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EMPEx.m (10269, 2013-06-08)

This codes implements the effective metamaterial extraction procedure presented in the paper: Zsolt Szabó, Gi-Ho Park, Hedge Ravi, Er Ping Li, A Unique Extraction of Metamaterial parameters based on Kramers-Kronig relationship, IEEE MTT, Vol. 58, No. 10, 2010, pp. 2***6-2653. Our effective metamaterial parameter retrieval procedure can be summarized as follows. Applying the Fresnel-Airy formulas, the wave impedance can be uniquely determined. However, the calculation of the refractive index involves the evaluation of a complex logarithm. The complex logarithmic function is a multi-valued function. The resulting uncertainty is referred as branching problem, which affects only the real part of the refractive index. To remove this ambiguity, the Kramers-Kronig relation can be applied to estimate the refractive index from the extinction coefficient. The physically realistic, exact values of the refractive index are determined by selecting those branches of the logarithmic function which are closest to those predicted by the Kramers-Kronig relation. The algorithm also enforces the continuity of the refractive index versus frequency. To codes comes with two sets of S parameters. The first set are the S parameters of a homogeneous slab with 40 nm thickness, the second set refers to a 200 nm thick slab. For details see the section of the paper: The origin of the branching problem, and a test of the algorithm.

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