Scattering parameter analysis of cascaded bi-anisotropic metamaterials

Forward and backward reflection and transmission scattering (S-) parameters of a metamaterial (MM) structure of bi-anisotropic slabs in cascade are analyzed. Signal flow graph technique is applied in this analysis for a cascaded connection of two and three bi-anisotropic MM slabs with different orientations. We also investigated effects of geometrical parameters (fabrication tolerances) of individual MM cells on forward and backward reflection and transmission S-parameters of cascade connection of MM cells. We note from our analysis the following important points. First, forward and backward reflection S-parameters become equal to one another for a MM structure composed of an even number of bi-anisotropic MM slabs (individually characterized by non-identical forward and backward reflection S-parameters) with proper orientations only if there exists symmetry of the structure in the propagation direction. Second, it is noted that it is not possible to obtain identical forward and backward reflection S-parameters of a MM structure composed of an odd number of bi-anisotropic MM slabs. Finally, reflection asymmetry (bi-anisotropy) of cascade connection of MM cells generally is enhanced for a change in geometrical parameters of individual MM cells.