Measurement of coherence-polarization matrix from a single-frame recording

Abstract

Characterization of statistical properties of a vector source requires fast and efficient measurement of all four elements of the square coherence-polarization (BCP) matrix. Here, we report a new experimental technique for measuring the BCP matrix of the stochastic field using a single-intensity recording. A detailed theoretical framework is presented to measure the elements of the BCP matrix of vector source through polarization correlation of the first two Stokes parameters (SPs), S₀ and S₁. We validate our technique through numerical simulations followed by proof-of-principle experiments. Experimental demonstration is performed by employing a specially designed folded interferometer to coherently sum a vector random field with a known reference and subsequently leverage a tuneable beam displacer to capture the orthogonal polarization components to determine the first two SPs in a single-frame recording. A correlation of these two SPs and their Fourier processing enables the extraction of all four elements of the BCP matrix from a single-intensity recording. The viability of our experimental technique is demonstrated by measuring all four elements of the BCP matrix for three different vector sources in the far-field. A good agreement between simulation and experimental results confirms the accuracy of the proposed technique. This method will find applications in the characterization of light fields, evaluating the polarization dynamics, looking through randomness, etc.