A partially coherent off-axis double vortex beam (PCOADVB) composed of two off-axis vortices is theoretically presented. The analytical equations of a PCOADVB in oceanic turbulence are presented, and the intensity profiles and the number of coherence vortices of the PCOADVBs are investigated based on the derived expressions. The numerical results show that the intensity profiles of PCOADVBs are determined by the initial topological charges $M_1$ and $M_2$ and the positions of the off-axis vortices $\left(x_{1d},y_{1d}\right)$ and $\left(x_{2d},y_{2d}\right)$. The intensity profiles of PCOADVBs will lose the off-axis ring intensity profile and acquire a Gaussian-like profile as $z$ increases, and stronger oceanic turbulence and a smaller $\sigma$ can help the PCOADVB evolve into a spot with a Gaussian-like profile faster on propagation. The number of coherence vortices of a PCOADVB in oceanic turbulence will increase on propagation. The PCOADVB may have potential applications in underwater laser sensing and wireless communications.

In this paper, rectangular multi-Gaussian Schell-model (MGSM) array beams, which consists N×D beams in rectangular symmetry, are first introduced. The analytical expressions of MGSM array beams propagating through free space and non-Kolmogorov turbulence are derived. The propagation properties, such as normalized average intensity and effective beam sizes of MGSM array beams are investigated and analyzed. It is found that the propagation properties of MGSM array beams depend on the parameters of the MGSM source and turbulence. It can also be seen that the beam size of Gaussian beams translated by MGSM array beams will become larger as the total number of terms, M, increases or coherence length, $\sigma$ , decreases, and the beam in stronger non-Kolmogorov turbulence (larger $\alpha$ and $l_0$ , or smaller $L_0$ ) will also have a larger beam size.

The theoretical descriptions for a radial phase-locked multi-Gaussian Schell-model vortex (RPLMGSMV) beam array is first given. The normalized intensity and coherence distributions of a RPLMGSMV beam array propagating in free space and atmospheric turbulence are illustrated and analyzed. The results show that a RPLMGSMV beam array with larger total number N or smaller coherence length $\sigma$ can evolve into a beam with better flatness when the beam array translating into the flat-topped profile at longer distance z and the flatness of the flat-topped intensity distribution can be destroyed by the atmospheric turbulence at longer distance z. The coherence distribution of a RPLMGSMV beam array in atmospheric turbulence at the longer distance will have Gaussian distribution. The research results will be useful in free space optical communication using a RPLMGSMV beam array.

The influence of a high-intensity laser field on the Coulomb explosion and stopping power for a swift C${}_{60}$ cluster ion in a plasma target is studied by means of the molecular dynamics method based on the linearized Vlasov-Poisson theory. In the presence of the laser field, the general expressions for the induced potential in the target among the ions within the cluster are derived. Based on the numerical solution of the equations of motion for the constituent ions, the Coulomb explosion patterns and the cluster's stopping power are discussed for a range of laser and plasma parameters. Numerical results show that the laser field affects the correlation between the ions and contributes to weakening the wake effect and the stopping power as compared to the laser-free case. On the other hand, the vicinage effects in the cluster Coulomb explosion dynamics and the stopping power are strongly affected by the variations in the laser parameters, cluster speed, and plasma parameters. For example, Coulomb explosions are found to be hindered in the longitudinal expansion with the increasing of laser intensity and laser angle, and the Coulomb explosions proceed faster for lower plasma densities and higher electron temperatures.