Yahong Chen

Higher-order polarization states, arising from the nonseparable coupling between the spatial and polarization degrees of freedom, have important applications in structured-light science. However, when directly carried by fully coherent beams, their spatial polarization distributions are readily distorted by atmospheric turbulence, obstructions, and other propagation disturbances. This review discusses partial-coherence engineering as an alternative strategy for robust polarization-state synthesis. In this approach, a prescribed higher-order polarization state is encoded into the two-point coherence structure of a partially coherent vector source and subsequently reconstructed through propagation. We review the description of higher-order Poincaré-sphere states, their behavior in atmospheric turbulence, and the theoretical foundations of vectorial spatial coherence engineering. We then explain how coherence-to-polarization conversion enables the target state to emerge in the far field, a focal plane, or a prescribed propagation plane and compare representative experimental implementations. Finally, we assess current limitations and outline future directions and potential applications of robust higher-order polarization states. Overall, partial coherence emerges as an active degree of freedom for the robust synthesis and transmission of spatially structured polarization.

Optical skyrmions have recently unlocked topological quasiparticle textures of light, rising in prominence for next-generation ultra-robust information processing. However, to date, their study has been mainly confined to coherent laser fields. Here we extend skyrmions to more general light sources of partially coherent, stochastic optical fields. We define stochastic optical skyrmions and uncover a hidden regime where spatial coherence acts as a primary determinant of topological stability. While environmental randomness typically degrades fully coherent states, we demonstrate that engineered partial coherence provides a self-healing mechanism that preserves topology under extreme turbulence. Moreover, we show that the coherence structure can be actively tailored to trigger on-demand topological phase transitions, such as skyrmion-to-skyrmionium conversion and skyrmion lattice splitting. These findings redefine the boundaries of topological photonics, paving the way for resilient and high-fidelity information platforms that remain operational in general, non-ideal, real-world environments.

Partially coherent vector beams generally undergo depolarization during propagation due to the incoherent superposition of spatial modes with different polarization states. Here we show that deterministic polarization states can, nevertheless, emerge in a partially coherent beam at a prescribed propagation distance. This effect is achieved by encoding mutually uncorrelated off-axis vector modes into a partially coherent and partially polarized source using a fractional Fourier transform optical system. During subsequent free-space propagation, the displaced vector modes evolve into overlapping and synchronized vector beams in a designed plane. As a result, the beam becomes fully polarized while remaining spatially partially coherent. The underlying mechanism is interpreted in terms of the cross-spectral density phase evolution of two orthogonally polarized partially coherent scalar modes that synthesize the partially coherent vector beam. Our results reveal a different route for controlling polarization structures in partially coherent light, with potential applications in optical angular momentum manipulation and optical trapping.

The second-order correlations of two orbital angular momentum (OAM) modes contained in a partially coherent vector light beam exhibit rich polarization-like geometric structures. In this Letter, we present a general method to measure the coherence-OAM-polarization (COAMP) matrix of such a beam, revealing OAM-resolved polarization properties. The principle of our method is thoroughly discussed and validated in the proof-of-principle experiment. The OAM-resolved generalized Stokes parameters and degree of polarization of an electromagnetic Gaussian Schell-model source are retrieved from the measured COAMP matrix and analyzed in detail. Our protocol paves the way for exploiting OAM-resolved polarization properties in optical sensing, imaging, and information processing.

We consider the strength of correlation between two propagating or evanescent, spatially coherent, plane waves, generally expressed in different frames. While for propagating waves the relevant correlation measure is obtained with traditional interferometric means, we demonstrate that for evanescent waves it can be found by employing a novel nanoscattering‐based procedure. We show theoretically and experimentally that the correlation measure remains invariant under unitary polarization changes and intensity scalings of propagating waves, as well as under the creation of evanescent waves in total internal reflection. These results provide new insights into the correlation properties of light fields and have potential applications in optical near‐field detection and sensing.

We analyze the modulation of the spatial coherence of a random, stationary electromagnetic light beam in Young’s two-pinhole interference. We derive a spectral interference law that governs the behavior of the four coherence (two-point) Stokes parameters and elucidates the contributions of spatial coherence and polarization of the incident field on the coherence properties of the superposition wave. We also show that these parameters as well as the degree of electromagnetic coherence generally exhibit spatial modulations that arise either from the nonvanishing coherence or the polarization properties of the fields in the openings. The formalism is demonstrated through a set of examples.

Optical coherence, encompassing both spatial and temporal coherence, describes the correlations among the components of a fluctuating electric field at two or more points in space and time

We present a general yet simple method for generating partially coherent Schell-model beams with controllable non-Gaussian intensity statistics. With our method, the second-order field statistics properties of the generated beams, such as the average intensity distribution and the degree of spatial coherence structure, remain effectively unchanged when the intensity correlations are modulated. The principle of our method is thoroughly analyzed and discussed. Furthermore, we carry out experiments involving a spatial light modulator to synthesize several types of random beams with super-Rayleigh intensity statistics. The average intensity distribution, degree of coherence, and intensity correlation are examined experimentally, demonstrating the validity and feasibility of the proposed method. Our technique can be directly implemented on existing random beam generators for coherence and intensity correlation control and beam shaping simultaneously.

A class of random, stationary, scalar beams with spatially varying correlations called Fractional-order non-uniformly correlated (FNUC) beams is introduced as an extended version of conventional non-uniformly correlated (NUC) beams. The evolution behavior of the coherence and average intensity distribution of the beams during free-space propagation is numerically analyzed in detail by means of the pseudo-mode decomposition and fast Fourier transform algorithm. We demonstrate that the FNUC beams exhibit the peculiar self-focusing properties during propagation and allow control of their focusing ability and focal depth through the newly introduced parameter (fractional-order number) and the radial phase. Furthermore, an experiment involving a programmable spatial light modulator is carried out to generate the FNUC beams with a controllable fractional-order number. The intensity evolution and self-healing properties of the beams are experimentally studied when blocked by an obstacle. The experimental results agree well with the theoretical predictions. The FNUC beams may find potential applications in optical manipulation and beam shaping, offering a new paradigm for designing customizable random sources with tailored propagation dynamics.