Research On Method Of Retrieving The Constitutive Parameter Matrix Of Magnetoelectric Coupling Metamaterial

Electromagnetic metamaterial is a kind of artificial structural material which has a special performance, its permittivity or permeability will exhibit negative under certain frenquency. This unconventional electromagnetic characteristics will generate many unusual phenomenon, and received considerable attention. Many research teams conducted a great deal of work, and achieved fruitful results. Electromagnetic metamaterials have broad application prospect, it will have a profound impact on humans.The constitutive parameters for single negative(only electric permittivity or only permeability less than zero) metamaterials and wires-SRR(split ring resonator,SRR)metamaterials can usually be retrieved using the S parameter method. Due to cross polarization phenomenon within the magnetoelectric coupling metamaterials,only two constitutive parameters─ permittivity and permeability─ cannot accurately to describe the electromagnetic characteristics of magnetoelectric coupling metamaterials. Traditional S parameter retrieval method starts off with the assumption that the metamaterial has only the two constitutive parameters─ permittivity and permeability, so the method to retrieve the constitutive parameters of magnetoelectric coupling metamaterials have obvious limitations.In this paper, the electric component and magnetic component within a magnetoelectric coupling metamaterial cell are equivalent to the surface current and surface magnetic flow, respectively. By deriving the relationship of the average electric flux density,average magnetic flux density and the external electromagnetic field, we obtain constitutive parameters matrix(2×2) of the magnetoelectric coupling metamaterial, and find analytical formula for the relationship between these four constitutive parameters of the magnetoelectric coupling metamaterial and the parameters such as the permittivity of the electric component, permeability of magnetic element, spatial dispersion and coupling coefficient, and then deduced the refractive index formula. We use the refractive index formula to nonlinearly fit to retrieval refractive index curves, and find very good agreement between the values of refractive index theoretically predicted by analytical formulas and those found from numerical retrievals based on full-wave simulations, which verify the proposedconstitutive matrix analytic formula and the refractive index expression. According to the fitting results, we obtained the frequency response curve of the four electromagnetic parameters in constitutive matrix. proposed constitutive matrix parameters retrieval methods will provide important theoretical reference for the related researchers engaged in analysis and research on the coupling phenomenon between electric component and magnetic component within a magnetoelectric metamaterial cell.