Measuring complex correlation matrix of partially coherent vector light via a generalized Hanbury Brown-Twiss experiment

Folded interferometer to measure coherence-polarization matrix

We present and experimentally demonstrate a new, to the best of our knowledge, technique to quantitatively measure coherence-polarization (BCP) matrix with correlations of only two Stokes fluctuations. The BCP matrix is a square matrix with four elements that involves two-point correlations among orthogonal polarization components. A theoretical framework of the technique is developed, and its viability is demonstrated by a proof of principle experiment. Experimental tests and measurement of the elements of the BCP matrix of statistically stationary beams are demonstrated.

Detecting topological index of randomly scattered V-point singularities using Stokes correlations

Topological defects in vector fields constitute polarization singularities that have numerous applications in classical and quantum optics. These beams are inhomogeneously polarized and are shown to self-heal under symmetric amplitude perturbations. Polarization singular beams are characterized using a singularity index that can be detected using Stokes polarimetry or other interferometric and diffraction approaches. However, the information about the singularity index is lost when these beams travel through random scattering media; this results in a spatially fluctuating polarization pattern known as polarization speckle. This paper proposes and experimentally demonstrates a new method to detect the topological index of these randomly scattered V-point singularities using higher-order Stokes correlations in a lensless condition. A detailed theoretical basis is developed, and the performance of the technique is demonstrated by retrieving the signature of polarization singularities with Poincaré-Hopf index |η|=1 and |η|=2. We also demonstrate that by studying the intensity-intensity correlations of the polarization speckle, it is possible to differentiate between different vector beams having the same magnitude as the Poincaré-Hopf index.

Single-shot generalized Hanbury Brown-Twiss experiments using a polarization camera for target intensity reconstruction in scattering media

To see through a random light field in real-time, single-shot generalized Hanbury Brown-Twiss experiments using a polarization camera are proposed. The target intensity distribution is obtained from a complex coherence function which is calculated from auto-correlation and cross correlation functions of phase-shifted speckle intensity distributions. The phase-shifted speckle intensity distributions are simultaneously obtained through a strategy of parallel phase-shifting digital holography. Experimental results show that the proposed method can image a moving object in a random light field using a measured complex coherence function through the van Cittert-Zernike theorem.

Statistical properties of a partially coherent vector beam with controllable spatial coherence, vortex phase, and polarization

We report on a partially coherent radially polarized power-exponent-phase vortex (PC-RP-PEPV) beam with various distributions of intensity, controllable coherence width, vortex phase, and polarization. The statistical properties of the PC-RP-PEPV beam depend on topological charge, power order, polarization states, and coherence width, which differ from those of conventional radially polarized beams. Here, the initial radial polarization state will transform to complex ellipse polarization state during propagation. By modulating the topological charge of the PC-RP-PEPV beam, the intensity structure of the beam can be adjusted from circular to polygonal. Finally, PC-RP-PEPV beams were experimentally generated, and were consistent with numerical simulation results. This work has applications in optical manipulation, optical measurements, and optical information processing.

Optical coherence encryption with structured random light

Information encryption with optical technologies has become increasingly important due to remarkable multidimensional capabilities of light fields. However, the optical encryption protocols proposed to date have been primarily based on the first-order field characteristics, which are strongly affected by interference effects and make the systems become quite unstable during light-matter interaction. Here, we introduce an alternative optical encryption protocol whereby the information is encoded into the second-order spatial coherence distribution of a structured random light beam via a generalized van Cittert-Zernike theorem. We show that the proposed approach has two key advantages over its conventional counterparts. First, the complexity of measuring the spatial coherence distribution of light enhances the encryption protocol security. Second, the relative insensitivity of the second-order statistical characteristics of light to environmental noise makes the protocol robust against the environmental fluctuations, e.g, the atmospheric turbulence. We carry out experiments to demonstrate the feasibility of the coherence-based encryption method with the aid of a fractional Fourier transform. Our results open up a promising avenue for further research into optical encryption in complex environments.