Geometric Phase and Spinor Beam Dynamics of Paraxial Beams

We show that treating a paraxially propagating electric field as a spinor provides a natural way to include geometric phase in beam propagation models. Importantly, by exploiting differences in the way geometric phase and dynamical phase accrue during propagation, we show that spatial variations in the former can have surprising and rather remarkable consequences for beam dynamics. As an example, we design a beam with a centroid that is predicted to follow a curved path through free space, a prediction we subsequently validate in experiment. The model presented herein does not contradict existing propagation models, but rather shows how to leverage the extra degree of freedom afforded by the spinor angle to make new predictions.