is placed in the visible and near-infrared spectral range. The surrounding material is either glass (refractive index 1.5) or air. 1 displays the Purcell factor F and the antenna efficiency η$_{a}$ for single and double nanocone antennas in glass as a function of the nanocone base b and the wavelength. The nanocone height is 80 nm and the tip end is flat with a fixed diameter of 20 nm. The black curves correspond to the case of a nanorod $^{37}$. Starting from this structure, the Purcell factor increases slightly and then decreases, confirming that there exists an optimal value for b $^{50,51}$. This trend is found for optical antennas made of one and two nanocones, as shown in 1(b) and 1(d). However, 1(a) and 1(c) reveal that η$_{a}$ steadily grows with b because the volume of the nanostructure increases. Intuitively, that occurs since scattering is proportional to the volume squared, while absorption only to the volume $^{32}$. Therefore, if both F and η$_{a}$ have to be considered in the assessement of the antenna performances, one sees that b might be different than the optimal value found when only the field enhancement is taken into account. The dips in 1(a) and 1(c) are associated with the excitation of higher-order reso- nances, which increase the non-radiative decay rate more strongly than the radiative one $^{36}$. An important advantage with respect to nanorods and nanospheroids is that here the res- onance can be tuned towards the visible spectrum simply by changing the nanocone angle, without a significant loss of enhancement. Indeed, for nanorods we found that shifting the resonance by 100 nm can lead to a reduction of F by more than a factor of two. 37 In 2 we consider another set of optical antennas, where the surrounding medium is air and the nanocone height is 140 nm. The redshift due to a longer optical antenna is compensated by a lower refractive index so that the resonances are in the same spectral region of those shown in 1. The overall behavior as a function of b is similar to the previous case. The main difference here is that the Purcell factor rises to as high as 2000 for a single nanocone and 8000 for a double nanocone antenna. Such large values combined with a very good antenna efficiency and a wide spectral tunability of the LSPP make them ideal systems for enhancing the radiative properties of solid-state quantum emitters. 6 B. Single and double conical optical antennas