Waveguiding driven by the Pancharatnam-Berry phase

We theoretically and numerically investigate the properties of waveguides based on the Pancharatnam-Berry phase, obtained by a longitudinally periodic rotation of the optic axis in a transversely twisted birefringent medium. In this paper we study the case where the period of the longitudinal modulation is chosen so that a net accumulation of geometric phase in propagation occurs. First, the interplay between different contributions to the optical potential is addressed. Second, a continuous evolution of the polarization structure of the quasimodes is observed in the numerical simulations. We explain it by a combination of plane-wave-based models and gauge transformations. We discover that, beyond the longitudinal oscillations, the polarization of the quasimode also varies through its cross section. The analogies with respect to charged particles moving in a magnetic field are outlined.