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.
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