通过表面传输共振生成定制化场浓度
Generating customized field concentration via virtual surface transmission resonance
AI总结：
本文提出通过表面传输共振在非均匀介质包含体周围生成强定制化场浓度的数学框架，证明可设计入射场在任意指定位置产生局域场浓度，并证明特定波数下存在满足要求的表面传输共振模式。
摘要：
本文开发了一个数学框架，通过表面传输共振在非均匀介质包含体局部周围生成强定制化场浓度。本文目的有二：首先，我们证明对于嵌入均匀背景空间中的给定包含体，可以设计入射场在包含体周围任意指定位置生成强局域场浓度。上述定制化场浓度关键依赖于某些传输本征函数的特殊谱和几何模式。其次，我们证明对于特定波数存在一序列传输本征函数，它们表现出不同的表面共振行为，伴随强表面局域化和表面振荡特性。这些本征函数作为表面传输共振模式满足生成场浓度的要求。
英文摘要：
In this paper, we develop a mathematical framework for generating strong customized field concentration locally around the inhomogeneous medium inclusion via surface transmission resonance. The purpose of this paper is twofold. Firstly, we show that for a given inclusion embedded in an otherwise uniformly homogeneous background space, we can design an incident field to generate strong localized field concentration at any specified places around the inclusion. The aforementioned customized field concentration is crucially reliant on the peculiar spectral and geometric patterns of certain transmission eigenfunctions. Secondly, we prove the existence of a sequence of transmission eigenfunctions for a specific wavenumber and they exhibit distinct surface resonant behaviors, accompanying strong surface-localization and surface-oscillation properties. These eigenfunctions as the surface transmission resonant modes fulfill the requirement for generating the field concentration.
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