1. Introduction
Light beams, as electromagnetic waves, can carry both energy and momentum. Meanwhile, we know that momentum can be classified into linear and angular momentum, and there are two particular kinds of angular momenta: spin angular momentum (SAM) and orbital angular momentum (OAM). More than a century ago, Poynting proposed that the SAM is related to the photon spin, namely, the circularly polarized light carries an SAM of per photon[1], whereas linearly polarized light carries no SAM, as illustrated in Fig. 1(a). In 1932, Darwin realized the photon can carry both SAM and OAM, and he even obtained the expression for each one[2]. But, it was not until 1992 that Allen et al. revealed the OAM of a light beam clearly[3]. It was shown that vortex beams with an azimuthal phase factor can carry OAM of per photon, where can be any integer number, named topological charge. The discovery of OAM of light has changed the way in which we understand and employ light. Different from traditional Gaussian beams, vortex beams exhibit a phase singularity in the center, which leads a doughnut-shaped intensity profile, as shown in Fig. 1(b). Figure 1(b) shows vortex beams with helical wavefronts, in which the number of intertwined helices and the handedness are dependent on the topological charge .