Wave propagation in periodic structures and negative refraction mechanisms

已知产生负折射的机制有三种。所有这些主题都得到了实验证实，进行了数值研究，并在文献中提供了一些基于均质化方法或布洛赫波分析的分析解释。第一种（也是现在的经典）方法涉及到负转位超材料（反过来，它可以用光子晶体来构建）。在第一种方法中，周期结构的尺寸与波长相比很小。第二种方法依赖于波与光子晶体的相互作用（波长和周期长度可比较）。第三种方法使用表面凹凸（在波的长度尺度上）。我们的目的是推导出研究负分数效应的解析和数值方法，提供有效的模型和有效的数值方案。

Three mechanisms are known to produce negative refraction. All of themare experimentally confirmed, numerical studies have been performed,and some analytical explanations on the basis of either homogenizationmethods or Bloch-wave analysis are available in the literature. Thefirst (and by now classical) method involves negative indexmetamaterials (which can, in turn, be contructed using a photoniccrystal). In this first approach, the size of the periodic structureis small compared to the wave-length. A second method relies on aninteraction of a wave with a photonic crystal (wave-length andperiodicity length are comparable). A third approach uses surfacecorrugations (at the length-scale of the wave). Our aim is to deriveanalytical and numerical methods to investigate the negativerefraction effect, to provide effective models and efficient numericalschemes.