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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) is achieved by tuning either the dipolar or the quadrupolar particle resonance to the rare earth ion's 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.

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