Second harmonic generation in three-dimensional structures based on homogeneous centrosymmetric metallic spheres

The theory of second harmonic generation (SHG) in three-dimensional structures consisting of arbitrary distributions of metallic spheres made of centrosymmetric materials is developed by means of multiple scattering of electromagnetic multipole fields. The electromagnetic field at both the fundamental frequency and second harmonic, as well as the scattering cross section, are calculated in a series of particular cases such as a single metallic sphere, two metallic spheres, chains of metallic spheres, and other distributions of the metallic spheres. It is shown that the linear and nonlinear optical response of all ensembles of metallic spheres is strongly influenced by the excitation of localized surface plasmon-polariton resonances. The physical origin for such a phenomenon has also been analyzed.