Flexible measurement of high-order optical orbital angular momentum with a variable cylindrical lens pair

We present a method to measure the high-order optical orbital angular momentum (OAM) with a variable cylindrical lens pair. The optical system consists of two cylindrical lenses with the opposite focal length. It produces a rotating position-spatial frequency transformation of phase modulation by changing the angle between the two cylindrical lenses. With this feature, the method can flexibly measure the OAM states of the vortex beams with different beam waists. The OAM states are determined by the number and direction of dark stripes of the diffraction pattern. The measurements of the topological charge and the radial index of Laguerre-Gaussian mode are demonstrated. As a compact high-order OAM measuring device, the variable cylindrical lens pair may find potential applications in optical communication.