Propagation Properties of an Off-Axis Hollow Gaussian-Schell Model Vortex Beam in Anisotropic Oceanic Turbulence

Xinguang Wang,Shengmei Zhao,Le Wang

doi:10.3390/jmse9101139

Abstract

Based on the extended Huygens–Fresnel principle and the power spectrum of anisotropic oceanic turbulence, the analytical expressions of the average intensity and coherence properties of an off-axis hollow Gaussian-Schell model (OAHGSM) vortex beam propagating through anisotropic oceanic turbulence were derived. The effects of turbulent ocean and beam characteristic parameters on the evolution properties of the OAHGSM vortex beam were analyzed in detail. Our numerical simulation results showed that the OAHGSM vortex beam with a larger position factor is more focusable. Meanwhile, the OAHGSM vortex beam eventually evolves into a Gaussian-like beam after propagating through the anisotropic oceanic turbulent channel. The speed of this process can be accelerated by the decrease of the hollow order, topological charge, beam width, and transverse coherence width of the beam. The results also indicated that the normalized average intensity spreads more greatly and the spectral degree of coherence decays more rapidly for the smaller dissipation rate of the kinetic energy per unit mass of fluid, the smaller anisotropic coefficient, the smaller inner scale factor, the larger dissipation rate of the mean-squared temperature, and the higher temperature–salinity contribution ratio.

Highlights

The results showed that the decrease of N, M, σ, and ω0 will accelerate the evolution of the off-axis hollow Gaussian-Schell model (OAHGSM) vortex beam into a Gaussian-like profile, which indicates that the beam with smaller N, M, σ, and ω0 is more affected by anisotropic oceanic turbulence
We derived the average intensity and the spectral degree of coherence of an OAHGSM vortex beam propagating through anisotropic oceanic turbulence based on the extended Huygens–Fresnel principle
Our results showed that the focusing distribution of the OAHGSM vortex beam becomes more obvious by increasing the position factor, and the beam gradually loses the initial dark hollow profile and evolves into a Gaussian-like beam due to the disturbance of oceanic turbulence with the increase of the transmission distance

Summary

Introduction

With the rise and development of underwater wireless optical communication and ocean remote sensing and imaging applications, more and more attention has been paid to the optical beams’ properties, such as the degree of coherence, the degree of polarization, the effective beam widths, and the average intensity of various kinds of laser beams propagating through a turbulent ocean environment [1,2,3,4,5,6,7,8,9,10,11]. Due to the significant difference between atmospheric and oceanic turbulence on the propagation of optical waves, together with the increasing demand for underwater wireless optical communication, it is very interesting to investigate the propagation of an OAHGSM vortex beam in the turbulent ocean environment. We derive the analytical formula of the strength of anisotropic oceanic turbulence, analyze the influence of various parameters on the turbulence effect, and derive the analytical formulas for the average intensity, as well as the spectral degree of coherence of the OAHGSM vortex beam. We numerically explore the effect of different beam and turbulent ocean characteristic parameters on the average intensity and the spectral degree of coherence of the OAHGSM vortex beam in detail.

Theoretical Analysis

Numerical Simulations

Discussion

Conclusions