An apparatus to achieve a single doughnut-like Laguerre-Gaussian (LG) mode with extremely high mode purity higher than 99.6% is reported. The proposed apparatus is a conceptual combination of a high-order HG mode selector and an astigmatic mode converter, which consists of only four simple and easily-made optical elements: three lens elements and one binary phase element. Theoretical simulations show that the apparatus has a good tolerance for both system production and alignment errors. With such high mode purity, the doughnut-like LG beam generated by the apparatus carrying an orbital angular momentum will be beneficial to numbers of studies including the trapping and rotating of micro and nano-particles, non-linear optics, and atom-light interaction.
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