We investigate the focusing properties of cylindrical vector beams (CVBs) generated from the combination of an array of beams, each with sub-apertures and controllable polarization. The analytical expression of the tight focusing field of the combined CVBs has been derived based on the Richard-Wolf vector diffraction integral. To obtain a desired focal spot size which includes efficient sidelobe suppression, the required parameters, such as the exit sub-aperture, numerical aperture and truncation parameter, have been studied in detail. The result shows that the combined CVB distribution has a good match with the theoretical ideal CVB distribution. However, compared with the ideal CVBs, the focal spot width produced by the combined radially polarized beams is smaller. With the increase of initial polarization rotation of sub-aperture, the focal spot width increases, and the focal shape shifts from Gaussian-like to a flat-topped distribution and then to an annular distribution. Furthermore, flexible focal field tailoring can also be realized by adjusting the initial polarization rotation of each sub-aperture. These results might provide a valuable reference for material processing, microlithography and multi-particle manipulation.

The effects of the jet engine turbulence on a Gaussian Schell-Model (GSM) beam array propagating in a jet engine plume are studied theoretically. The analytical expressions of the cross-spectral density (CSD) function, the spectral degree of coherence (DOC) and the mean-squared beam width for a GSM beam array propagating through a jet engine plume region are derived based on the extended Huyens-Fresnel integral. It is found that the profile of intensity and the DOC of a GSM beam array gradually transfer to an elliptical shape as the propagation distance increases, and the elliptical degree becomes greater with increasing source coherence length. Besides, as the source coherence length decreases, the effect of the jet engine turbulence on the beam broadening is smaller and the profile of the DOC appears sidelobes at short distance. It is also found that the values of effective coherence width nearly remain the same for different values of source coherence length after propagating a certain distance. Furthermore, the effects of the number of beamlets on the beam width and effective coherence width are investigated in detail.

Since optical vortices carrying orbital angular momentum (OAM) were proved by L. Allen in 1992,¹ it has aroused great interest in the study of structured light. Due to the novel properties of OAM modes, such as orthogonality between different modes and infinite topological charges, it provides potential application prospects for free-space optical communication (FSOC).^2,3 Exceeding the capabilities of traditional multiplexing, such as time, wavelengths, frequency, and polarization,^4,5 OAM modes possess the potential to provide a new degree of freedom for multiplexing data transmission.

Phase locking of laser arrays is of fundamental importance for the flexible generation of free-space structured light, particularly in scenarios requiring high-power output and rapid switching. However, conventional supervised learning approaches encounter two critical limitations: the prohibitive cost of obtaining phase labels in real-world systems and the performance degradation attributed to the domain gap between simulated and real data. To address these challenges, we introduce an unsupervised learning framework that integrates a physical model to eliminate arduous and time-consuming labeling work. This framework features an elegantly designed incremental training strategy, which leverages unlabeled data collected from actual setups, achieving an impressive 94% improvement in dynamic phase locking for a 397-channel laser array. Experimental evaluations demonstrate that our method outperforms existing techniques, significantly boosting resilience against sensor noise and optical aberrations. Across diverse large-scale laser array configurations, we further validate the advantages of the proposed method through three applications: coherent beam combining, structured light generation, and free-space optical communication, highlighting its broad applicability and practical significance.

We theoretically propose and experimentally demonstrate a flexible approach to generate an arbitrary shape-invariant structured array beam during propagation with the prescribed intensity distribution. An algorithm for generating flexible desired phase is presented according the reverse engineering and Huygens–Fresnel theory. In this paper, we outline the theory for creating the shape-invariant array beams. The numerical simulation results show that the shape of generated array beams is invariant and its size increases gradually from the near field to the far field. The generation of shape-invariant structured array beams can be realized by the phase-only and amplitude-only elements encoded on the spatial light modulators. The generated arbitrary shape-invariant structured array beams are verified and are in excellent agreement with the theory.

Cylindrical vector beams (CVBs) with unique spatial polarization states have attracted great interest in recent years. However, the generation of high-power CVBs faces a significant challenge due to the limited output power of a single laser. Here, we capitalize on the brightness enhancement offered by coherent beam combining (CBC) technique and propose an architecture for generating arbitrary CVBs based on a CBC system. The phase noise is effectively compensated using an all-fiber internal phase-locking technique. By designing the polarization direction of each beamlet in the laser array, the desired mode of CVB can be generated. This work could provide a reference for generating high-power CVBs.