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## D. Effect of a supporting substrate 

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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 

