Asymmetric metal-dielectric nanostructures are demonstrated superior optical properties arise from the combination of strong enhancement of their near fields and controllable scattering characteristics which originate from plasmonic and high-index dielectric components. Here, being inspired by the recent experimental work [Dmitry~Zuev, textit{et al.}, Adv. Mater. textbf{28}, 3087 (2016)] on a new technique for fabrication of asymmetric hybrid nanoparticles via femtosecond laser melting at the nanoscale, we suggest and study numerically a novel type of hybrid dimer nanoantennas. The nanoantennas consist of asymmetric metal-dielectric (Au/Si) nanoparticles and can allow tuning of the near- and far-field properties via laser melting of the metal part. We demonstrate a modification of scattering properties, near electric field distribution, normalized local density of states, and power patters of radiation of the nanoantennas upon laser reshaping. The parameters used to investigate these effects correspond to experimentally demonstrated values in the recent work.
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