Rotational Doppler shift tripling via third-harmonic generation of spatially structured light in a quasi-periodically poled crystal

The rotational Doppler effect—the angular version of the Doppler effect—shows a frequency shift phenomenon happening when light passes through a rotating object and its angular momentum is changed. The rotational Doppler effect has been widely studied with various light waves based on different angular momentum transform mechanisms and successfully utilized to detect the rotation of objects. However, these studies are mostly limited to linear optics. As the rotational Doppler effect is closely related to the frequency degree of freedom and frequency conversion always happens in nonlinear optics, it is of great significance to explore the rotational Doppler effect in nonlinear optics. Although nonlinear rotational Doppler phenomena have been observed in second-harmonic generation with circularly polarized Gaussian fundamental light and a rotating nonlinear crystal, there is still the open challenge of how to realize Doppler frequency shift conversion (similar to conventional nonlinear frequency conversion), such as doubling or tripling. Here we report the experiment observation of rotational Doppler shift conversion in nonlinear optics. We demonstrate the tripling of a rotational Doppler frequency shift in third-harmonic generation of a spatially structured fundamental wave. Frequency shifts can be extracted from the intensity beating signals with the interference of two components of vector fields with opposite topological charges and the measured modulation frequency of the beating signal for the generated third harmonic. Our results will excite more research on nonlinear optics with spatially structured light, and our method may create opportunities for precision measurement of frequency shifts.