We report on a partially coherent power-exponent-phase vortex beam (PC-PEPV), whose spatial coherence is controllable and the initial phase exhibits a periodic power exponential change. The PC-PEPV beam was generated experimentally with various spatial coherence widths, and its propagation properties were studied both numerically and experimentally. By modulating the topological charge (TC) and power order of the PC-PEPV beam, the structure of the vortex beam can be adjusted from circular to elliptic, triangular, quadrangle, and pentagon. When the power order is odd, the PC-PEPV beam with a negative TC can be generated, and the profiles of the PC-PEPV beam can be precisely controlled via adjusting the value of the power order. For the case of high spatial coherence width, the number of the dark cores in the polygonal intensity array of the PC-PEPV beam equals the magnitude of the TC. However, when decreasing the spatial coherence width, the dark cores vanish and the intensity gradually transforms into a polygonal light spot. Fortunately, from the modulus and phase distributions of the cross-spectral density (CSD), both the magnitude and sign of the TC can be determined. In the experiment, the modulus and phase distribution of the CSD are verified by the phase perturbation method. This study has potential applications in beam shaping, micro-particle trapping, and optical tweezers.
Propagation of the power-exponent-phase vortex beam in paraxial ABCD system