Discreteness and local fields in weakly rarefied media

A generalized method of integral equations (GMIE) is applied to a weakly rarefied (not so dense) medium when the distance $b$ between the neighboring elementary radiators is already not negligibly small in comparison with the wavelength of light λ. In this paper discreteness is treated not as a conceptual idea only but as a quantitatively measured parameter $b/\lambda .$ It was found that the extinction theorem and Maxwell’s equations remain valid even in such conditions. A striking contradiction with the energy conservation law arising with allowance of the radiation damping effect into the Lorentz-Lorenz formula is resolved by means of a proper account of the discreteness of the medium. The approach developed enabled us to calculate the local field factors and dielectric permittivity of a rarefied medium. An essential quantitative and qualitative distinction between the gaslike, jellylike, and a cubic lattice media, customarily treated as optically isotropic, was revealed. For a cubic lattice crystal an optical anisotropy is predicted. The possibility of application of the GMIE to calculation of the integral light scattering in an irregular medium is discussed. Our results may be applied to calculation of the optical properties of some specific types of media, such as a cooled atomic gas, composite materials, and quantum dots structures.