Fig. 1. Illustration of the concepts. (a) Schematic of the designed integrated THz vortex beam emitter. The insets depict the geometry of the waveguide cross section and grating scatterers, which are all cuboid in shape. (b) Optical microscope images of the fabricated device. The inset is a zoomed-in view of the grating scatterers and the coupling section between the bus waveguide and the resonator. (c) Schematic of rotational Doppler effect. A tiny scatterer from a rotating body is taken out to analyze the relationship between the Poynting vector and the scatterer velocity on the condition of coaxial incidence. $\overrightarrow{p_{\phi }}$ and $\overrightarrow{p_{\mathrm{z}}}$ are the angular and the propagation components, respectively.

Fig. 2. (a) Measured transmission spectrum of the THz vortex emitter for the TE mode. Note that the black annotation indicates the topological charge $l_{TC}$. The orange region represents the frequency range used for near-field and rotational Doppler experiments. (b) Experimental setup for device near-field characterization.

Fig. 3. Simulated and measured radiation cross-sectional field distributions of the $x$ and $y$ polarization components for our device with the corresponding $l_{TC}$. Note that $l_{TC}=p-q$ is the topological charge, where $p$ is the azimuthal order of WGM, and $q$ is the number of grating elements.

Fig. 4. Simulated and measured radiation cross-sectional field distributions of the LHCP and RHCP components for our device with the corresponding $l_{TC}$.

Fig. 5. Schematic diagram for experimental setup of rotation speed measurement of a spinning object using the vortex beam generated by the integrated THz chip.

Fig. 6. Measurement results of rotating speed using vortex beam generated on-chip. (a)–(i) The observed power spectrum at the indicated rotational speed. (j) The measured results at different rotating speeds for OAM mode $+1$. (k) The measured results at different rotating speeds for OAM mode $-1$. For (j) and (k), the rotational speeds are from 251 to 628 rad/s. The red points are the measured data, and the solid blue lines are the theoretical values. Note that $\delta$ is the absolute error.