Based on nonlinear holography, we propose a 2D spirally poled LiNbO3 nonlinear photonic crystal that generates orbital angular momentum (OAM) states of second-harmonic (SH) waves. In this crystal, the generated SH waves from positive and negative domains have a π phase difference, which is used to compose a nonlinear Fresnel zone plate for an experimental demonstration of generating SH OAM states at the designed focusing spot. In addition, the crystal can be used to detect input OAM states of fundamental beams without significantly disturbing their wave fronts.
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