the generation and measurement of optical vortex (OV) are the basis for a variety of related applications. However, the special case of high-order OVs has not been sufficient addressed yet. Herein, a generation and measurement method of high-order OV via utilizing the CP is investigated. In the experiment, we generate OVs with 60 l  , 20 p  and successfully measure OVs with 200 l  , 0 p  , where experimental results agree well with simulation outcome. On this basis, the intensity distributions of LG and HG beams (corresponding to the generation and measurement) versus waist radius of initial light beams is discussed. This work provides an alternative method to generate or measure high-order OV, which will facilitate applications in optical micro-manipulation, quantum entanglement and rotation speed detection.

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The vortex beam has extensively demonstrated impressive significance in many applications. As a key parameter, the mode purity (MP) of a vortex beam is easily influenced by beam deviation. In this paper, the deviation models of the vortex beam — a beam wander model (BWM) and a phase singularity wander model (PSWM) are proposed. The MP expressions of these models are derived, and the influence of beam parameters on MP are studied through numerical methods. It is found that MP remains constant with the variation of azimuth of phase singularity, the maximally relative radial distance varies with the topological charge inversely and the influence of PSWM on MP is greater than BWM. Furthermore, the MP of a radially symmetrical vortex beam array is equal to that of each beamlet, and will increase with the decline of relative radial distance of each beamlet. The results can provide theoretical basis for further researches on orbital angular momentum (OAM) communication and vortex beam synthesis.