Interplay between geometric and dynamic phase in liquid crystals

As stated by Fermat’s principle, light propagation is dictated by the phase of the field. The phase is in turn dependent on the refractive index and its gradient in isotropic media; such a phase is called dynamic. In the presence of more complicated constitutive relationships, other effects contribute to the phase: e.g., in inhomogeneously twisted anisotropic materials, the electromagnetic phase depends also on the local rotation of the dielectric tensor. This is due to the geometric or Pancharatnam-Berry phase, physically related to the changes in the optical polarization [1] . The index gradient and the geometric phase can be interpreted as an effective electric and magnetic field acting on the photons respectively, and stemming from the light-matter interaction.