Propagation of an Airy beam with a spiral phase

The propagation of an Airy beam with a spiral phase is studied. The centroid position and spread of the beam are investigated analytically for different topological charges. Study shows that the centroid position of the Airy beam with a spiral phase keeps moving during propagation. The motion with positive topological charge is in the direction opposite to that with negative topological charge. The speed of the motion of the centroid position is proportional to the topological charge and the normalized distance. From the variation of the second moment of the beam, we can also see that the beam spread is speeded up by the spiral phase during propagation. The speed of the beam spread is proportional to the square of the topological charge.