Optical Self-Localization Based upon the Pancharatnam-Berry Phase

The self-focusing effect is associated with a change in the refractive index proportional to the field intensity, in turn inducing a power-dependent manipulation of the wave front [1]. In long enough samples and for the proper input conditions, self-focusing can compensate the natural spreading due to diffraction, thus generating a shape-preserving nonlinear wave called spatial soliton [1]. On the other hand, in the last few years much attention has been dedicated to the tailoring of optical beams by means of the Pancharatnam-Berry phase (PBP). Whereas a gradient in the refractive index can be associated with a dynamic phase, PBP is a geometric phase, that is, it depends on the geometrical path made by the system in the parameter space [2]. In the case of the PBP, the phase delay comes from the motion of the polarization vector on the Poincare sphere [3]. In practice, a twisted anisotropic material encompassing a point-wise rotation angle φ impart a phase modulation on the crossing beam equal to 2φ. Despite this property being widely used to realize flat optical devices, much less works have been dedicated to the investigation of the PBP influence on light propagation over bulk samples. Recently, it has been demonstrated that a periodic modulation of the optical axis along the propagation direction induces a novel type of waveguide [4]. Nonetheless, the technological realization of a twisted anisotropic material in 3D is currently prohibitive. Here we show that such kind of waveguides are generated spontaneously in liquid crystals by means of the reorientational nonlinearity, that is, the rotation of the optical axis driven by the impinging light.