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In the framework of the discrete dipole approximation   we develop a theoretical approach, allowing analyzing the role of multipole modes in the extinction and scattering spectral resonances of arbitrary shaped nanoparticles.   The method is applied to nonspherical Si nanoparticles with resonant multipole responses in the visible optical range. It is shown  that it is possible to design silicon particles for which the electric dipole and magnetic dipole resonances are located at the same wavelength under certain propagation directions of incident light, providing new
possibilities in metamaterial developments.

metamaterials;nanophotonics