Boundary Effects on the Determination of Metamaterial Parameters from Normal Incidence Reflection and Transmission Measurements

TL;DR

This paper introduces a novel method for extracting metamaterial parameters from reflection and transmission data that explicitly accounts for boundary effects, improving accuracy and consistency over traditional techniques.

Contribution

The authors develop a boundary-aware parameter extraction method using S-parameters, validated against established techniques and simulations, enhancing metamaterial characterization accuracy.

Findings

Method accurately determines effective parameters considering boundary effects.

Results are consistent under changes in reference plane location.

Validation shows improved accuracy over traditional NRW method.

Abstract

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.