Study of the properties of non-integer order vortex beams at Fraunhofer zone

The intensity and phase distributions of an optical vortex beam with non-integer values of the topological charge are analyzed in Fraunhofer region. There are two annular rings with different size and shape in the intensity patterns. The petal-like bright spots appear on the larger annular rings with higher intensity, and the small rings with lower-intensity. There are ellipse-like dark spots in the middle of the annular rings. The intensity patterns for positive and negative topological charges of vortex beams are mirrored in the x axis, and the number of bright spots and dark spots is related to the topological charge of vortex beam. In phase patters, the new born phase vortex moves gradually to the origin along the y axis, and the positions of phase vortices within the central region move regularly with the increase of the non-integer topological charge of vortex beam.