Symmetric Swallowtail Beams in the Rectangle Frame

A new type of symmetric swallowtail beam (SSB) in the rectangle frame is introduced here. These kinds of beams are highly tunable with multiple manipulation parameters. The focal length and the focus intensity can be controlled precisely. The SSBs can guide the off-axis vortex to their center. And the experimental results agree well with the numerical simulations. Besides, stable trapping of particles by utilizing the SSBs' auto-focusing property and rectangle symmetry is also observed.