Sampling theorem in macroscopic electrodynamics of crystal lattices

Two ways may be used to describe the electromagnetic field-condensed media interaction. When one way is to get over a discrete structure of a medium by the averaging procedure, another way may be conceived as follows: to discretize fields on the basis of the discrete structure of a medium. When initial restrictions to the wave number spectrum take place, one can use the so-called sampling theorem for a medium modeled as a triple infinite periodic array of identical δ-functional scattering elements. Taking into account the Lorenz-Lorentz model one can develop a dynamical theory which considers strong field fluctuations in crystal lattices.