Spatial-dispersion (nonlocal) effects are non-negligible in periodic multilayered metamaterials under certain specific conditions, which cannot be completely understood based on the local effective-medium theory, even though the metamaterials are constructed by deep subwavelength meta-atoms. Here, we present a simple yet robust effective-medium model for such media in which the nonlocal effects are properly considered. Our proposed nonlocal model is established by the analysis of the dispersion relation of the effective medium without any expansion-based approximation, which is applicable for description of the optical behavior of the multilayered metamaterials even under critical conditions, and works well for both TE and TM polarized waves. We believe our model will be a powerful tool for the investigation of electromagnetic nonlocality in the realm of metamaterials and subwavelength optics.

在某些特定条件下，周期性多层超材料中的空间色散（非局域）效应是不可忽略的，即使超材料是由深亚波长超原子构成的，基于局域有效介质理论也无法完全理解这一点。在这里，我们为此类媒体提出了一个简单而强大的有效媒体模型，其中适当地考虑了非局部效应。我们提出的非局部模型是通过分析有效介质的色散关系建立的，没有任何基于膨胀的近似，即使在临界条件下也适用于描述多层超材料的光学行为，并且适用于 TE 和 TM极化波。