A Unique Extraction of Metamaterial Parameters Based on Kramers–Kronig Relationship

In this paper, an improved algorithm for extracting the effective constitutive parameters of a metamaterial is derived. The procedure invokes the Kramers-Kronig relations to ensure the uniqueness of the solution. The accuracy of the method is demonstrated by retrieving the effective material parameters of a homogeneous slab. This study reveals under which conditions the calculation of the refractive index involves more than one branch of the complex logarithmic function. A metamaterial built up from wires and split-ring resonators is then investigated. The applicability and limits of the presented algorithm are explored by observing how the effective parameters of a metamaterial slab converge as its thickness is increased.