Zenghui Gao

Propagation of Riemann–Silberstein vortices through an astigmatic lens

The propagation of Riemann-Silberstein (RS) vortices for Gaussian vortex beams with topological charges m=+1 through a lens is studied. It is shown that if there is an ideal lens, a RS vortex and a circular edge dislocation appear for Gaussian on-axis vortex beams, while only RS vortices take place for Gaussian off-axis vortex beams. In the presence of an astigmatic lens, there exist RS vortices but no edge dislocations for both Gaussian on-axis and off-axis beams. By varying the astigmatic coefficient, the off-axis parameter, and the propagation distance, the motion, creation, and annihilation of vortices may take place, and in the process, the total topological charge of RS vortices remains unchanged.

Interaction between a vortex and an edge dislocation nested in a cos‐Gaussian beam passing through a tilted lens

The interaction between a vortex and an edge dislocation nested in a cos‐Gaussian beam passing through a tilted lens was studied analytically and numerically. It is shown that in the presence of the tilted lens, by varying the cos‐part parameter of the beam, the slope of the edge dislocation, or the tilt coefficient of the lens, the topological charge is conserved for the case of the off‐axis edge dislocation, while charge conservation does not hold true for the case of an on‐axis edge dislocation, irrespective of the on‐axis or off‐axis vortex. The relation between the transverse positions (x, y) of vortices and the tilt coefficient is linear, and is interpreted.

Evolution behavior of two edge dislocations passing through an astigmatic lens

The evolution behavior of two edge dislocations passing through an astigmatic lens is studied. It is shown that the edge dislocations are unstable in general. They may vanish or decay into vortices under certain conditions. The appearance, disappearance and motion of phase singularities may take place by varying the off-axis distance of the edge dislocations, the astigmatic coefficient of the lens, the angle between two edge dislocations, and the propagation distance. Vortices or edge dislocations may appear at the geometrical focal plane for two perpendicular edge dislocations, whereas no phase singularities occur for two parallel edge dislocations.

Interaction of two singular Lissajous lines in free space

The interaction of two singular Lissajous lines emergent from a polychromatic vector beam is studied. It is shown that singular Lissajous lines disappear with propagation; meanwhile Lissajous singularities take place. The handedness reversal, the changes in the shape of Lissajous figures, and the degree of polarization of Lissajous singularities, as well as the creation and annihilation of a single singularity, may appear by varying the control parameters. In addition, the transformation of the shape of line h=0, the creation and annihilation of pairs of Lissajous singularities not only with opposite topological charge and same handedness, but also with same degree of polarization, take place with propagation.

Transformation of the V-dipole by an astigmatic lens

The transformation of the V-dipole by an astigmatic lens is studied analytically and numerically. It is found that after passing through the lens, the V-dipole splits into four C-points which make up two C-dipoles with same singularity index and opposite handedness. By a suitable choice of the astigmatic coefficient, off-axis distance, or propagation distance, the creation and annihilation of more than two C-dipoles may take place, as well as C-points may occur at the focal plane of the astigmatic lens. As a special case, only two C-dipoles annihilate or recreate and no polarization singularities appear at the focal plane in the presence of an ideal lens.

Propagation of the Lissajous singularity dipole through an astigmatic lens

The propagation was investigated of a pair of Lissajous singularities of opposite singularity index called the Lissajous singularity dipole (LSD) through an astigmatic lens. It is shown that after passing through the lens the positions of the singularities are inverted and more than two LSDs occur. Changes in the degree of polarization of the LSDs as well as in the shape of the Lissajous figures also occur. In addition, Lissajous singularities may take place at the focal plane, and a single Lissajous singularity may appear and vanish under certain conditions. The results are compared with those of previous work.