标题： 电磁散射共振和亚波长环形间隙中的场增强的数学理论 显示英文标题

标题： Mathematical theory for electromagnetic scattering resonances and field enhancement in a subwavelength annular gap

摘要： 这项工作提出了一个数学理论，用于研究嵌入在金属板中的亚波长环形孔的电磁散射共振，环形孔的宽度为$h\ll1$。该模型代表了许多三维亚波长孔结构，这些结构能够引起电磁波的共振散射和所谓的超常光学透射。我们基于外部区域的积分方程和微小孔洞内部的波导模展开相结合的方法，为基本的散射问题建立了一个多尺度框架。在孔洞开口处对电磁场进行匹配，得到一系列解耦的无限系统，这些系统用于建立散射问题的共振条件。通过对无限系统和共振条件进行严格的分析，我们在复平面上的一个有界区域内表征了所有的共振。结果表明，这些共振与环形孔中的TE和TEM波导模式有关，并且它们接近实轴，虚部的阶数为${\cal O}(h)$。我们还研究了存在入射波时的共振散射。证明了在与环形孔中的TE模式相关的共振频率处，电磁场的放大倍数为${\cal O}(1/h)$。另一方面，与TEM模式相关的一个特定共振不能由平面波激发，但可以由近场电偶极子源激发，从而导致场增强的阶数为${\cal O}(1/h)$。 显示英文摘要

摘要： This work presents a mathematical theory for electromagnetic scattering resonances in a subwavelength annular hole embedded in a metallic slab, with the annulus width $h\ll1$. The model is representative among many 3D subwavelength hole structures, which are able to induce resonant scattering of electromagnetic wave and the so-called extraordinary optical transmission. We develop a multiscale framework for the underlying scattering problem based upon a combination of the integral equation in the exterior domain and the waveguide mode expansion inside the tiny hole. The matching of the electromagnetic field over the hole aperture leads to a sequence of decoupled infinite systems, which are used to set up the resonance conditions for the scattering problem. By performing rigorous analysis for the infinite systems and the resonance conditions, we characterize all the resonances in a bounded domain over the complex plane. It is shown that the resonances are associated with the TE and TEM waveguide modes in the annular hole, and they are close to the real axis with the imaginary parts of order ${\cal O}(h)$. We also investigate the resonant scattering when an incident wave is present. It is proved that the electromagnetic field is amplified with order ${\cal O}(1/h)$ at the resonant frequencies that are associated with the TE modes in the annular hole. On the other hand, one particular resonance associated with the TEM mode can not be excited by a plane wave but can be excited with a near-field electric dipole source, leading to field enhancement of order ${\cal O}(1/h)$.