Self-Generated Chiral Rotation in Whispering-Gallery Optomechanics

Backscattering in whispering-gallery-mode resonators is usually a passive mode-splitting mechanism produced by a fixed defect. Here, we show that, when the backscatterer is a mechanical angular degree of freedom, the same process becomes an angular-recoil backaction channel capable of generating chirality under reciprocal driving. A localized movable scatterer coherently converts photons between clockwise and counterclockwise whispering-gallery modes, transferring angular recoil in each circulation-changing event. In a weak-scattering driven-dissipative model, reciprocal bidirectional pumping gives zero net torque at rest, but rotation Doppler-shifts the two opposite scattering rates in opposite directions. For suitable detuning, this feedback produces negative angular friction, destabilizes the nonrotating reciprocal state, and selects one of two symmetry-related steady rotations. The threshold scales inversely with the square of the WGM azimuthal index. The mechanically chiral state produces a direction-dependent weak-probe response, visible as a Doppler splitting of the backscattered spectra, turning passive WGM mode splitting into a minimal mechanism for autonomous chiral optomechanics.