Self-Trapping of Light Using the Pancharatnam-Berry Phase

Abstract

Since its introduction by Berry in 1984, the geometric phase has become of fundamental importance in physics, with applications ranging from solid-state physics to optics. In optics, the Pancharatnam-Berry phase allows the tailoring of optical beams by a local control of their polarization. Here, we discuss light propagation in the presence of an intensity-dependent local modulation of the Pancharatnam-Berry phase. The corresponding self-modulation of the wave front counteracts the natural spreading due to diffraction; i.e., self-focusing takes place. No refractive index variation is associated with the self-focusing: The confinement is uniquely due to a nonlinear spin-orbit interaction. The phenomenon is investigated, both theoretically and experimentally, by considering the reorientational nonlinearity in liquid crystals, where light is able to rotate the local optical axis through an intensity-dependent optical torque. Our discoveries pave the way to the investigation of a new family of nonlinear waves featuring a strong interaction between the spin and the orbital degrees of freedom.

Geometric Phase in Optics: From Wavefront Manipulation to Waveguiding

“…Finally, the rotation angle will be bell‐shaped on the transverse plane , given that the local optical torque depends on the point‐wise value of the field intensity. This qualitative explanation is confirmed by numerical simulations as shown in reference [206]. After it is established that a CP beam is capable to induce a periodic rotation of the optical axis, the results from the linear case can be applied.…”

“…Existence of this exotic type of waveguiding in a continuous (along ) structure has been recently provided. [ 206 ] Counter‐intuitively, the easiest way to write these guides is in the nonlinear regime, that is, where the perturbation in the material is induced by light itself via a nonlinear optical effect. To demonstrate this effect, reorientational nonlinearity in NLCs has been employed.…”

“…[ 208 ] The basic mechanism can be grasped in simple terms: the optical electric field induces dipoles in the NLC molecules, which then tend to realign to the external field to minimize the interaction energy. [ 206,208 ] The external rotation is counteracted by internal mechanical forces, microscopically originating from the dipole‐dipole interactions between molecules. [ 208 ] On a macroscopic scale, the net result is a rotation angle of the optical axis which depends on the intensity and the polarization of the incident electric field.…”

“…Restated in more general terms, the soliton is due to a nonlinear spin‐orbit interaction, yielding a power‐dependent exchange of angular momentum between light and matter, triggered by the intensity profile of the beam. [ 178,206 ]…”

Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals

“…On the other hand, our proposed PhC consists of a single anisotropic dielectric material, but the band peculiarity comes entirely from the nontrivial periodic rotation of the optical axes inside the material. Although recent studies have shown that artificial gauge fields 47 , 48 , Pancharatnam-Berry phases 49 , and synthetic spin-orbit interactions 50 for light can be achieved by arranging the dielectric polarization, there are still few works that study the photonic band topology of PhCs made of anisotropic dielectrics. Our results suggest that the intrinsic material anisotropy has irreplaceable features compared to the structural anisotropy, and anisotropic dielectrics, such as liquid crystals 49 , 50 , could become a platform for probing the unique topological effects of EM fields.…”