We have fabricated two-segment carbon nanotube (CNT) based structures. We prove their ability to operate as optical antennas, where the field enhancement, distinct resonances, as well as radiation patterns are thoroughly investigated. Optical antennas are capable of coupling far-field radiation to the near-field in the sub-wavelength range. They can be used to tailor light-matter interactions in the nanoscale, leading to various applications (like nano-scale lithography, field-enhanced microscopy etc.) . The optical responses of an optical antenna heavily depend on the surface plasmon resonances  in the structure, which are quite sensitive to the material properties, the geometry and the operating environment. Based on a full-wave electromagnetic analysis we propose a two-segment CNT based nanostructure  to operate as a “fat” dipole-type optical antenna. The field enhancement, the resonances, and the radiation patterns are thoroughly investigated. Our study reveals that the advantages of pure metallic antennas and CNT antennas could be combined, providing additional degrees of freedom in tailoring both the material properties and the wavelength response, and, hence, the overall emission characteristics. Segmented composite nano-antennas turned out to carry a great potential for engineering nanoscale emitters and receivers, for e.g. biosensing applications or within advanced nanophotonic circuit topologies.