Microwave effective medium theory for two-component magnetic metamaterials

In this paper, Effective Medium Theory for two-component metamaterial media as infinite host dielectric medium embedded periodically with cylindrical iron inclusions and spherical ones saturated with an external biasing magnetic field is developed in the microwave frequencies. The long wave approximation of effective permeability tensors for the considered metamaterial media has been obtained using the microwave extension of Effective Medium Approximation for polycrystalline ferrites and the long wave approximation of expressions of the effective magnetic permeability for two-component undiluted metal-dielectric composites with infinitely long non-magnetic metal cylindrical and spherical inclusions. The effective magnetic properties of the metamaterial media for the case of microwave propagation transverse to bias have been studied. It is shown that the considered metamaterial can exhibit the ultra-low refractive index phenomenon and the phenomenon of negative magnetic permeability for the case of microwave propagation transverse to bias.