The Poynting vector and angular momentum density of the autofocusing Butterfly-Gauss beams

Three different Butterfly-Gauss beams are proposed by introducing higher order Butterfly catastrophe to the field of optics, where an autofocusing Butterfly-Gauss beam with a special profile is emphatically studied and it can be regarded as the sum of two Half-Butterfly-Gauss beams. Based on the Collins integral formula, the autofocusing behavior, Poynting vector and angular momentum density of the corresponding Butterfly-Gauss beams during propagation in free space, focus system and chiral medium are investigated, respectively. The results show that the Butterfly-Gauss beam not only exhibits autofocusing behavior similar to the Pearcey beams or circular Airy beams, but also presents rotation in analogy with the Swallowtail beam during propagation in free space. In the focus system, the tail directions of special patterns in the focal plane can be controlled by scaling lengths. In the chiral medium, the greater chirality parameters correspond to the increasing of phase velocity of beam, which results in the fact that the distance of autofocusing plane becomes smaller, and it is easier to autofocus the beam. The proposed Butterfly-Gauss beams have the application possibility in the field of manipulating microparticles along intensity channels due to their special spatial structures in focal plane, where the Poynting vectors flow from center spot to the controlled tail.