  We theoretically and numerically investigate metal enhanced fluorescence of
plasmonic core-shell nanoparticles doped with rare earth (RE) ions. Particle
shape and size are engineered to maximize the average enhancement factor (AEF)
of the overall doped shell. We show that the highest enhancement (11 in the
visible and 7 in the near-infrared) are achieved by tuning either the dipolar
or quadrupolar particle resonance to the rare earth ions excitation wavelength.
Additionally, the calculated AEFs are compared to experimental data reported in
the literature, obtained in similar conditions (plasmon mediated enhancement)
or when a metal-RE energy transfer mechanism is involved.
