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A new power-exponent-phase vortex beam with nonlinear phase winding has shown flexible control freedom compared with conventional vortex beams. In order to further enrich the modulation freedom and expand the ability of self-healing to meet current application requirements, we conducted a detailed study on the characteristics of the Airy transform of the new power-exponent-phase vortex beam. The influences of the Airy function, the power exponent, and the topological charge on normalized intensity and phase distributions are investigated theoretically and experimentally. More importantly, the self-healing properties of the new power-exponent-phase vortex beam with and without the Airy transform are compared. This shows that the new power-exponent-phase vortex beam with the Airy transform exhibits better self-healing ability when obstructed by obstacles. This study has potential applications in optical trapping and free-space optical communication. [ABSTRACT FROM AUTHOR]

Acquiring topological charge in real-time for vortex beams encounters numerous challenges due to the turbulent atmosphere and coherence degradation. We propose an experimental scheme employing the strong detail extraction capability of deep neural networks to recognize the topological charge of partially coherent vortex beams propagating through the turbulent atmosphere and encountering unknown obstacles. Notably, coherence modulation has demonstrated advantages in deep neural network-based recognition. By comparing with high-coherence vortex beams, the deep neural network accurately recognizes topological charges for low-coherence vortex beams using only half of the available dataset. Furthermore, when the turbulent atmosphere and obstacles were considered, the accuracy of low-coherence vortex beams surpassed that of high-coherence vortex beams with equal amounts of training data. Additionally, the encrypted optical communication using partially coherent vortex beams was demonstrated. The coherence parameter significantly enhanced the channel capacity. This study holds potential for applications in free-space optical communication. [ABSTRACT FROM AUTHOR]

Measuring the complete complex correlation matrix of a partially coherent vector beam is extremely important for transmission calculation, encryption, and decryption for free-space optical communication and optical imaging. Based on self-referencing holography, we introduce a simple and efficient setup to measure the complex-valued cross spectral density matrix of a partially coherent vector beam, without any priori assumptions or approximations of the source. To verify the feasibility of our method, 2 × 2 complex-valued cross spectral density components in the matrix function of particularly correlated radially polarized partially coherence beam have been measured. The experimental measurements are in good agreement with the theoretical model. [ABSTRACT FROM AUTHOR]

The analytical nonparaxial propagation formula of an anomalous hollow beam (AHB) with orbital angular momentum (OAM) in free space is derived based on the generalized Raleigh–Sommerfeld diffraction integral. The nonparaxial properties of AHB with OAM such as intensity, phase and OAM density distributions are studied in detail, using the pertinent nonparaxial propagation formula. The comparison between the paraxial and nonparaxial results is also carried out. The results show that the nonparaxial properties of an AHB with OAM are determined by the initial beam parameters, such as beam waist size and topological charge and propagation distance. [ABSTRACT FROM AUTHOR]

Analytical propagation formulae for partially coherent anomalous hollow beams in uniaxial crystals are derived. Paraxial propagation of partially coherent anomalous hollow beams in uniaxial crystals orthogonal to the optical axis is investigated based on the beam propagation equations. The propagation properties of partially coherent anomalous hollow beams in uniaxial crystals and in free space are studied numerically and comparatively. It is found that the propagation properties of partially coherent anomalous hollow beams in uniaxial crystals behave very differently from those in free space and are closely determined by the parameters of the uniaxial crystals and the initial coherence width. The uniaxial crystals provide an effective way for generating astigmatic beams. [ABSTRACT FROM AUTHOR]