Creating Band Gaps in Periodic Media
Creating Band Gaps in Periodic Media
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DOI：
10.1137/16m1083396
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发表时间：
2016-07
期刊：
影响因子：
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通讯作者：
R. Lipton;Robert Viator
中科院分区：
文献类型：
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作者：
R. Lipton;Robert Viator
我们确定了在二维光子和三维声学晶体中产生带隙的几何和材料对比度的明确条件。这种方法是新颖的，它利用了晶体的静电共振和准周期无源共振。源自由模式提供了与电磁波和声波在周期性高对比度介质内传播相关的解算符的频谱表示。根据散射体的形状和几何形状，可以精确地描述准周期和静电共振谱。这些信息连同狄利克雷光谱和与内含物相关的类诺伊曼光谱提供了在有限对比度下打开带隙的充分条件。该理论为识别特定频率范围内的光子和声子带隙提供了一种系统的方法。
We identify explicit conditions on geometry and material contrast for creating band gaps in two-dimensional photonic and three-dimensional acoustic crystals. This approach is novel and makes use of the electrostatic and quasi-periodic source free resonances of the crystal. The source free modes deliver a spectral representation for solution operators associated with propagation of electromagnetic and acoustic waves inside periodic high contrast media. An accurate characterization of the quasi-periodic and electrostatic resonance spectrum in terms of the shape and geometry of the scatters is possible. This information together with the Dirichlet and a Neumann-like spectra associated with the inclusions deliver conditions sufficient for opening band gaps at finite contrast. The theory provides a systematic means for the identification of photonic and phononic band gaps within a specified frequency range.