Parabolic-accelerating vector waves

Complex vector light fields have become a topic of late due to their exotic features, such as their non--homogeneous transverse polarisation distributions and the non-separable coupling between their spatial and polarisation degrees of freedom. In general, vector beams propagate in free space along straight lines, being the Airy-vector vortex beams the only known exception. Here, we introduce a new family of vector beams that exhibit novel properties that have not been observed before, such as their ability to freely accelerate along parabolic trajectories. In addition, their transverse polarisation distribution only contains polarisation states oriented at exactly the same angle but of different ellipticity. We anticipate that these novel vector beams might not only find applications in fields such as optical manipulation, microscopy or laser material processing, but extend to others.