  The terahertz radiation-induced conductivity and dielectric polarization
tensors as well as the Faraday and Kerr rotation angles and the non-equilibrium
spin textures are studied for two-dimensional electron gas with strong
spin-orbit coupling subjected to high magnetic field and to tunable periodic
potential of a two-dimensional gated superlattice. It is found that both real
and imaginary parts of the frequency-dependent induced conductivity approach
maximum values with sharp and detectable peaks at frequencies corresponding to
the inter-subband transitions between spin-split magnetic subbands. The
observed properties of the conductivity tensor frequency dependence are applied
for the description of the Kerr and Faraday rotation angles which can be used
as another experimental tool for describing the electron gas in periodic
structures with significant spin-orbit coupling. The formation of
radiation-induced spin textures is predicted having both in-plane and
out-of-plane components with space distribution scale comparable to the
superlattice cell size which can be observed experimentally.
