Metamaterial's effective electric permittivity model

In this paper we study an artificial material composed of a periodic structure defined by a unit cell containing cylindrical electrical conductors. These materials, called metamaterials, have special electromagnetic properties such as simultaneously negative magnetic permeability and electrical permittivity, which could not be obtained from homogeneous materials that exist in nature. An analytical model for effective electrical permittivity of the entire system in terms of the dimensions of the unit cell and frequency is obtained. We also study how to vary the resonance frequency of the artificial material in which the effective permittivity is negative. This analysis enables the fabrication of structures whose properties can be modified to be applied in shieldings. Kramers Kronig relations, suited for verifying causality in electrical permittivity models by relating the real and the imaginary parts of the dielectric permittivity is also studied. The imaginary part of the effective permittivity has been obtained numerically by applying the Hilbert transform to the real part of the permittivity simulated by the proposed Model thus verifying the Kramers-Kronig relations.