  Due to their many potential applications, there is an increasing interest in
studying hybrid systems composed of optically active media and plasmonic
metamaterials. In this work we focus on a particular system which consists of
an optically active silica core covered by a gold shell. We find that the
spaser (surface plasmon amplification by stimulated emission of radiation)
conditions can be found at the poles of the scattering cross section of the
system, a result that remains valid beyond the geometry studied. We explored a
wide range of parameters that cover most of the usual experimental conditions
in terms of the geometry of the system and the wavelength of excitation. We
show that the conditions of spaser generation necessarily require full loss
compensation, but the opposite is not necessarily true. Our results, which are
independent of the detailed response of the active medium, provide the gain
needed and the wavelength of the spasers that can be produced by a particular
geometry, discussing also the possibility of turning the system into optical
amplifiers and SERS (surface enhanced Raman spectroscopy) substrates with huge
enhancements. We believe that our results can find numerous applications. In
particular, they can be useful for experimentalists studying similar systems in
both, tuning the experimental conditions and interpreting the results.
