antennas $^{20–23}$. 

The concept of optical antennas is closely linked to the physics of near-field microscopy, in which a tip mediates between a far-field illumination and the sample in its subwavelength vicinity $^{24,25}$. Progress in nanofabrication has motivated the realization of structures sim- ilar to radiowave antennas, 26 for operating in the optical domain 23,27–31 although various issues have to be considered. For example, metal nanoparticles support localized surface plasmon-polariton (LSPP) modes that depend on the nanoparticle shape, composition and surroundings. 32 Moreover, losses due to absorption by real metals are not negligible at op- tical frequencies. 33 In addition, the molecule is coupled to the antenna via the displacement current, which is strongly position and orientation dependent $^{8}$. In this respect, there are ongoing efforts to reconcile these differences with standard antenna theory. 34,35 

Recently, we proposed a few simple rules for designing optical antennas to enhance spon- taneous emission by more than three orders of magnitude while avoiding quenching $^{36}$. First, the plasmon resonance should be in a spectral region where dissipation in the metal is small. Second, the nanoparticle should have sharp corners to strongly increase the near field. Third, the antenna and the molecule dipole moment should be aligned in a head-to-tail configura- tion to maximize coupling and radiation. Fourth, the structure should be compatible with state-of-the-art nanofabrication. We then performed a detailed analysis of nanorods and nanospheroids for enhancing fluorescence by varying their aspect ratio and composition. We found that nanospheroids perform better than nanorods when the plasmon resonance needs to be shifted towards shorter wavelengths $^{37}$. Moreover, by choosing different plasmonic ma- terials, such as aluminum, silver, copper and gold, we could obtain large Purcell effects and quantum efficiencies in a broad spectral region, from ultraviolet to near infrared $^{38}$. One of the issues that we identified is that the antenna efficiency η$_{a}$ , which is the power that reaches the far field divided by the total emitter power, and the Purcell factor F , which represents the enhancement of the radiative decay rate, are maximal for different antenna parameters. In particular, we found that for gold nanorods and nanospheroids increasing η$_{a}$ involves a rapid decrease of F in the visible and near-infrared range $^{37}$. 

The question now is if one can improve the antenna design to increase F without de- creasing η$_{a}$ and losing control on the spectral position of the resonance. In this work, we propose that a simple solution based on using a nanocone, where one end can be sharp to increase the field enhancement and the Purcell factor, while the other larger end increases 

