Effects of positional disorder upon the nonlocal effective parameters of a metamaterial composed of coated spheres

Abstract

An electromagnetic characterization of a bianisotropic medium based on nonlocal homogenization theory with small positional disorders has been presented. The proposed theory is general and can be used for any type of random positional disorders provided that the probability density functions associated with these positional disorders are known. Later, the proposed general theory was used for a nonlocal metamaterial composed of coated spheres with Gaussian types of positional disorder in the microwave and infrared range of frequencies. It is studied that by increasing the positional disorder, the epsilon negative, mu negative and double negative bandwidths of a metamaterial reduce and even vanish for some special cases. It is found that the bandwidths of absorption peaks associated with the imaginary parts of effective permittivity and effective permeability become wider with the increase in positional disorder. It is also concluded that magnetoelectric coupling arising due to lattice effects become almost negligible for the relatively large positional disorder for a weak nonlocal or spatially dispersive metamaterial. The proposed findings are helpful in the designing of nonlocal disordered metamaterials.