2. Modeling metamaterial structure

Some methods are developed to determine the effective parameters of these structures. The electromagnetic properties of an inhomogeneous composite can be determined exactly by solving Maxwell's equations, which relate the local electric and magnetic fields to the local charge and current densities. To solve this set of equations, a relationship must be assumed that relates the four macroscopic field vectors that arise from the averaging or homogenization procedure [3].

On the other hand, many researchers have in practice used an approach based upon the reflection and transmission coefficients of a metamaterial sample of some defined thickness [2]. The Nicolson-Ross-Weir (NRW) approach is then used to obtain the effective material properties of the bulk metamaterials. The solution of equation in this method is dependent on square root function. Typically, the choice of the sign of a square root is made unambiguous by ensuring positive power flow in the direction of propagation [2]. In some situations, local effects near the boundaries of the sample must also be taken into account.

In contrast, there are some metasurface studies that have modeled the film as a single-layer metamaterial. In this way, a metasurface is replaced with a boundary plane with surface susceptibilities. It is called the Generalized Sheet Transition Condition (GSTC) [2, 4, 5].
