Exploring the impact of longitudinal modulation on the twisting angle in Pancharatnam-Berry phase-based waveguides.

A circularly polarized (CP) beam propagating in a rotated anisotropic material acquires an additional phase delay proportional to the local rotation angle. This phase delay is a particular kind of geometric phase, the Pancharatnam-Berry phase (PBP), stemming from the path of the beam polarization on the Poincaré sphere. A transverse gradient in the geometric phase can thus be imparted by inhomogeneous rotation of the material, with no transverse gradient in the dynamic phase.