Rotational Doppler effect in nonlinear optics

The translational Doppler effect of electromagnetic and sound waves has been successfully applied in measurements of the speed and direction of vehicles, astronomical objects and blood flow in human bodies, and for the Global Positioning System. The Doppler effect plays a key role for some important quantum phenomena such as the broadened emission spectra of atoms(9) and has benefited cooling and trapping of atoms with laser light(10-12).. Despite numerous successful applications of the translational Doppler effect, it fails to measure the rotation frequency of a spinning object when the probing wave propagates along its rotation axis. This constraint was circumvented by deploying the angular momentum of electromagnetic waves(13)-the so-called rotational Doppler effect. Here, we report on the demonstration of rotational Doppler shift in nonlinear optics. The Doppler frequency shift is determined for the second harmonic generation of a circularly polarized beam passing through a spinning nonlinear optical crystal with three-fold rotational symmetry. We find that the second harmonic generation signal with circular polarization opposite to that of the fundamental beam experiences a Doppler shift of three times the rotation frequency of the optical crystal. This demonstration is of fundamental significance in nonlinear optics, as it provides us with insight into the interaction of light with moving media in the nonlinear optical regime.