Abstract
We apply the equivalent theory to orthorhombic anisotropic materials and provide a general unit-cell design criterion for achieving a length-independent retrieval of the effective material parameters from a single layer of unit cells. We introduce a graphical retrieval method and phase unwrapping techniques. The graphical method utilizes the linear regression technique. Our method can reduce the uncertainty of experimental measurements and the ambiguity of phase unwrapping. Moreover, the graphical method can simultaneously determine the bulk values of the six effective material parameters, permittivity and permeability tensors, from a single layer of unit cells.
Highlights
Metamaterials (MMs) are artificial materials engineered to achieve unusual electromagnetic (EM) properties that are not normally found in nature[1]-[3]
The phase ambiguity is a common issue for the parameter retrieval of the general composite materials, this issue becomes more significant for metamaterials where typically resonances, positive refractive index, and negative refractive index are all present in the same frequency band
We introduce a graphical retrieval method and phase unwrapping techniques, which can simultaneously determine the six material parameters, the permittivity and permeability tensors, from one unit cell
Summary
Metamaterials (MMs) are artificial materials engineered to achieve unusual electromagnetic (EM) properties that are not normally found in nature[1]-[3]. It has been found that the retrieved effective metamaterial parameters are often dependent on the number of unit cells along the propagation direction[5, 9]. It appears that there is no clear methodology on how to accurately predict the bulk values of the effective permittivities and permeabilies through a single layer of unit cells. We apply Herpin’s equivalent theorem[10] to orthorhombic anisotropic media and provide a simple way to accurately predict the effective bulk material parameters from a single layer of unit cells. We introduce a graphical retrieval method and phase unwrapping techniques, which can simultaneously determine the six material parameters, the permittivity and permeability tensors, from one unit cell
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