Propagation Characteristics of Exponential-Cosine Gaussian Vortex Beams

We propose a controllable exponential-Cosine Gaussian vortex (ECGV) beam, which can evolve into the different beam profiles with three parameters: distance modulation factor (DMF), split modulation factor (SMF) and rotation modulation factor (RMF). When SMF is 0, the ECGV beam appears as a perfect single-ring vortex beam and the ring radius can be adjusted by the DMF. We deduce from mathematics and give the reason for the single-ring characteristics. When SMF is not 0, the beam splits symmetrically. DMF, SMF and RMF control the number, distance and rotation angle of the split, respectively. Our experiments verify the correctness of the theory.