  The Bloch spinors, energy spectrum and spin density in energy bands are
studied for the two-dimensional electron gas (2DEG) with Rashba spin-orbit (SO)
interaction subject to one-dimensional (1D) periodic electrostatic potential of
a lateral superlattice. The space symmetry of the Bloch spinors with spin
parity is studied. It is shown that the Bloch spinors at fixed quasimomentum
describe the standing spin waves with the wavelength equal to the superlattice
period. The spin projections in these states have the components both parallel
and transverse to the 2DEG plane. The anticrossing of the energy dispersion
curves due to the interplay between the SO and periodic terms is observed,
leading to the spin flip. The relation between the spin parity and the
interband optical selection rules is discussed, and the effect of magnetization
of the SO superlattice in the presence of external electric field is predicted.
