  Nano- and microparticles are popular media to enhance optical signals,
including fluorescence from a dye proximal to the particle. Here we show that
homogeneous, lossless, all-dielectric spheres with diameters in the mesoscale
range, between nano- ($\lesssim 100$~nm) and micro- ($\gtrsim 1$ $\mu$m)
scales, can offer surprisingly large fluorescence enhancements, up to $F\sim
10^4$. With the absence of nonradiative Ohmic losses inherent to plasmonic
particles, we show that $F$ can increase, decrease or even stay the same with
increasing intrinsic quantum yield $q_0$, for suppressed, enhanced or intact
radiative decay rates of a fluorophore, respectively. Further, the fluorophore
may be located inside or outside the particle, providing additional flexibility
and opportunities to design fit for purpose particles. The presented analysis
with simple dielectric spheres should spur further interest in this
less-explored scale of particles and experimental investigations to realize
their potential for applications in imaging, molecular sensing, light coupling,
and quantum information processing.
