Plane waves in regular arrays of dipole scatterers and effective-medium modeling

A simple analytical theory for finding eigensolutions for plane electromagnetic waves propagating along an axis in infinite regular arrays of small dipole particles is presented. The spacing between dipoles in every plane is assumed to be smaller than the wavelength; separation between the planes is arbitrary. The influence of evanescent modes is taken into account. This theory gives a model for an effective propagation constant that can be applied in a wide frequency range from the quasi-static regime to the Bragg reflection (photonic bandgap) region.