Modulating and identifying an arbitrary curvilinear phased optical vortex array of high-order orbital angular momentum

•Our paper reports on a phased optical vortex array with high-order orbital angular momentum.•Its OAM mode distribution size is analyzed using OAM spectrum expansion.•Our results substantiate the feasibility of generating a high-order optical vortex array using this method.•We also consider the phase singularity and OAM distributions at high orders. Vortex beams can be used in optical communication, imaging, and processing applications. In this study, we generate a phased optical vortex array with high-order orbital angular momentum (OAM) based on a phased Gaussian optical array and high-order phase multiplication. We then analyze the OAM mode distribution using the OAM spectrum expansion, and the number of high-order phase singularities in the array verified in interference experiments. Our results substantiate the feasibility of generating a high-order optical vortex array using this method. At the same time, because the phase Gaussian optics array that forms the phased optical vortex array is discrete and separable, we can use the phase Gaussian optics array with different phase differences to generate the phased optical vortex array with different phase gradients. The shape of the generated optical vortex array can be arranged along any curve. The phase singularity and OAM distributions at high orders are also detailedly analyzed. The ability to control the high-order OAM and phase structure has possible applications in particle manipulation and free-space optical communication.