异向介质中的倏逝波边界层及其变分方法的求解
Evanescent Wave Boundary Layers in Metamaterials and Sidestepping them through a Variational Approach
摘要：
所有的超材料应用都是基于这样的想法，即通过适当的动态均匀化复合材料可以实现极端的材料特性。这种均匀化几乎总是对无限域进行，然后将结果应用于有限样本。这个过程忽略了出现在这种有限样本边界处的倏逝波。在本文中，我们首先澄清这些倏逝波的出现和目的在一个模型问题组成的分层复合材料和均匀介质之间的界面。我们发现，这些倏逝波形成边界层的界面的两侧，超过该复合材料可以表示适当的无限域均匀化的关系。我们表明，如果忽略边界层，那么位移和应力场是不连续的整个界面。因此，在这样的界面处的散射系数不能通过仅涉及传播模式的常规连续性条件来确定。在这里，我们提出了一个近似的变分方法来避开这些边界层。其目的是确定的散射系数，而无需的倏逝模式的知识。通过各种数值例子，我们表明，我们的技术给出了很好的估计的实际散射系数超过长波长的限制。
英文摘要：
All metamaterial applications are based upon the idea that extreme material properties can be achieved through appropriate dynamic homogenization of composites. This homogenization is almost always done for infinite domains and the results are then applied to finite samples. This process ignores the evanescent waves which appear at the boundaries of such finite samples. In this paper we first clarify the emergence and purpose of these evanescent waves in a model problem consisting of an interface between a layered composite and a homogeneous medium. We show that these evanescent waves form boundary layers on either side of the interface beyond which the composite can be represented by appropriate infinite domain homogenized relations. We show that if one ignores the boundary layers then the displacement and stress fields are discontinuous across the interface. Therefore, the scattering coefficients at such an interface cannot be determined through the conventional continuity conditions involving only propagating modes. Here we propose an approximate variational approach for sidestepping these boundary layers. The aim is to determine the scattering coefficients without the knowledge of evanescent modes. Through various numerical examples we show that our technique gives very good estimates of the actual scattering coefficients beyond the long wavelength limit.
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