  Strong effects of optical polarization anisotropy observed previously in the
quantum wells subjected to the in-plane magnetic field arrive at complete
description within microscopic approach. Theory we develop involves two sources
of optical polarization. First source is due to correlations between electron
and heavy hole (HH) phases of $\psi $-functions arising due to electron Zeeman
spin splitting and joint manifestation of low-symmetry and Zeeman interactions
of HH in an in-plane magnetic field. In this case, four possible
phase-controlled electron-HH transitions constitute the polarization effect,
which can reach its maximal amount ($\pm $1) at low temperatures when only one
transition survives. Other polarization source stems from the admixture of
excited light-holes (LH) states to HH by low-symmetry interactions. The
contribution of this mechanism to total polarization is relatively small but it
can be independent of temperature and magnetic field. Analysis of different
mechanisms of HH splitting exhibits their strong polarization anisotropy. Joint
action of these mechanisms can result in new peculiarities, which should be
taken into account for explanation of different experimental situations.
