  In a recent work [20], we predicted and experimentally validated a new
physical mechanism for altering the propagation path of a monochromatic beam.
Specifically, we showed that by properly tailoring the spatial distribution of
the linear state of polarization transverse to the direction of propagation,
the beam followed a curved trajectory in free space. Here we extend the model
to the partially coherent, polychromatic case by redefining the beam amplitude,
phase, and polarization angle as appropriate statistical quantities. In
particular, we propose an entirely new definition of linear polarization
gradient as an average over the third generalized Stokes parameter in the
spatial frequency domain. In the new model, the beam curvature matches that of
our previous work in the fully coherent case, but is predicted to gradually
vanish as the beam loses coherence and becomes depolarized. The model also
clearly predicts, however, that there does not exist a natural mechanism in
free space or due to atmospheric turbulence that will cause significant
depolarization. Simulated beam trajectories are shown for varying levels of
initial partial coherence and for different polarization profiles. A new class
of non-diffracting beams is also suggested by way of example. Lastly, as a
byproduct of the derivation we generalize a previously known result concerning
the free-space propagation of generalized Stokes parameters [13] by showing the
result also holds for propagation in inhomogeneous media.
