  It is well known that the Dresselhaus spin-orbit coupling (SOC) in
semiconductor two dimensional electron gases (2DEGs) possesses both linear and
cubic in momentum contributions. Nevertheless, the latter is usually neglected
in most theoretical studies. However, recent Kerr rotation experiments have
revealed a significant enhancement of the cubic Dresselhaus interaction by
increasing the drift velocities in 2DEGs hosted in GaAs quantum wells. Here, we
present a study of the optical spin Hall conductivity in 2DEGs under the
simultaneous presence of Rashba and (linear plus cubic) Dresselhaus SOC. The
work was done within the Kubo formalism in linear response. We show that the
coexistence of the Rashba and cubic Dresselhaus SOC in 2DEGs promotes a strong
anisotropy of the band spin splitting which in turn leads to a very
characteristic frequency dependence of the spin Hall conductivity. We find that
the spin Hall conductivity response could be very sensible to sizeable
cubic-Dresselhaus coupling strength. This may be of relevance for the optical
control of spin currents in 2DEGs with non-negligible cubic-Dresselhaus SOC.
