Polarization-modulation-based orientation metrology of optically levitated rotating birefringent particles

The ultrafast rotation of optically levitated particles has propelled advancements in sensing and precision measurement, while its orientation remains largely unexplored for the spherical shape. Here, we proposed an orientation measurement method for the birefringent rotating particles, which extracts both the azimuthal and polar angles of the optical axis from the polarization of the transmitted laser. A bulk birefringent crystal with a known orientation is measured by this method to verify its effectiveness, and then the orientation of vaterite particles is extracted from the rotational signal. This method paves the way to investigate the orientational dynamics and gyroscope application.