We investigate the generation of broadband terahertz (THz) pulses with phase singularity from air plasmas created by fundamental and second harmonic laser pulses. We show that when the second harmonic beam carries a vortex charge, the THz beam acquires a vortex structure as well. A generic feature of such THz vortex is that the intensity is modulated along the azimuthal angle, which can be attributed to the spatially varying relative phase difference between the two pump harmonics. Fully space and time resolved numerical simulations reveal that transverse instabilities of the pump further affect the emitted THz field along nonlinear propagation, which produces additional singularities resulting in a rich vortex structure. The predicted intensity modulation is experimentally demonstrated with a thermal camera, in excellent agreement with simulation results. The presence of phase singularities in the experiment is revealed by astigmatic transformation of the beam using a cylindrical mirror.
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