  A wide class of nonuniformly totally polarized beams is introduced that
preserve their transverse polarization pattern during paraxial propagation.
They are obtained as suitable combinations of Gaussian modes and find
applications in polarimetric techniques that use a single input beam for the
determination of the Mueller matrix of a homogeneous sample. The class also
includes beams that present all possible polarization states across their
transverse section (Full-Poincar\`e beams). An example of such beams and its
use in polarimetry is discussed in detail. The requirement of invariance of the
polarization pattern can be limited to the propagation in the far field, in
which case less restrictive conditions are found and a wider class of beams is
obtained.
