Although many effective-medium theories have been proposed for studying metamaterials, most of them do not work well for multilayer metamaterials with small interlayer distances. Based on rigorous mode-expansion analyses on a model system consisting of multiple layers of subwavelength gratings, we identify that the failures of conventional effective-medium theories are caused by neglecting strong near-field couplings in homogenizing such systems. These understandings motive us to propose an alternative homogenization approach for strongly coupled multilayer metamaterials, in which predominant near-field corrections have been considered automatically. Our effective-medium theory can well describe multilayer metamaterials with arbitrary interlayer distances including particularly those systems for which conventional effective-medium theories fail. We finally extend our theory to multilayer metamaterials with complicated microstructures and validate the theory by full-wave simulations as well as microwave experiments. Our theory not only well complements the available effective-medium theory formalisms, but also provides a powerful tool to study the properties of strongly coupled metamaterials, which may find many applications in practice.

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多层超材料的有效介质理论：近场校正的作用

尽管已经提出了许多有效的介质理论来研究超材料，但大多数理论不适用于层间距离较小的多层超材料。基于严谨在由多层亚波长光栅组成的模型系统上的模式扩展分析中，我们确定了常规有效介质理论的失败是由于在均匀化此类系统中忽略了强近场耦合引起的。这些理解促使我们提出一种用于强耦合多层超材料的替代均质化方法，其中已自动考虑了主要的近场校正。我们的有效介质理论可以很好地描述具有任意层间距离的多层超材料，特别是那些常规有效介质理论无法实现的系统。最后，我们将理论扩展到复杂的多层超材料微结构，并通过全波模拟和微波实验验证了该理论。我们的理论不仅很好地补充了可用的有效介质理论形式主义，而且为研究强耦合超材料的性质提供了强大的工具，在实践中可能会发现许多应用。