We propose and experimentally demonstrate a noninterferometric method to quantitatively determine the topological charge and complete phase structure of a vortex beam scrambled by a random scattering medium. In the proposed technique, the vortex beam with an arbitrary topological charge coaxially enters into the scattering medium with another nonvortex beam with an orthogonal polarization state. This couples the spatial and polarization modes of the coherent light prior to entering the scattering medium. Correlation of the orthogonal polarization states of a random field encodes the signature of the twisted mode of the vortex beam. Recovery of the complex polarization correlation functions and hence twisted modes of the beam are retrieved from the Stokes parameters of a randomly scattered field. Two-point correlations of the Stokes parameters form a 4 × 4 matrix with a total of 16 elements. Out of these 16 elements, only four elements of the matrix are used to retrieve real and imaginary parts of the complex polarization correlation function and are subsequently applied in the reconstruction of twisted wavefronts. A complete theoretical basis is developed to retrieve the twisted wavefront of propagating light through random scattering media and is also supported by numerical simulation and experimental demonstration. As an application of the proposed technique, recovery of the complete phase maps of the different vortex beams from the random light is experimentally demonstrated and the twisted modes of the incident light are quantitatively analyzed using orthogonal projections. The experimental results are in good agreement with the theoretical basis and numerical results.

• Received 12 February 2021
• Accepted 12 July 2021

DOI:https://doi.org/10.1103/PhysRevA.104.013525