0.5 0.6 0.7 0.8 Q u antum Efficiency 10 3 10 4 10 5 Fluo re scence Enhancement 20 30 40 50 60 70 80 Nanocone Base Diameter [nm] 0.6 0.7 0.8 0.9 Quantum Efficiency 10 4 10 5 Fluorescence Enhancement 0.01 0.05 0.1 0.2 1 η$_{o}$ (a) (b) FIG. 3: Single (a) and double (b) conical optical antennas in air (refractive index 1.0). Fluorescence enhancement S/S o (solid curves) and quantum efficiency η (dashed curves) as a function of the base diameter b at the wavelength corresponding to the maximal Purcell factor. The bold black solid curve represents the Purcell factor. The nanocone is 140 nm long and it has a fixed tip diameter of 20 nm. The optical antenna gap for the case of two nanocones is 20 nm. See the inset to 2 for details on the coupling geometry. D. Effect of a supporting substrate An important aspect for the experimental realization of nanoantennas is the effect of a supporting substrate. Often, the optical antenna is grown on a dielectric substrate, 62–65 or is attached to the end of a fiber. 16,66–68 Previous works concluded that the presence of a substrate has a negligible effect on the field enhancement and on the spectral position of the LSPP for nanocones. 50,51 Here, in 4, we show that adding a glass substrate can shift the resonance by more than 50 nm. Furthermore, the LSPP exhibits a stronger radiative broadening, which decreases the Purcell factor F and the field enhancement, 69 and increases the antenna efficiency η$_{a}$ . Note that the shift is smaller for the nanocone having the largest 9