论文标题
用小谐振器在定期媒体中创建和控制乐队差距
Creating and controlling band gaps in periodic media with small resonators
论文作者
论文摘要
我们研究了Neumann Laplacian $ \ Mathscr {a} _ \ Varepsilon $在周期性无界域$ω__\ varepsilon $上的光谱属性，这取决于小参数$ \ varepsilon> 0 $。域$ω__\ varepsilon $是通过从$ \ mathbb {r}^n $ $ m \ in \ mathbb {n} $的$ \ varepsilon $ - periododoodoodoodody分布的小共振器中删除来获得的。我们证明$ \ Mathscr {a} _ \ Varepsilon $的频谱至少具有$ m $差距。第一个$ m $差距将$ \ varepsilon \ to $ \ varepsilon \至0 $收敛到某些间隔，其位置和长度可以由合适的选择谐振器控制；其他差距（如果有）转到无限。讨论了光子晶体理论的应用。
We investigate spectral properties of the Neumann Laplacian $\mathscr{A}_\varepsilon$ on a periodic unbounded domain $Ω_\varepsilon$ depending on a small parameter $\varepsilon>0$. The domain $Ω_\varepsilon$ is obtained by removing from $\mathbb{R}^n$ $m\in\mathbb{N}$ families of $\varepsilon$-periodically distributed small resonators. We prove that the spectrum of $\mathscr{A}_\varepsilon$ has at least $m$ gaps. The first $m$ gaps converge as $\varepsilon\to 0$ to some intervals whose location and lengths can be controlled by a suitable choice the resonators; other gaps (if any) go to infinity. An application to the theory of photonic crystals is discussed.
