The beam spreading and evolution behavior of the intensity profile and coherent vortices of partially coherent, four-petal elliptic Gaussian vortex beams propagating in atmospheric turbulence are studied. The analytical expressions for cross-spectral density function, as well as root mean square (rms) beam width, are derived based on the extended Huygens–Fresnel principle. Results showed that, unlike the partially coherent four-petal Gaussian vortex beams, the partially coherent four-petal elliptic Gaussian vortex beam could change its petal number into six. The dependencies of occurrence, appearance, and transition speed from four- to six-petal profile on the topological charge, the beam order, and the ellipticity factor are illustrated. The far field behaviors of partially coherent four-petal elliptic Gaussian vortex beams propagating in atmospheric turbulence and are compared in free space. Beams with larger topological charge, smaller beam order, and larger ellipticity factor were found to be less influenced by atmospheric turbulence. Further, the ellipticity factor can be used as an additional degree of freedom in controlling the conservation distance of coherence vortices’ topological charge.

The multi-perturbation stochastic parallel gradient descent (SPGD) method for adaptive optics is presented in this work. The method is based on a new architecture. The incoming beam with distorted wavefront is split into N sub-beams. Each sub-beam is modulated by a wavefront corrector and its performance metric is measured subsequently. Adaptive system based on the multi-perturbation SPGD can operate in two modes – the fast descent mode and the modal basis updating mode. Control methods of the two operation modes are given. Experiments were carried out to prove the effectiveness of the proposed method. Analysis as well as experimental results showed that the two operation modes of the multi-perturbation SPGD enhance the conventional SPGD in different ways. The fast descent mode provides faster convergence than the conventional SPGD. The modal basis updating mode can optimize the modal basis set for SPGD with global coupling.

To solve the problem of the low diagnosis rate of early weak faults of rolling bearings, a novel bearing fault diagnosis method based on Variational Mode Decomposition (VMD) and convolutional neural network (CNN)−Bidirectional Long Short-Term Memory (BiLSTM) was proposed. Based on the basic Sparrow Search Algorithm, the tent chaotic mapping, the Osprey Optimization Algorithm, and the Cauchy mutation were used to enhance the global search ability of the algorithm. To improve the accuracy of fault diagnosis, the BiLSTM layer is introduced into CNN to preserve the global and local features to the maximum extent. The experimental results show that VMD avoids the end effect problem in Empirical Mode Decomposition (EMD). The accuracy rate of the diagnosis model based on CNN-BILSTM reached 97.6667%, which was higher than that of the common diagnosis model.

Coupled simulation based on intracavity partially coherent light model and 3D CFD model is firstly achieved in this paper. The dynamic equation of partially coherent intracavity field is derived based on partially coherent light theory. A numerical scheme for the coupled simulation as well as a method for computing the intracavity partially coherent field is given. The presented model explains the formation of the sugar scooping phenomenon, and enables studies on the dependence of the spatial mode spectrum on physical parameters of laser cavity and gain medium. Computational results show that as the flow rate of iodine increases, higher order mode components dominate in the partially coherent field. Results obtained by the proposed model are in good agreement with experimental results.

The beam spreading and evolution behavior of a partially coherent, Hermite-cosine-Gaussian (HcosG) rectangular multi-Gaussian correlated Schell-model beam propagating in oceanic turbulence is studied. Analytical expressions for the cross-spectral density function, as well as the root mean square (rms) beam width and the spectral degree of coherence, are derived based on the extended Huygens-Fresnel principle. The HcosG rectangular multi-Gaussian correlated Schell-model beam exhibits a multi-lobe pattern at short propagation distances. The dependencies of the number, size, shape, and centroid of the lobes on displacement parameters, source size, order of field distribution, and displacement are investigated. As the propagation distance increases, the spectral coherence decreases, and the differences between the spectral coherence curves gradually diminish. Additionally, for HcosG rectangular multi-Gaussian correlated Schell-model beams, better propagation performance was found in oceanic turbulence with larger mean square temperature dissipation rate, smaller turbulent kinetic energy dissipation rate per unit mass of fluid, and larger relative strength of temperature and salinity fluctuation.