Spatial shift for generating terahertz perfect vortex beams with trigonometric-function azimuthal phase gradients

In traditional perfect vortex beams (PVBs), the azimuthal phase gradient is typically constant or piecewise constant, while achieving a continuously tunable azimuthal phase gradient remains a challenge. Herein, we propose and experimentally demonstrate a spatial shift approach for generating terahertz PVBs with trigonometric-function azimuthal phase gradients. Based on the Fourier shift theorem, shifting the optimal phase mask relative to the optical axis introduces an azimuthally varying phase term in the Fourier plane while preserving the PVB intensity. Simulations and experiments using 3D-printed optimal phase elements show that the phase gradient and orbital angular momentum density both follow trigonometric-function distributions. The modulation amplitude and azimuthal orientation can be controlled by the shift distance and shift azimuth, respectively, providing a simple way to continuously tune the azimuthal phase gradients and orbital angular momentum density distributions in terahertz PVBs.