Extraction and control of permittivity of hyperbolic metamaterials with optical nonlocality

Metal nanorod arrays exhibit hyperbolic dispersion and optical nonlocality under certain conditions. Therefore, their optical behaviors can hardly be expressed by incident-angle-independent effective permittivity. Here we extract effective permittivity of silver nanorod arrays with diameters of 4 nm, 12 nm, and 20 nm by polarized transmission method in the visible range. The incident angles are chosen from 20° to 60° to study the influence of optical nonlocality on permittivity. We demonstrate how the diameter of the nanorods can control the effective permittivity beyond the effective medium theory. The results suggest that the effective permittivity gradually loses its accuracy as the diameter increases due to the optical nonlocality. Our experiment verifies that ultrathin nanorod arrays can resist the fluctuations caused by changes in incident angle. We also extract k-dependent effective permittivity of nanorods with larger diameters.