E. V. Golovacheva, A. M. Lerer, P. V. Makhno, G. P. Sinyavskiy

The solution of two dimensional intego-differential equation, which describes the diffraction of electromagnetic waves on metallic nanovibrators lying at the boundary between dielectrics an on nanocrystalls, coated with metallic film, was obtained. Integro-differential equations (IDE) were solved by means of method, which combines Galerkin and collocation methods. The matrix elements in obtained systems of linear algebraic equations (SLAE) are expressed in the form of Fourier integrals. Such expression of kernels and matrix elements allows to easily overcome difficulties, associated to singularity of IDE's kernels. Rapid internal convergence of solution is shown. The properties of copper nanoantennas on the ZnO substrate were theoretically investigated in optical frequency range. It is mentioned that the dependency of scattered field on frequency shows resonant character, and resonance wavelengths are almost independent on dielectric constant of substrate.