| In recent years, metamaterials have attracted much attention because of their promising applications (e.g. perfect lenses, superlenses, antennas with improved performance, controllable reflection and transmission devices, electromagnetic absorbers, device miniaturizations, etc.). Metamaterials with simultaneously negative permittivity and permeability are often needed to achieve design goals. Needless to say, accurate extraction of material parameters is very important since it allows the potential features of metamaterials to be taken advantage of in design. A commonly used extraction method uses S-parameters (reflection and transmission) resulting from a normally incident wave on a metamaterial slab assuming that the boundaries of a slab are well defined and that the Fresnel formulas for reflection and transmission hold at the interface between the air and the metamaterial. However, the tangential components of the macroscopic electromagnetic field in a metamaterial are not continuous at the boundaries while the local fields are.;This thesis presents a method for extracting the effective electromagnetic parameters of a metamaterial taking boundary effects at the interfaces between a conventional material and metamaterial into account. In the approach in this thesis, 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. The approach presented here is thus analogous to the line-reflect-line (LRL) calibration method in microwave measurements. The refractive index can be determined from S-parameter measurements on two material samples of different lengths. 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 follow easily.;In this thesis, explicit expressions for extracting the effective refractive index, wave impedance, permittivity, and permeability are offered in the case when an incident wave propagates normally on a metamaterial slab. Then, the expressions are extended and given in the case of an oblique incidence. To validate these equations, ordinary materials whose parameters are known are tested. Comparisons of the results from our method and methods which do not account for boundary effects are discussed using S-parameters numerically or experimentally obtained. |
