Nonlocal Effective-Medium Theory For Periodic Multilayered Metamaterials

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.