Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials

Abstract

We show in this paper that metamaterials in which some components of the permittivity and permeability tensors can have negative real values (thus associated with left-handed metamaterials) call for a reconsideration of the common concepts of critical angle and Brewster angle. By studying the reflection coefficient for isotropic and biaxial half-spaces and slabs, we show that a metamaterial for which the Brewster angle appears beyond the critical angle is realizable. In addition, we also show that the Goos-Hänchen shift induced by left-handed isotropic slabs is not necessarily negative but could be positive when the second interface of the slab supports a surface plasmon. Finally, upon studying a bianisotropic metamaterial, we show that propagation at a negative angle can occur, although it would not if only the permittivity and permeability tensors were considered. All the results have been obtained using an eigenvalue method which we extend to bianisotropic media in this paper.