We
develop a method to find the quality (Q) factor
of the eigenmodes of a dielectric spherical resonator as a function
of its complex refractive index. First, we analytically show that
the Q factor of magnetic and electric multipolar
modes in a lossless spherical resonator with high refractive index
(n ≫ 1) scale as n
2j+1 and n
2j+3, respectively, where j denotes the multipolar
order. We numerically validate these results and show that our high-n analytical relation is accurate for the dipolar modes
when n > 5. For higher multipolar orders, the
analytical
relation becomes valid for increasingly lower n.
We study the dependence of the Q factor on absorption
losses and determine a general functional form that describes the Q factor of all multipolar modes as a function of any complex
refractive index. Finally, we observe that this functional form predicts
a multipolar-dependent singular value of optical gain, which gives
rise to a lasing condition with an infinite Q factor.