Average Plasmonic Enhancement of Molecules-Doped Au-NS@SiO₂ on Fluorescence

The average plasmonic enhancement of Au nanoshell (Au-NS) coated by a molecules-doped silica layer (Au-NS@SiO₂) on molecular fluorescence is studied theoretically to estimate the overall performance of a large number of Au-NS@SiO₂. Using Mie theory and dyadic Green's functions, analytical solutions of the excitation rate and the apparent quantum yield are obtained to calculate the enhancement factor of Au-NS@SiO₂ on the fluorescence of a molecule with a specific orientation and location at a specific excitation wavelength λ_ex and an emission wavelength λ_em. Subsequently, the average enhancement factor (AEF) is calculated by averaging all possible orientations and locations of the molecule. For example, AEF of Au-NS@SiO₂ (a ₃ = 50 nm t ₂ = 15 nm, t ₁ = 25 nm) is 4.544 for a NIR fluorescence at λ_ex = 780 nm and λ_em = 820 nm. Our results show that Au-NS is a broadband enhancer for NIR fluorescence; the bandwidth and the peak depend on the core size and the thickness of Au shell.