Regular papers

On the unambiguous determination of effective optical properties of periodic metamaterials: a one-dimensional case study

¹ Department of Photonics Engineering, DTU Fotonik, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
² Laboratory of Optics, Photonics and Quantum Electronics, Department of Microelectronics and Applied Physics, Royal Institute of Technology (KTH), Electrum 229, 16440 Kista, Sweden
³ Department of Mechanical Engineering, Technical University of Denmark, Nils Koppels Allé Building 403, DK-2800 Kongens Lyngby, Denmark
⁴ Department of Electrical Engineering, Technical University of Denmark, Building 348, DK-2800 Kongens Lyngby, Denmark

^* asger@mailaps.org

Received: 13 November 2009

Abstract

We show how branch ambiguities in the extraction of effective parameters is arising as a direct consequence of the underlying Bloch state physics. The mutual importance of the different branches in general depends on the experimental context, and we show how the Fourier spectrum of the field inside the metamaterial can be used to access this. Different numerical examples illustrate how a predominant branch may be identified for λ ≫ a while at higher frequency the power may be distributed over more branches. This is in particular true near bandedges and strong resonances. Extensions to two- and three-dimensional metamaterial designs are discussed.