  Large scale simulations are performed by means of the transfer-matrix method
to reveal optimal conditions for metal-dielectric core-shell particles to
induce the largest fluorescence on their surfaces. With commonly used plasmonic
cores (Au and Ag) and dielectric shells (SiO2, Al2O3, ZnO), optimal core and
shell radii are determined to reach maximum fluorescence enhancement for each
wavelength within 550~850 nm (Au core) and 390~500 nm (Ag core) bands, in both
air and aqueous hosts. The peak value of the maximum achievable fluorescence
enhancement factors of core-shell nanoparticles, taken over entire wavelength
interval, increases with the shell refractive index and can reach values up to
9 and 70 for Au and Ag cores, within 600~700 nm and 400~450 nm wavelength
ranges, respectively, which is much larger than that for corresponding
homogeneous metal nanoparticles. Replacing air by an aqueous host has a
dramatic effect of nearly halving the sizes of optimal core-shell
configurations at the peak value of the maximum achievable fluorescence. In the
case of Au cores,the fluorescence enhancements for wavelengths within the first
near-infrared biological window (NIR-I) between 700 and 900 nm can be improved
twofold compared to homogeneous Au particle when the shell refractive index ns
> 2. As a rule of thumb, the wavelength region of optimal fluorescence (maximal
nonradiative decay) turns out to be red-shifted (blue-shifted) by as much as 50
nm relative to the localized surface plasmon resonance wavelength of
corresponding optimized core-shell particle. Our results provide important
design rules and general guidelines for enabling versatile platforms for
imaging, light source, and biological applications.
