In this paper, we propose the analytical solution of nano-rod antennas utilizing a cylindrical harmonics expansion. By treating the metallic nano-rods as plasmonic cavities, we derive closed-form expressions for both the internal and the radiated fields, as well as the resonant condition and the radiation efficiency. With our theoretical model, we show that besides the plasmonic resonances, efficient radiation takes advantage of (a) rendering a large value of the rods' radius and (b) a central-fed profile, through which the radiation efficiency can reach up to 70% and even higher in a wide frequency band. Our theoretical expressions and conclusions are general and pave the way for engineering and further optimization of optical antenna systems and their radiation patterns.
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