This paper presents a method for the determination of the effective electromagnetic parameters of a metamaterial, taking boundary effects at the interfaces between a conventional material and metamaterial into account. In the technique presented here, plane-wave reflection and transmission coefficients at the interfaces are regarded as additional unknowns to be determined, rather than explicitly dependent on the material parameters. Our technique is thus analogous to the line-reflect-line (LRL) calibration method in microwave measurements. The refractive index can be determined from S-parameter (reflection and transmission) measurements on two material samples of different thickness. The effective wave impedance requires the additional assumption that generalized sheet transition conditions (GSTCs) account for the boundary effects. Expressions for the bulk permittivity and permeability then follow easily. Our method is validated by comparison with the results using the Nicolson-Ross-Weir (NRW) and the two-length techniques for determining properties of an ordinary material measured in a coaxial line. Utilizing S-parameters obtained from 3-D full wave simulations, we test the method on magnetodielectric metamaterials. We compare the results from our method and the conventional one that does not consider boundary effects. Moreover, it is shown that results from our method are consistent under changes in reference plane location, whereas the results from other methods are not.
Citation: IEEE Transactions on Antennas and Propagation
Pub Type: Journals
Metamaterial, line-reflect-line (LRL), generalized sheet transition conditions (GSTCs).