A method is described for the determination of the effective electromagnetic
parameters of a metamaterial based only on external measurements or
simulations, taking boundary effects at the interfaces between a conventional
material and metamaterial into account. 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-parameters for two 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) 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.Comment: 16 pages, 16 figures. Submitted to IEEE Transactions on Antennas and
Propagatio