Homogenisation of negative refractive index metamaterials: comparison of effective parameters of broadside-coupled and edge-coupled split-ring resonators

Different approaches have been considered to realise negative refractive index (NRI) metamaterials. We focus on the use of split-ring resonators (SRR), and investigate edge-coupled SRR (EC-SRR) and broadside coupled SRR (BC-SRR). We propose a free-space matched metamaterial consisting of BC-SRR. Firstly, a homogenisation procedure accounting for the transverse periodicity of the composite in the plane of incidence is developed. This analysis has, to our knowledge, not been done elsewhere. Secondly, this procedure is applied to the two different SRR-based metamaterials. They are compared in terms of their effective permittivity, ε_eff, and permeability, μ_eff. Moreover, the influence on μ_eff and ε_eff of the variation of the different constituents of the metamaterial, namely the dielectric substrate permittivity and loss tangent and the pattern layout, is investigated. The sensitivity of both metamaterials to dielectric and metallic losses is also discussed.