{'fraction_non_alphanumeric': 0.019593613933236574, 'fraction_numerical': 0.0, 'mean_word_length': 5.183856502242152, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Trajectories and rotations controlled off-axis winding beams in nonlocal nonlinear media.

Off-axis winding beams are discussed in nonlocal nonlinear media, whose trajectories and rotations can be controlled by the optical power and the orbital angular momentum (OAM). By changing optical power or the OAM, optical beams can propagate along different trajectories including ellipses, circles, rectangles, rhombus and so on. Due to the OAM stemming from a combination of the cross phase and the vortex phase, different parts of the optical beam exhibit distinct rotating characteristics. The elliptic envelope revolves around the beam center resulting from the cross phase, while optical peaks spin about their own axes because of the vortex phase. The two rotating velocities can be adjusted separately by the optical power and the OAM, respectively. Optical power plays a global role on the revolving velocity and the spinning velocity and can enhance the two rotations synchronously. In contrast, the OAM has a local effect and can change the relative magnitudes of these two velocities. Our results may provide a tailoring tool of evolution properties for optical beams. The property of controllable trajectories may find applications in all-optical controlling. While, the controllable rotating property can be used as in optical spanners to operate micro- or nanoparticles.