Arslanagic, Samel1; Hansen, Troels Vejle1; Mortensen, N. Asger7; Gregersen, Anders Heidemann8; Sigmund, Ole5; Ziolkowski, R. W.9; Breinbjerg, Olav1
1 Department of Electrical Engineering, Technical University of Denmark2 Electromagnetic Systems, Department of Electrical Engineering, Technical University of Denmark3 Department of Photonics Engineering, Technical University of Denmark4 Structured Electromagnetic Materials, Department of Photonics Engineering, Technical University of Denmark5 Department of Mechanical Engineering, Technical University of Denmark6 Solid Mechanics, Department of Mechanical Engineering, Technical University of Denmark7 Center for Nanostructured Graphene, Center, Technical University of Denmark8 Department of Micro- and Nanotechnology, Technical University of Denmark9 University of Arizona
The scattering-parameter extraction method of metamaterial homogenization is reviewed to show that the only ambiguity is that related to the choice of the branch of the complex logarithmic function (or the complex inverse cosine function). It is shown that the method has no ambiguity for the sign of the wavenumber and intrinsic impedance. While the method indeed yields two signs for the intrinsic impedance and thus the wavenumber, the signs are dependent. Moreover, both sign combinations lead to the same permittivity and permeability, and are thus permissible. This observation is in distinct contrast to a number of statements in the literature where the correct sign of the intrinsic impedance and wavenumber resulting from the scattering-parameter method is chosen by imposing additional physical requirements, such as passivity. The scattering-parameter method is reviewed through an investigation of a uniform plane wave normally incident on a planar slab in free space. The severity of the branch ambiguity is illustrated through simulations of a known metamaterial realization. Several approaches for proper branch selection are reviewed, and the suitability to metamaterial samples is discussed.
I E E E Antennas and Propagation Magazine, 2013, Vol 55, Issue 2, p. 91-106