Average intensity of radial phased-locked partially coherent standard Hermite-Gaussian beam in oceanic turbulence

A model to describe laser array called the radial phased-locked partially coherent standard Hermite-Gaussian (PCSHG) beam has been introduced. Based on the extended Huygens-Fresnel principle, the cross-spectral density function of a radial phased-locked PCSHG beam propagating in oceanic turbulence has been derived, and the average intensity properties are numerically calculated and analyzed in detail. The results show that the beam with smaller radius R or smaller coherence length σ will become flat-topped beam and Gaussian beam faster, and the beam propagating in stronger oceanic turbulence will lose the array distribution and become flat-topped beam and Gaussian beam more quickly. This research is useful to the practical application of the radial phased-locked PCSHG beam in underwater oceanic turbulence.