有限频率范围内双互补介质的反常局域共振隐身
Cloaking via anomalous localized resonance for doubly complementary media in the finite frequency regime
摘要：
Milton和Nicorovici在\cite{MiltonNicorovici}中发现了通过反常局域共振（ALR）来掩盖源。通过ALR进行源掩蔽的一般设置是双互补介质的设置。这在\cite{Ng-CALR}中针对准静态状态进行了介绍和研究。在本文中，我们研究了通过ALR在有限频率范围内的双互补介质作为自然延续的\cite{Ng-CALR}的源的掩盖。我们建立了以下结果：1）通过ALR隐藏源出现当且仅当功率爆炸; 2）功率爆炸，如果源是“放置”附近的等离子体结构; 3）功率保持有界，如果源是远离等离子体结构。关于分析，我们从\cite{Ng-CALR}扩展的想法，并添加新的见解的问题，使我们能够克服困难的有限频率制度，并获得新的信息的问题。特别是，我们能够表征的行为的字段足够远的等离子体壳的损失为0的{ \bf任意源}的核壳结构以外的双互补介质设置。
英文摘要：
Cloaking a source via anomalous localized resonance (ALR) was discovered by Milton and Nicorovici in \cite{MiltonNicorovici}. A general setting in which cloaking a source via ALR takes place is the settting of doubly complementary media. This was introduced and studied in \cite{Ng-CALR} for the quasistatic regime. In this paper, we study cloaking a source via ALR for doubly complementary media in the finite frequency regime as a natural continuation of \cite{Ng-CALR}. We establish the following results: 1) Cloaking a source via ALR appears if and only if the power blows up; 2) The power blows up if the source is ``placed" near the plasmonic structure; 3) The power remains bounded if the source is far away from the plasmonic structure. Concerning the analysis, we extend ideas from \cite{Ng-CALR} and add new insights on the problem which allows us to overcome difficulties related to the finite frequency regime and to obtain new information on the problem. In particular, we are able to characterize the behaviour of the fields far enough from the plasmonic shell as the loss goes to 0 for an {\bf arbitrary source} outside the core-shell structure in the doubly complementary media setting.
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