Generally, the properties of metamaterials are analyzed based on the infinite array of the unit cells. In real application of the metamaterial, however, the array has to be finite. Hence, it is important that a method can analyze the effect of the finite array of the metamaterial. In this paper, a model is proposed which can calculate the scattering by a large-size finite array of an I-shaped metamaterial without a full-wave simulation. The proposed model is based on the surface current estimation of each unit cells. The ratio of the current distribution on a finite array of the metamaterial to that of the infinite array of the same metamaterial for a TM polarized incident wave is approximated as a quartic polynomial. The coefficients of the polynomial are a function of the physical dimension of the metallic patch. Hence, the current distribution of the finite metamaterial can be estimated based on the proposed polynomial and the current of the infinite array. The scattered field is calculated by using the surface current model. The proposed model is numerically and experimentally verified by comparing calculated and measured RCS(Radar Cross Section) data.
The IPO(Iterative Physical Optics) method repeatedly applies the well-known PO(Physical Optics) approximation to calculate the scattered field by a large object. Thus, the IPO method can consider the multiple scattering in the object, which is ignored for the PO approximation. This kind of iteration can improve the final accuracy of the induced current on the scatterer, which can result in the enhancement of the accuracy of the RCS(Radar Cross Section) of the scatterer. Since the IPO method can not exactly but approximately solve the required integral equation, however, the convergence of the IPO solution can not be guaranteed. Hence, we apply the famous techniques used in the inversion of a matrix to the IPO method, which include Jacobi, Gauss-Seidel, SOR(Successive Over Relaxation) and Richardson methods. The proposed IPO methods can efficiently calculate the RCS of a large scatterer, and are numerically verified.
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