，可使这些邻域内总电场和总磁场的梯度任意大。定位半径可根据规定的梯度大小选择，描述了各向异性散射体附近电磁场的局部高梯度集中机制。主要策略基于引入附着在边界的辅助电磁邻域及其相关电场和磁场，利用麦克斯韦 - 赫尔格洛茨波函数的逼近性质，用物理上可允许的入射波在散射体邻域内逼近这些辅助场，结合各向异性散射问题的适定性和连续依赖性，可控制相应散射场在相关层区域足够弱，从而使总场在指定点附近由入射场主导并继承其大梯度行为。
英文摘要
This work investigates time-harmonic electromagnetic scattering governed by the Maxwell system, where bounded anisotropic scatterers are embedded in a homogeneous electromagnetic background. We focus on the localized enhancement of the gradients of the total electric and magnetic fields in small boundary-attached neighborhoods of finitely many prescribed points near boundaries of anisotropic electromagnetic scatterers. We show that, through a suitable construction of incident electromagnetic waves, the gradients of both the total electric field and the total magnetic field can be made arbitrarily large in these neighborhoods. The main strategy is based on the introduction of auxiliary boundary-attached electromagnetic neighborhoods and the associated electric and magnetic fields, which exhibit strong gradient variation near the prescribed points. Using the approximation property of Maxwell Herglotz wave functions, these auxiliary fields are then approximated by physically admissible incident waves in the neighborhood of the scatterers. Together with the well-posedness and continuous dependence of the anisotropic scattering problem, this implies that the corresponding scattered field can be controlled to be sufficiently weak in the relevant region. Consequently, the total field is dominated by the incident field near the prescribed points and inherits its large-gradient behavior. The result provides a theoretical mechanism for localized gradient enhancement in anisotropic electromagnetic scattering and may have implications for field concentration, high-resolution probing, and sensitivity analysis of electromagnetic responses in complex media.
