  We study the dielectric properties of graphene in the presence of Rashba and
intrinsic spin-orbit interactions in their most general form, i.e., for
arbitrary frequency, wave vector, doping, and spin-orbit coupling (SOC)
parameters. The main result consists in the derivation of closed analytical
expressions for the imaginary as well as for the real part of the polarization
function. Several limiting cases, e.g., the case of purely Rashba or purely
intrinsic SOC, and the case of equally large Rashba and intrinsic coupling
parameters are discussed. In the static limit the asymptotic behavior of the
screened potential due to charged impurities is derived. In the opposite limit
($q=0$, $\omega\to0$), an analytical expression for the plasmon dispersion is
obtained and afterwards compared to the numerical result. Our result can also
be applied to related systems such as bilayer graphene or topological
insulators.
