论文标题
电磁散射共振和次波长环形间隙中的现场增强的数学理论
Mathematical theory for electromagnetic scattering resonances and field enhancement in a subwavelength annular gap
论文作者
论文摘要
这项工作提出了一种数学理论，用于在金属板中嵌入的亚波长孔中电磁散射共振，并带有环形宽度$ h \ ll1 $。该模型是许多3D亚波长孔结构的代表性，这些孔结构能够诱导电磁波的共振散射和所谓的非凡光学传输。我们基于外部域中积分方程的组合和小孔内的波导模式扩展，为基础散射问题开发了一个多尺度框架。孔孔径上电磁场的匹配导致一系列分离的无限系统，这些系统用于为散射问题设置共振条件。通过对无限系统和共振条件进行严格的分析，我们表征了复杂平面上有界域中的所有共振。结果表明，共振与环形孔中的TE和TEM波导模式相关联，它们与订单$ {\ cal o}（h）$的假想部分的真实轴接近。我们还会研究存在事件波时的谐振散射。证明，电磁场在与环形孔中与TE模式相关的谐振频率处用$ {\ cal o}（1/h）$放大。另一方面，与TEM模式相关的一种特定共振不能被平面波激发，但可以用近场电偶极子源激发，从而导致订单$ {\ cal O}（1/h）$的场增强。
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 ${\cal O}(1/h)$.
