0 200 400 600 800 1000 Pu rcell Factor 700 800 900 1000 1100 Vacuum Wavelength [nm] 0 400 800 1200 1600 2000 2400 2800 3200 Purcell Factor b b 0.0 0.2 0.4 0.6 0.8 1.0 An t enna Efficiency 600 700 800 900 1000 Vacuum Wavelength [nm] 0.0 0.2 0.4 0.6 0.8 1.0 Antenna Efficiency (b) (d) (a) (c) 20 24 28 32 40 48 56 64 b  (nm) FIG. 1: Single, (a) and (b), and double, (c) and (d), conical optical antennas in glass (refractive index 1.5). Purcell factor F , (b) and (d), and antenna efficiency η$_{a}$ , (a) and (c), as a function of the base diameter b . The nanocone is 80 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. The insets in (b) and (d) sketch the antenna cross section, indicating the emitter position and orientation, and the nanocone parameter that is varied. According to Eq. (3), the fluorescence enhancement depends on F , on η$_{a}$ , and on the initial quantum efficiency η o . We anticipated that the value of b that maximizes F should not correspond to the value that maximizes S/S o . To discuss this point further we plot in 3 the fluorescence enhancement as a function of the nanocone base diameter b and η o . For each b we choose the wavelength associated with the maximum F . For the same wavelength, we also take η$_{a}$ and use these quantities in Eq. (3). For a given η o , S/S o is maximal when b is about 30 nm in place of 24 nm obtained for F (see the bold black curve). The difference C. Role of the initial quantum efficiency 7