Fig. 1: Experimental setup to drive micro-rotors asynchronously.

a Optical setup for introducing a broad (D ≈ 440 μm) circularly polarized beam into a microscope sample. b Schematic and polarized microscopy image of birefringent vaterite particles rotating while moving freely in the illuminated region. The transmitted light intensities of two particles (blue and green) are tracked over the duration of the experiment and are shown in (c) and the inset of (d). c One-half of the particles' (blue and green) blinking cycle, demonstrating that their optical axes are asynchronous. The incident electric field—whose direction is set by the orientation of the polarizer (P)—is de-polarized whenever the optical axis of the rotating particles is aligned with neither the polarizer nor analyzer (A). d Computing the magnitude of the Fourier transform (\(\sqrt{{{{{{{{\mathcal{F}}}}}}}}{{{{{{{{\mathcal{F}}}}}}}}}^{*}}\)) of the blinking patterns (inset) of the two particles in (b) shows that the frequencies at which the particles de-polarize the incident L.E.D. light are centered around 0.5 Hz, corresponding to a rotation frequency of 0.125 Hz. The magnitude of the sum of transforms, \({\left|{\sum }_{i}{{{{{{{{\mathcal{F}}}}}}}}}_{i}\right|}^{2}\) (solid line), decays, confirming that the particles' orientations are out of phase. Scale bar: 5 μm.