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An optical vortex, which consists of blue phase and isotropic phase, is generated from azobenzene liquid crystal cell with computer generated hologram pattern. This device is optically switchable and can be erased and generated by ultraviolet or green light, respectively. An intensity modulation is formed between blue phase and isotropic phase of liquid crystal cell, where the blue phase liquid crystal selectively reflects circular polarization light due to the Bragg reflection, resulting in a circularly polarization-dependent optical vortex. The proposed method can be applied to any other diffractive optical elements.