An Improved Approach to Determine the Branch Index for Retrieving the Constitutive Effective Parameters of Metamaterials

Abstract

Accurately retrieving the constitutive effective parameters is the prerequisite for the research and application of metamaterials. When the constitutive effective parameters are retrieved from the transmission and reflection characteristics of metamaterials, the determination of the branch index m is a key but difficult step. In 2004, Chen et al. proposed a robust and effective retrieval method. But our study finds that this method may fail to determine the branch index m in some cases, which may occur not only in the resonance band but also in non-resonance bands. To circumvent this problem, an improved approach to determine the branch index m is proposed. By relaxing the constraint on m, the improved approach converts the determination of m to a constrained minimization problem, and thus a unique m can be determined. Two examples are presented to demonstrate the applicability and accuracy of the improved approach.