DETERMINATION OF EFFECTIVE PARAMETERS OF METAMATERIALS WITH SPHERICAL INCLUSION AT GHz FREQUENCIES

Abstract

This thesis is devoted to the theoretical description of two component metamaterials as arrays of spherical inclusions. Metamaterials include both electric and magnetic phenomena. We study the long wave approximation for electromagnetic response of the generalized infinite chain and develop Effective Medium Theory for two types of two component composite metamaterials. One type is composed of a host dielectric material embedded periodically with spherical inclusions (iron/copper/cobalt/ferrites) and the other is a 2-D sandwich metamaterial structure in which the central material contains a chain of infinitely long metallic cylinders and the lateral slabs are embedded with spherical metallic inclusions. In this thesis the microwave frequency range 0 to 5 GHz has only been considered. The metamaterial media / structures are being considered in the thesis as artificial ferrites with their own effective complex dielectric and magnetic constants. So, the metamaterial media/ structures presented in the thesis are considered as perfect crystals with their own dispersive properties in the microwave frequency range. The lattice constant of the crystal is equal to the constant of the unit cell of metamaterial under consideration. The expressions for effective permeability tensors of the considered metamaterial medium have been obtained in microwave approximation. Using Effective Medium Theory (EMT) and Effective Medium Approximation we obtain expressions for effective saturation magnetization of the considered metamaterial medium. The effective magnetic properties for the case of the microwave propagation transverse to bias and in the direction of bias have also been obtained. Our polycrystalline metaferrites designed as metamaterial exhibited the Ultra-Low Refractive Index (ULI) phenomenon. In our thesis we have also performed an analytical modeling and numerical analysis of the effective electromagnetic response of the proposed metamaterial medium. The analytical modeling has been done using two different modified mathematical models of the complex relative permittivity and permeability for unbounded composite medium with spherical inclusions. Numerical simulations of the above mentioned parameters have been made using S‐parameters obtained from Finite‐Difference Time‐Domain technique. The numerical simulation has been carried out for different radii of the inclusions. Remarkable coincidence between analytical and numerical results is found. The enhancement in effective relative permittivity and refractive index of the considered composite has been observed. The generalization has been done by the approaches of S- and T-matrices. The analytically obtained results are compared with the numerically calculated ones. All of the numerical simulations presented in the thesis have been done with the help of the free Meep FDTD software package while analytical modeling has been carried out using MATLAB software. Recommendations for the practical application of presented artificial material for designing microwave patch antennas have also been discussed.