Measuring the orbital angular momentum states of vortex beams with defocusing intensity

Optical vortex beams (VB) have been extensively applied in many fields for their unique features. In this paper, we explore the defocusing intensity of VB modulated by axial symmetry polarization. Combining appropriate polarization order of the modulator, we show that defocusing can result in a spiral structure of intensity distribution, of which the number of spiral arms is determined by the polarization order of the modulator, and the rotation direction of spiral arms depends on the topological charge (TC) of incident beams. The helical structure of defocusing intensity holds a small solid spot when the TC value of VB matches the polarization order number. Therefore, the magnitude of the tested TC can be inferred from the small solid spot distribution, and the sign of the TC can be determined by the rotation direction of the helical intensity. The peculiar phenomena exploited in this paper stimulate the new applications of VB in many fields.