Beam spreading scaling law of a focused Laguerre-Gaussian beam propagating through oceanic turbulence

The numerical simulation of LG beams propagating through oceanic turbulence by the multi-layer phase screen method is credible but time-consuming, whereas the scaling law to predict the beam spreading of LG beams through oceanic turbulence is regarded as an effective and rapid way. Here, by using the oceanic power spectrum and the multi-layer phase screen method, the beam spreading of focused LG beams under different beam and oceanic turbulence parameters is investigated in detail, thus laying a solid foundation for the scaling law. Subsequently, the scaling formula for the beam spreading of focused LG beams through oceanic turbulence is developed. Results indicate that, within the proper parameter range in practical applications, the beam spreading estimated by the scaling law is close to that by numerical simulation, with an error of less than 11%. We hope that the scaling formula can provide an effective reference for the potential applications of LG beams in oceanic environments.