  Characterization and analysis of spin-orbit coupled (SOC) states, as a
measurement problem, play a vital role in research on the modern optics and
photonics based on structured light. Here, we demonstrate determination of
photonic SOC states via spatial-Stokes measurement, in which two spatial
complex probability amplitudes of spin-dependent spatial modes within SOC
states and their relative (intramode) phase can be measured directly. Compared
with the standard quantum-state tomography, by avoiding wavefront-flattening
operations, the apparatus can completely record photons' realistic SOC
structure, leading to a more accurate and precise determination of
wavefunction. This simple and general approach for SOC state determination can
provide a powerful toolkit for in-situ measuring photonic SOC state,
characterizing the quality of SOC light source and associated geometric-phase
devices.
