Increasing attention on plasmonics materials has been paid due to their exciting physical behaviors and potential applications. Here, we present the application of the Kubo formula by providing a description of the underlying mechanisms to realize the effective permittivity. We obtain plasma frequency and linear relation of frequencies with the effective permittivity. We have proposed an improved method to retrieve the effective parameters (index of refraction, impedance, permittivity, and permeability) of metamaterials from transmission and reflection data. Extents far above the calculated relations are very good match with effective permittivity-related environment, including nanospheres of some metals and a samples of the high refractive index dielectric material.
