Topological Zeeman effect and circular birefringence in twisted photonic crystal fibers

The propagation of light guided in optical fibers is affected in different ways by bending or twisting. Here we treat the polarization properties of twisted six-fold symmetric photonic crystal fibers. Using a coordinate frame that follows the twisting structure, we show that the governing equation for the fiber modes resembles the Pauli equation for electrons in weak magnetic fields. This implies index splitting between left and right circularly polarized modes, which are degenerate in the untwisted fiber. We develop a theoretical model, based on perturbation theory and symmetry properties, to predict the observable circular birefringence (i.e., optical activity) associated with this splitting. Our overall conclusion is that optical activity requires the rotational symmetry to be broken so as to allow coupling between different total angular momentum states