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We consider theoretically and experimentally the precession of the optical vortex in a singular beam propagating nearly perpendicular to the crystal optical axis, the beam and the crystal axis rotating with different angular velocities. The precession is a result of different scales along the major axes in a uniaxial crystal. Also we analyze the properties of the optical reducer consisting of two rotating crystals and a wave retarder between them permitting us to control the form of the vortex trajectory.

In this paper, we review the existing approaches for vortex and vector beam shaping and generation in the terahertz frequency range. The particular focus of this review is on the possibility of homogeneous topological charge formation in the ultra-wide spectral interval inherent to ultrashort terahertz pulses. We review the available materials and components, analyse proposed and potentially possible solutions for broadband terahertz vortex and vector beam shaping, compare all developed approaches, and put forward a unified concept for constructing passive shapers of such beams from the existing component base.

In this paper, we demonstrate the capabilities of the terahertz pulse time-domain holography in visualisation, simulation, and assessment of broadband THz vortex beam formation dynamics upon its shaping by elements of beam converter, and further propagation and manipulation. By adding Jones matrix formalism to describe broadband optical elements, we highlight the differences in the spatial-spectral and spatio-temporal structure of the formed vortex and vector beams dependence on the modulator used and visualise their modal features. The influence of diffraction field structure from each element in the broadband vortex modulator is revealed in numerical simulation and the formed beams are analysed against the simplified Laguerre-Gaussian beam model.

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