Single-shot measurement of the space-varying polarization state of light through interferometric quantification of the geometric phase

A light beam carrying a spatially varying state of polarization generates a space-varying Pancharatnam-Berry geometric phase while propagating through a homogeneous anisotropic medium. We show that determination of such a space-varying geometric phase provides a unique way to quantify the space-varying polarization state of light using a single-shot interferometric measurement. We demonstrate this concept in a Mach-Zehnder interferometric arrangement using a linearly polarized reference light beam, where full information on the spatially varying polarization state is successfully recovered by quantifying the space-varying geometric phase and the contrast of interference. The proposed method enables single-shot measurement of any space-varying polarization state of light from the measured interference pattern with a polarized reference beam. This approach shows considerable potential for instantaneous mapping of complex space-varying polarization of light in diverse applications, such as astronomy, biomedical imaging, and nanophotonics, where high precision and near real-time measurement of spatial polarization patterns are desirable.