Extraction algorithm for retrieving the effective constitutive parameters of metamaterials based on TE10 rectangular waveguide

A novel retrieval method of the effective constitutive parameters of metamaterials based on TE10 rectangular waveguide is proposed, which is adopted to extract effective relative permittivity epsilon and permeability mu for the composite ferrite and wire array metamaterial in multiple symmetrical unit cell configuration. Much attention has been paid to choose the correct branch of the real part of the propagation constant beta for the metamaterial with multiple unit cells, and in terms of the relationship between the measured values and theoretical values in the measurement theory, beta values in the case of multiple unit cells are determined by taking the extracted beta values for a single unit cell as the measured values for the multiple unit cells case. Owing to the coupling effect between the unit cells of the metamaterial with multiple unit cells, the electromagnetic wave mainly behaves as the periodic Bloch wave, which is usually negligible for a single unit cell, so the extracted effective constitutive parameters for a single unit cell generally can not be assigned as those for the metamaterial with multiple unit cells directly. However, beta values for a single unit cell is generally prone to be extracted, which can be the first step to extract the beta values in multiple unit cells case. It is pointed out that the extracted effective constitutive parameters can be physically meaningful only if attenuation coefficients of higher Bloch wave modes are larger than that of the fundamental Bloch mode in the periodic metamaterial, and under this condition, higher Bloch wave modes will get further attenuated with increase of the unit cell number, leaving only the fundamental mode propagation, which makes the extracted epsilon and mu more stable and convergent.