Editorial for the Special Issue “Coherence Properties of Light: From Theory to Applications”

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. Partially coherent light beams occupy an important position between fully coherent and incoherent fields, offering additional degrees of freedom for tailoring light propagation through their statistical properties [1,2,3,4,5,6,7,8,9,10]. Among these features, the twist phase has emerged as a distinctive and powerful characteristic of partially coherent beams. Unlike conventional phase modulation applied to fully coherent beams, the twist phase is embedded in the cross-spectral density and directly influences the statistical structure of the optical field, leading to rich and unconventional propagation behaviors. Beyond twist phase-dominated phenomena, the subsequent contributions of this Special Issue extend coherence control to vectorial, temporal, and application-oriented regimes.

Beams that are partially coherent have a unique twist phase. The effect of the twist phase on the statistical properties of partially coherent beams are studied in contributions 1–4. The authors of contribution 1 study the propagation of a Gaussian Schell-model beam carrying both the twist and cross phases in a turbulent atmosphere. It was found that the twist phase can retard the degeneration of the intensity distribution and spectral degree of coherence of the beam in a turbulent atmosphere. Also, the effect of the twist and cross phases on the distributions of orbital angular momentum flux density was discussed. The authors of contribution 2 investigate the propagation of a twisted electromagnetic elliptical vortex beam through non-Kolmogorov atmospheric turbulence. The results show that the effect of atmospheric turbulence on the beam wander can be effectively reduced by regulating the spatial coherent width and the twist phase of such a beam. In contribution 3, the authors introduce a twisted multi-cosine Gaussian Schell-model beam array, and study the propagation properties of such a beam array in free space. The beam array exhibits a nonuniform lattice profile in the far zone and an unusual rotation behavior, which is due to the twist phase. In contribution 4, the authors develop an algorithm to solve the problem of identifying the conditions under which untwisted bona fide cross-spectral density can be made twistable for Schell-model sources.

In contribution 5, the tight focusing properties of circular partially coherent radially polarized circular Airy vortex beams are discussed. The results show the effect of topological charge on the intensity distribution, spatial coherence, and degree of polarization. Especially, the radial dimension of the dark channel can be easily controlled by adjusting the topological charge. In contribution 6, the full Poincaré polarization state is initially encoded into the spatial coherence structure of the beam source. After propagation of the partially coherent beam, the vectorness reverts to the polarization state, resulting in the re-emergence of the encoded full Poincaré polarization in the output plane.

The authors of contribution 7 introduced the generalized Gaussian and multi-Gaussian Schell-model pulse sources, whose complex degree of temporal coherence is described by a function of the nth power difference of two instants. After propagation in dispersive media, the coherent time and the dispersive coefficient significantly impact the self-focusing and self-shifting behaviors of the beams.

The authors of contribution 8 propose a technique that can improve the spatial resolution of a new optical system with the potential for time-lapse observation of living cellular tissue beyond diffraction, using traditional speckle interferometry-handling methods. In contribution 9, the authors provide a charge transfer mechanism to achieve low-threshold and high-quality random lasers.

In contribution 10, uniform and nonuniform spiral coherent lattices are constructed by manipulating the initial coherence structure. In the source plane, phasesingularities of the complex degree of coherence are discovered, which may be useful for constructing vortex beams without utilizing the vortex phase. The intensity distributions of the beams in the far field are investigated both theoretically and experimentally to show the effect of the initial coherence structure.

In summary, these contributions collectively highlight the versatility of coherence engineering, including spatial, temporal, and polarization-related regimes, which may be used as a powerful tool for controlling light propagation and enabling novel optical functionalities across fundamental studies and practical applications. It is hoped that this Special Issue will serve not only as a synthesis of diverse research directions but also as a catalyst for further exploration and advancement in this exciting field.