Transport Model for the Propagation of Partially-Coherent, Polarization-Gradient Vector Beams

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.