In this talk I will report our current theoretical results regarding the electromagnetic properties of discrete dipole structures. The basis of our consideration is the discrete dipole approximation and the formalism of dyadic Green function. The main questions that will be discussed in the talk are as follows:
-review of the results related to the nonlocal homogenization theory (on the examples of the discrete dipole structure, wire medium, etc.).
-presentation of the calculated dispersion properties of the structure composed of the uniaxial electric dipoles [Gorlach, Belov. Phys.Rev.B 90, 115136 (2014)]. The discussion of the so-called mixed dispersion regime that corresponds to the strong spatial dispersion in the system.
-current results for the discrete structure composed of the isotropic particles possessing electric polarizability.
-nonlinear nonlocal homogenization theory: theoretical description of second harmonic generation in the discrete dipole structure composed of nonlinear scatterers.