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In this paper, we present a picosecond pulsed, synchronously pumped optical parametric oscillator producing vortex beam output with tunable wavelengths in the near- to mid-infrared range. The system utilizes a Nd:YVO₄ picosecond pulsed solid-state laser emitting at a wavelength of 1.064 µm to pump a Z-shaped, singly resonant OPO which contains a MgO:PPLN crystal with a fan-shaped grating. The wavelength tuning characteristics of the OPO output are examined both as a function of the MgO:PPLN grating period and crystal temperature. The orbital angular momentum of the pump field can be selectively transferred to either the signal or idler fields by appropriately adjusting the location of the MgO:PPLN crystal within the OPO cavity. The maximum output power of the signal and idler vortex fields are 5.12 W and 3.46 W, respectively, for an incident pump power of 19 W.