Wave propagation in periodic structures and negative refraction mechanisms

已知有三种机制可以产生负折射。所有这些都是实验证实，数值研究已经进行，和一些分析的基础上，无论是homogenizationmethods或布洛赫波分析的解释是在文献中。 第一种方法（现在是经典的）涉及负折射率的超材料（反过来，它可以用光子晶体来构造）。 在第一种方法中，周期性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（波长和周期长度相当）。第三种方法使用表面波纹（在波浪的长度尺度上）。 我们的目标是推导出研究负折射效应的解析和数值方法，提供有效的模型和高效的数值格式。

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.