Analytical modelling of double-negative composites

Analytical model of metamaterials comprising lattices of small resonant scatterers and (optionally) infinite wires is developed for the case when the planar grids of magnetic dipoles alternate with those of electric dipoles (or those of wires) along the direction of the wave propagation. An important question on the possibility to extract material parameters from measurements or simulations of the plane-wave scattering matrix for finite-thickness slabs of left-handed metamaterials is revisited. It is shown that the class of Bloch lattices (for which this extraction makes sense) is broader than one could judge upon the previous works. Also, it is shown that the spatial dispersion that destroys the operation of double-negative media can arise for the oblique propagation with respect to crystal planes even if it is not revealed from the analysis of the normal propagation.