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 lambda ex and an emission wavelength lambda 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 (a3 = 50 nm t2 = 15 nm, t1 = 25 nm) is 4.544 for a NIR fluorescence at lambda ex = 780 nm and lambda 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.