Effective-medium theory for anisotropic magnetic metamaterials

We have developed an effective-medium theory within the coherent-potential approximation, which is especially suitable to retrieve the effective constitutive parameters (permittivity and permeability) of the anisotropic magnetic metamaterials consisting of the ferrite rods. The anisotropy originates from the gyromagnetic property of the ferrite material whose permeability is a tensor with nonzero off-diagonal components. To confirm the validity of our method the photonic band structures of the two-dimensional periodic magnetic metamaterials are calculated, which are in agreement with the effective-medium theory in the long wavelength limit, in addition, even when a/lambda(0) similar to 0.4 the effective-medium theory can still be applied, where a and lambda(0) are the lattice constant and the vacuum wavelength, respectively. The simulations on the electric field patterns for a plane wave illuminated on the magnetic metamaterials and the equal-size effective scattering objects are performed, the results corroborate the effectiveness of the effective-medium theory once again. We also perform the simulation for the metamaterial composed of disordered ferrite rods, which is still in agreement with the effective-medium theory, suggesting the powerfulness of the effective-medium theory. Moreover, our results suggest that the anisotropy must be considered exactly in order to retrieve the effective constitutive parameters accurately.