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<img src='content_image/344886.jpg'>

## C. Role of the initial quantum efficiency 

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 

