  We consider a two-dimensional electron gas with Rashba's spin-orbit
interaction and two in-plane potentials superimposed along directions
perpendicular to each other. The first of these potentials is assumed to be a
general periodic potential while the second one is totally arbitrary. A general
form for Bloch's amplitude is found and an eigen-value problem for the band
structure of the system is derived. We apply the general result to the two
particular cases in which either the second potential represents a harmonic
in-plane confinement or it is zero. We find that for a harmonic confinement
regions of the Brillouin zone with high polarizations are associated with the
ones of large group velocity.
