Abstract
In this paper, a polarizability matrix retrieval method for bianisotropic metamaterials is presented. Assuming that scatterers can be modeled by electric and magnetic pointdipoles located at their centers, the induced dipole moments are analytically related to the normally incident fields, while the scattered fields are also analytically obtained for two individual cases of normal wave incidence. The latter can be combined with the incident fields, to express the desired polarizabilities, with regard to the measured or simulated scattering parameters. In this way, the polarizability matrix can be extracted by solving the resulting non-linear system of equations. The proposed technique is applied to two different split-ring resonator structures and reveals very good agreement with previously reported techniques.
Highlights
Over the past years, the problem of homogenization in metamaterials, i.e. their modeling via appropriate sets of effective parameters, has risen as a crucial subject for the sound comprehension of their properties as well as for design purposes
Two basic techniques for the calculation of effective parameters exist. The former extracts the effective constitutive parameters from the S-parameters of plane waves normally incident on bulk metamaterial structures, via the analytical inversion of the Fresnel-Airy equations [1], [2]
Our polarizability matrix extraction technique is systematically described, starting from its typical form for a well-known bianisotropic particle; the edge-coupled splitring resonator (EC-split-ring resonators (SRRs)). This structure can generally be modeled by three dipole moments, which can be directly estimated from the incident field and the polarizability matrix
Summary
The problem of homogenization in metamaterials, i.e. their modeling via appropriate sets of effective parameters, has risen as a crucial subject for the sound comprehension of their properties as well as for design purposes. Two basic techniques for the calculation of effective parameters exist The former extracts the effective constitutive parameters from the S-parameters of plane waves normally incident on bulk metamaterial structures, via the analytical inversion of the Fresnel-Airy equations [1], [2]. This approach has gained significant popularity due to its simplicity and adequate accuracy. Several issues have occurred concerning the correct branch selection for the real part of the refraction index, as elaborately discussed in [3], while recently it has been proven that the constitutive parameters, so obtained, do not always represent meaningful material parameters [4] These problems have been attributed to the bianisotropic properties of most metamaterials as well as to the effect of periodicity on the constitutive (non-local) parameters. We implement an algorithm for the extraction of the polarizability matrix, bearing in mind its common form for the most popular bianisotropic metamaterials, namely the split-ring resonators (SRRs)
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