Fig. 1. Schematic of THz radiation in a parabolic plasma channel. (a) Schematic of the laser trajectory in a cylindrical spiral along the channel and the generated conical THz radiation with an open angle of $2\alpha$. (b) Illustration of the laser injection conditions from the side view in the $x\text{-}y$ plane with an initial offset distance on the $z$-axis and the transverse density profile of the plasma channel. (c) Transverse distributions of the THz radiation at different positions along the $x$-axis at $x=0,{\mathrm{\Lambda }}_0/4,{\mathrm{\Lambda }}_0/2,3{\mathrm{\Lambda }}_0/4$ as marked in panel (b). (d) Snapshots of the transverse electric field associated with the THz radiation around the plasma channel at $x=0,{\mathrm{\Lambda }}_0/4,{\mathrm{\Lambda }}_0/2,3{\mathrm{\Lambda }}_0/4$, where the field strength is normalized by $m_e{\omega }_{0}c/e$ or $\sim 4000\mathrm{GV}/\mathrm{m}$ for a wavelength of $0.8\mu \mathrm{m}$.

Fig. 2. 3D PIC simulation results. (a) Laser trajectories found in the simulation under two different laser injection conditions. The arrows denote the chirality of the trajectories. (b) Contour of the THz radiation. The display threshold of the THz electric field is $7.8\mathrm{MV}/\mathrm{m}$. The color of the contour is only associated with the position away from the plasma channel center. (c) Phase distribution of the THz radiation collected at $t=2300T_0$. (d) Waveforms of the THz radiation collected at a radius of $100\mu \mathrm{m}$ from the channel center [marked in panel (c) as the green dashed circle] for different azimuth angles $\phi$.

Fig. 3. Manipulation of the OAM of the THz radiation. (a) THz radiation spectra under different offset distances $z_0$. (b) Simulated THz central frequencies and radiation angles under different $z_0$ while ${\theta }_y=88.5\mathrm{deg}$. The blue solid line gives the calculated plasma frequency at the laser centroid. The red solid line is a fitting of $\alpha$ with $\alpha (\mathrm{deg})=4.46\lg [z_0+0.8(\mu \mathrm{m})]+1.18$. (c) Calculated $\ell$ utilizing the calculation and fitting lines in panel (b) and the simulated peak amplitude of the THz radiation under different $z_0$ while ${\theta }_y=88.5\mathrm{deg}$. The blue dots give the calculated $\ell$ with the simulation results in panel (b). (d) Phase distribution of the THz radiation under the injection condition of $z_0=5{\lambda }_0$ and ${\theta }_y=88.5\mathrm{deg}$. (e) Phase distribution of the THz radiation under the injection condition of $z_0=12.5{\lambda }_0$ and ${\theta }_y=88.5\mathrm{deg}$. (f) Phase distribution of the THz radiation under the injection condition of $z_0=10{\lambda }_0$ and ${\theta }_y=91.5\mathrm{deg}$. (g) THz conversion efficiency under the injection condition of $z_0=10{\lambda }_0$ and ${\theta }_y=88.5\mathrm{deg}$ after different propagation lengths $L$.