Rotation of a Tricomi–Gaussian beam and its focusing characteristics through a thin lens system

The rotation behaviors of an asymmetric Tricomi–Gaussian beam (aTGB) propagating in free space and through a thin lens system are mainly investigated. The focusing characteristics of TGB with symmetric and asymmetric modes propagating through a thin lens system are also presented. Influences of complex constants α and β , the topological charge n , and the lens focal length f on the field distributions of TGB are studied thoroughly. The results indicate that when a symmetric TGB propagates through a thin lens system, a perfect vortex beam could be generated at the lens focal plane. TGB undergoes two focusing processes through the thin lens system, and the peak intensities at two focal planes, the rotation, and the focal characteristics of TGB can be manipulated by α , β , n , and f . Moreover, f has more significant effects on the focal depths of two foci and the self-focusing focal length than α , β , and n .