Reconstruction of wave function via spin-orbit interaction of light

The measurement of a wave function plays a pivotal role in quantum physics and presents a distinctive challenge in experiment. Recent works have shown that both the real and imaginary components of the wave function can be extracted by employing weak or strong measurements, thereby enabling the determination of its amplitude and phase. Here, we propose a simple approach for reconstructing the wave function utilizing the spin-orbit interaction of light at the air-glass interface. By directly measuring the amplitude and employing spatial differentiation to capture the phase gradient, it becomes possible to successfully reconstruct an unknown wave function. To demonstrate its feasibility, we experimentally measure the pure wave function of photons with a Gaussian state. Furthermore, we conduct measurements on a custom state featuring a targeted phase jump to examine the accuracy of our methodology. The measured results show a distribution with high contrast and considerable accuracy, with a fidelity that can exceed 85%. We believe that this work contributes valuable insights into the practical applications of spin-orbit interaction, including optical image processing, wave-front sensing, and quantitative phase imaging.