Single-channel direction-resolved rotational Doppler metrology via bispectral closure phase.

Abstract

Rotational Doppler metrology with orbital-angular-momentum (OAM) beams enables non-contact angular-velocity measurement, but scalar Fourier-magnitude readout cannot distinguish opposite rotation directions. The direction remains encoded in the harmonic phases, although the phase of an individual Doppler harmonic is coupled to the unknown initial angular position. Here, we employ bispectral closure phase to construct an initial-angle-independent directional observable from deterministic inter-harmonic phase correlations. A phase-engineered scalar OAM field generates closed harmonic triads in which the initial-angle-dependent phase cancels, while rotation reversal reverses the closure-phase signs. The Doppler harmonic comb provides the angular-speed magnitude, and a combined closure chirality identifies the rotation direction. Both are retrieved from a single intensity trace without polarization analysis, additional time-dependent optical modulation, or an auxiliary interferometric reference. This work establishes higher-order spectral phase invariants as a route to direction-resolved scalar Doppler metrology.