  The theory of the generation and transfer of polarized radiation, mainly
developed for interpreting solar spectropolarimetric observations, allows to
reconsider, in a more rigorous and elegant way, a physical mechanism that has
been suggested some years ago to interpret the high degree of polarization
often observed in astronomical masers. This mechanism, for which the name of
'dichroic maser' is proposed, can operate when a low density molecular cloud is
illuminated by an anisotropic source of radiation (like for instance a nearby
star). Here we investigate completely unsaturated masers and show that
selective stimulated emission processes are capable of producing highly
polarized maser radiation in a non-magnetic environment. The polarization of
the maser radiation is linear and is directed tangentially to a ring
equidistant to the central star. We show that the Hanle effect due to the
presence of a magnetic field can produce a rotation (from the tangential
direction) of the polarization by more that 45 degrees for some selected
combinations of the strength, inclination and azimuth of the magnetic field
vector. However, these very same conditions produce a drastic inhibition of the
maser effect. The rotations of about 90 degrees observed in SiO masers in the
evolved stars TX Cam by Kemball & Diamond (1997) and IRC+10011 by Desmurs et al
(2000) may then be explainedby a local modification of the anisotropy of the
radiation field, being transformed from mainly radial to mainly tangential.
