Optical dispersion in waveguides based upon the Pancharatnam-Berry phase

Optical waveguides usually exploit modulation of the dynamic phase, i.e., transverse gradient in the refractive index, to guide light. Recently, a novel type of optical waveguides based upon the Pancharatnam-Berry phase (PBP) has been introduced [1]. The PBP is a type of geometric phase which is determined by the path traced by the polarization on the Poincaré sphere. For example, PBP gained by a circularly polarized (CP) beam after crossing a half-wave plate (HWP) is twice the rotation angle of the crystal, the sign being dictated by the photon helicity [2]. Hence, an inhomogeneous rotation in the transverse plane induces a transverse phase gradient. However, the PBP does not accumulate in propagation if the structure is uniform along the longitudinal (propagation) direction. A net accumulation, and thus localization, is achieved when the anisotropic material is periodically perturbed along the propagation direction. The optimum is indeed attained when the longitudinal modulation is synchronized with the natural rotation of the polarization [1,3].