Restricted equivalence of paired epsilon–negative and mu–negative layers to a negative phase–velocity material (alias left–handed material)

The time–harmonic electromagnetic responses of (a) a bilayer made of an epsilon–negative layer and a mu– negative layer, and (b) a single layer of a negative phase–velocity material are compared. Provided all layers are electrically thin, a restricted equivalence between (a) and (b) exists. The restricted equivalence depends on the linear polarization state and the transverse wavenumber. Implications for perfect lenses and parallel–plate waveguides are considered.