0 300 600 900 1200 1500 1800 2100 Pu rcell Factor 700 800 900 1000 1100 Vacuum Wavelength [nm] 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 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) 36 44 52 60 68 20 24 28 b  (nm) FIG. 2: Single, (a) and (b), and double, (c) and (d), conical optical antennas in air (refractive index 1.0). 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 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. The insets in (b) and (d) sketch the antenna cross section, indicating the emitter position and orientation, and the nanocone parameter that is varied. is small because F is so large that Eq. (3) can be well approximated by S/S o = F η$_{a}$/η o . Since η$_{a}$ does not change much compared to F , it turns out that maximizing F and S/S o give similar values for b . This can also be inferred from the quantum efficiency η , which is shown by dashed curves in 3. η is close to η$_{a}$ , corresponding to the curve for η o = 100%, even when η o = 5%. For smaller Purcell factors, the difference between the optimal b for F and for S/S o would be larger and vary with η o . 8