We solve the problem of the scattering of an electromagnetic plane wave from a planar array of equispaced cylindrical scatterers with strong resonances. We apply this theory to calculate the reflectivity of an array of quantum wires using the electromagnetic properties of the single wire as the only input. We find electromagnetic interference between the wires, whose effects are additional shifts and broadenings of the isolated wire resonances. A detailed analysis of some commonly used experimental configurations is also presented, with evidence of interference effects. Resonance shifts and broadenings are also interpreted as properties of the mixed modes of the quantized electromagnetic fields and the full grating excitations, i.e., grating polaritons. Stationary modes of the grating polaritons are also found, which have the peculiar property of being guidelike modes sustained by electronic excitations confined along one propagation direction.