Fig. 1: Theoretical construction of toroidal phase topologies. | Communications Physics

Fig. 1: Theoretical construction of toroidal phase topologies.

From: Toroidal phase topologies within paraxial laser beams

Fig. 1

a Three-dimensional toroidal amplitude isosurface of the complex function u. The toroidal vortices are represented by a black trajectory, and the local vortex phase structure around the torus is marked with colored arrows. b Several local phase structures arising from the vortex phase of the complex function v, with straight vortex line passes through the interior. c Hopfionic phase textures embedded in the complex scalar function uv. Local colored arrows rotate due to axial vortices, the circular trajectory formed by the end of the arrow is shown in the illustration. The isovalue of the 3D surfaces is set to 0.3, and the colored curves in the illustration represent the phase fibers formed on the torus.

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