Singular optics

Optical vortices, or wavefront dislocations, are singular points where the field goes to zero and around which the phase screws up as an n armed spiral, with n the topological charge. When appearing in a large number, as in speckle fields or after the propagation through a distorting medium, such phase singularities, also called topological defects, have been seen as disturbances imposing severe limitations to aberration correction systems. More recently, the characterization of vortices in low-order Gauss-Laguerre beams has been revisited showing the exchange of angular momentum between light an matter and related useful applications, as the realization of optical tweezers, quantum computation and improvement of astronomical imaging. The generation of optical vortex beams is, therefore, an important field of investigation in modern optics. Several methods for vortex beam generation have been demonstrated, including the synthesis through holographic masks, the suitable deformation of segmented adaptive mirrors, spiral glass plates or pre-imposed director orientations in liquid crystal samples, so-called, q-plates. On the other hand, nonlinear interactions have also been considered in view of vortex beam generation. The investigated experimental situations comprise second harmonic generation (SHG), parametric down-conversion in solid-state crystals, Raman-resonant four-wave mixing (4WM) in atomic vapors.



Theoretically, nonlinear mixing of vortices in general wave-mixing processes has been predicted to induce a cascaded generation of vortices, leading to fundamental effects such as, for instance, the generation of helical soliton beams or Bose-Einstein condensation in two-dimensional wave-turbulence. By performing two-wave mixing experiments in a liquid crystal light-valve, LCLV we have demonstrated that optical vortex beams interact and exchange topological charge. Arbitrarily charged vortex beams can be created and controlled through this process. The topological charges mix-up during the wave-mixing process and new charges are observed on the output orders. The selection rules are fixed by the vortex interaction inside the medium.Theoretically, nonlinear mixing of vortices in general wave-mixing processes has been predicted to induce a cascaded generation of vortices, leading to fundamental effects such as, for instance, the generation of helical soliton beams or Bose-Einstein condensation in two-dimensional wave-turbulence. By performing two-wave mixing experiments in a liquid crystal light-valve, LCLV we have demonstrated that optical vortex beams interact and exchange topological charge. Arbitrarily charged vortex beams can be created and controlled through this process. The topological charges mix-up during the wave-mixing process and new charges are observed on the output orders. The selection rules are fixed by the vortex interaction inside the medium.


Another approach to generate vortex beam has been recently developed, which resorts to an homeotropic liquid crystal light valve. The liquid crystals are aligned orthogonally to the confined walls and with a negative anisotropy, therefore, they naturally produce topological defects when they reorient under the application of an electric field. In our system, by sending circularly polarized light beams onto the photosensitive wall of the LCLV, it is possible to locally induce the reorientation and to generate vortex-like defects that remain, each, stable and trapped at the chosen location. The system is able to create optical vortices with opposite topological charge that, consistently with angular momentum conservation, both derive from the same defect created in the liquid crystal texture. The vortex induction is a reconfigurable and self-centering process, opening the way to the realization of dynamical vortex arrays.Another approach to generate vortex beam has been recently developed, which resorts to an homeotropic liquid crystal light valve. The liquid crystals are aligned orthogonally to the confined walls and with a negative anisotropy, therefore, they naturally produce topological defects when they reorient under the application of an electric field. In our system, by sending circularly polarized light beams onto the photosensitive wall of the LCLV, it is possible to locally induce the reorientation and to generate vortex-like defects that remain, each, stable and trapped at the chosen location. The system is able to create optical vortices with opposite topological charge that, consistently with angular momentum conservation, both derive from the same defect created in the liquid crystal texture. The vortex induction is a reconfigurable and self-centering process, opening the way to the realization of dynamical vortex arrays.


LCLV and process of optical vortex induction. The phase profiles of the input and output beam are shown together with the molecular projection on the transverse plane. The corresponding alignment of the nematic director is depicted from y-cut in the middle of the valve.



Profiles of the generated optical vortices: a) d) typical doughnut profile of order 2 for the LH/RH polarized Laguerre-Gauss beam LG02 obtained with a RH/LH input beam. Corresponding b-e) spherical and c-f) plane wave interference patterns of the -2/+2 charged optical vortices.