Based on the generalized Huygens–Fresnel principle, propagation characteristics of a linear phase-locked hollow beam (PLHB) array propagating through atmospheric turbulence are investigated. Analytical expressions of the average intensity and mean-squared beam width of the PLHB array are derived. It is shown that propagation properties of a PLHB array are related to the initial beam parameters (i.e., number of beamlets, size of beam waist, range of wavelength) of the PLHB array and the strength of turbulence. These findings may provide potential applications in free-space optical communications, lidar, remote sensing, and related fields.

When a high-power laser beam propagates in an absorbing medium, the thermal blooming effect cause the phase distortion of the beam, which will seriously affect the beam quality. In this paper, with the help of the laser propagation theory and thermo-optic coefficient experiment, the phase change of Gaussian beam propagating in various concentrations of ink-ethanol is investigated. The result shows that the phase change is proportional to the input power, which may provide the theoretical and experimental basis for phase compensation, and have potential applications in the adaptive optics, underwater optical communications, biological tissue imaging and other related field.