Nonlinear beam steering by fractional vortex dipoles

Propagation of optical beams in nonlinear media NLM has been a subject of continuing interest for more than 4 decades due to the possibility for creation of reconfigurable waveguides through the intensity-dependent refractive index change 1,2 . Such optically induced waveguides can guide weak signal beams and pulses 3,4 , which motivates the investigation of novel techniques for manipulation of the transverse beam dynamics and correspondingly opens possibilities for realization of waveguides with complex geometries. Optical beams can be spatially manipulated by introducing chirp to their transverse phase profiles 5–7 . Therefore, the implementation of steering schemes utilizing beams with complex spatial phase profile, in the form of phase singularities 8 , appears especially attractive. An example of such a beam is an optical vortex with its helical phase profile described by exp im multiplier, where is the azimuthal coordinate and m is the vortex topological charge. Due to the presence of a point phase singularity in the beam center, the optical vortices are associated with intrinsic energy flow and orbital angular momentum 9 . Propagation of optical vortices in nonlinear media has received great attention with their ability to form bright or dark optical vortex solitons OVSs in self-focusing and self-defocusing nonlinear media, respectively 2,10,11 . In a self-defocusing medium, OVSs can guide signal beams in their core 12–14 . Therefore by controlling the position of an optical vortex core, one can effectively steer a signal beam. The transverse velocity of an OVS has a radial and an angular component arising from the transverse phase and intensity gradients, respectively 15,16 . Two practical ways to control the vortex position have their origin in the Guoy phase shift on both sides of a background beam waist 16,17 and in the interaction of ordered structures of OVSs 18 controlled by their topological charges. Though the OVS is a stationary and stable nonlinear state in self-defocusing media, other schemes implementing nonstationary moving two-dimensional dark solitons have also shown great abilities for manipulation of signal beams. The possibility to branch a single input probe beam into ordered structures of sub-beams by quasi-two-dimensional dark spatial solitons has been demonstrated numerically in 19 . Other branching and steering schemes have also been realized by employing the inherent dynamics of ring dark solitary waves 20–22 or the decay of higher-order vortices 23 . Finally, dark beams containing mixed step-screw phase dislocation i.e., semispirals separated by a onedimensional 1D phase step have shown important potential for signal beam steering due to their defined spatial velocity, controlled through geometrical parameters 24–26 . Despite the large activities on beam steering in defocusing nonlinear materials, manipulation of signals by beams with complex phase structure in self-focusing nonlinear media remains unexplored. This is somewhat surprising since selffocusing materials are more common in nature. However, the implementation of beams with phase singularities for beam steering in self-focusing media has been hindered by the intrinsic azimuthal and modulational instabilities. Due to such instabilities, the OVS experiences breakup into a number of fundamental solitons that fly away from the vortex center 28–31 . In this work, we show that such instabilities are not a limiting factor for beam steering when beams with mixed phase dislocations are utilized. We demonstrate experimentally and describe theoretically the ability of such beams, also called fractional vortex dipoles, to steer signals in a self-focusing nonlinear medium. In particular, we employ the self-focusing photorefractive nonlinearity in a biased strontium barium niobate SBN crystal and demonstrate bright signal beam deflection that can be controlled by the geometrical parameters of the fractional vortex dipole.

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