论文标题
介电纳米颗粒具有高折射率的电磁散射的数学分析
Mathematical analysis of electromagnetic scattering by dielectric nanoparticles with high refractive indices
论文作者
论文摘要
在这项工作中，我们关注电磁（EM）散射的数学建模，该模型通过具有高折射率的任意形状的非磁性纳米颗粒。当通过可见光照亮时，由于入射波与EM场的圆形位移电流的耦合，这种颗粒可以表现出非常强的各向同性磁反应。这项工作的主要目的是在数学上说明这一现象。我们将首先介绍EM散射的分解和介电下波共振的概念。然后，我们得出亚波长度共振和相关谐振模式的先验估计值。我们还展示了共振的存在，并根据较小的粒径和高对比度参数获得了它们的渐近膨胀。之后，我们研究了出现共振时散射幅度和横截面的增强。在此过程中，我们开发了一种新型的多极辐射框架，该辐射框架直接分离了电气和磁性多极矩，并使我们能够清楚地看到它们的数量级和打击速度。我们证明，在介电下波长谐振频率下，具有高折射率的纳米颗粒的行为就像电偶极子和谐振磁偶极子的总和。还提供了一些明确的计算和数值实验，以验证我们的一般结果和公式。
In this work, we are concerned with the mathematical modeling of the electromagnetic (EM) scattering by arbitrarily shaped non-magnetic nanoparticles with high refractive indices. When illuminated by visible light, such particles can exhibit a very strong isotropic magnetic response, resulting from the coupling of the incident wave with the circular displacement currents of the EM fields. The main aim of this work is to mathematically illustrate this phenomenon. We shall first introduce the EM scattering resolvent and the concept of dielectric subwavelength resonances. Then we derive the a priori estimates for the subwavelength resonances and the associated resonant modes. We also show the existence of resonances and obtain their asymptotic expansions in terms of the small particle size and the high contrast parameter. After that, we investigate the enhancement of the scattering amplitude and the cross sections when the resonances occur. In doing so, we develop a novel multipole radiation framework that directly separates the electric and magnetic multipole moments and allows us to clearly see their orders of magnitude and blow--up rates. We prove that at the dielectric subwavelength resonant frequencies, the nanoparticles with high refractive indices behave like the sum of the electric dipole and the resonant magnetic dipole. Some explicit calculations and numerical experiments are also provided to validate our general results and formulas.
