Optical twists and transverse focal shift in a strongly focused, circularly polarized vortex field

摘要： Twisting behaviors of the optical vortices and the intensity patterns of a strongly focused, circularly polarized field with two off-axis vortices are investigated in this article. The transverse focal shift (TFS) which is mainly caused by the off-axis vortices and the strong focusing effect is also studied. It is very interesting to find that in the focal region the two off-axis vortices can coil many circles with each other as the beam propagates, and their trajectories form a double helical structure. Three factors for this twisting behavior are analyzed. It is also found that the intensity maxima of the total field are not strongly influenced by the twisting behavior of the vortices and rotate only a quarter circle (90?) to the focal plane. In contrast to the TFS in the linearly polarized field, the 'actual focus/foci' in this circularly polarized field does/do not move between the +ys axis and the ?ys axis or the ys axis and the xs axis, but is/are always confined on the +ys/ys axis. These results will be useful in understanding the general rotational behaviors in optical fields with off-axis vortices and can have applications in optical manipulations.