Underwater Propagation of Vortex Beams Based on Monte Carlo Method

Objective With the exploitation of marine resources and the rapid development of underwater detection and communication, underwater wireless optical communication (UWOC) has become a research hotspot due to its high bandwidth and low latency. However, the underwater environment is complex and variable, and the performance of UWOC is limited by various factors: suspended particles cause strong scattering (multipath propagation, delay extension), the absorption effect rapidly attenuates the optical signal energy, and the ocean turbulence caused by temperature/salinity changes and current disturbances further aggravates the signal fluctuations. These factors lead to an increase in the communication bit error rate, which affects the reliability of the system. In UWOC, vortex beams [e. g., Laguerre-Gaussian beams (LGBs)] show significant advantages in anti-scattering, which can effectively reduce signal attenuation and optical field distortion caused by suspended particles in seawater. In order to accurately evaluate the potential of vortex beams for underwater wireless optical communications, it is crucial to construct a transmission model of vortex beams in a real water environment. However, most of the existing Monte Carlo methods only focus on particle scattering effects or simplified turbulence effects, which makes it difficult to accurately evaluate the beam transmission characteristics in complex water environments. To this end, a semi-analytical electric field Monte Carlo method is proposed in this paper to establish a more accurate underwater transmission model of vortex beams by considering the combined effects of suspended particle scattering and turbulence perturbation. Methods In this study, a semi-analytical electric field Monte Carlo method is proposed. The method combines rigorous vector diffraction theory with generalized Lorentz Mie theory (GLMT) for in-depth modeling. Specifically, the method divides the input vortex beam into multiple photon packets carrying amplitude and phase information, emitting them sequentially into a complex underwater channel. The propagation paths and phase changes of the photon packets are tracked during the simulation. For particle scattering, the interaction between the vortex beam and suspended ocean particles is calculated using GLMT, accounting for the effects of particle size and concentration on scattering. For turbulence effects, the ocean turbulence power spectrum is used to calculate the turbulence-induced attenuation as well as a scattering phase function to characterize the turbulence-induced changes in the direction of beam propagation. The method calculates the sum of the particle-induced extinction coefficient and the turbulence-induced attenuation coefficient as the total attenuation coefficient, and determines the type of scattering event (particle scattering or turbulent scattering) by probabilistic comparison and random sampling. During photon transmission, the survival probability of the photon is updated based on the energy loss, and the probability of the photon reaching the receiver after each scattering event is calculated. By traversing all photons and obtaining the final statistics, the analytical reception of photon packets in the channel is achieved, which greatly improves the computational efficiency. Results and Discussions Simulation and experimental results based on the proposed method show that the LGB has stronger penetration and scattering resistance in turbid water compared to the Gaussian beam (GB). When the attenuation length (AL) increases and multiple scattering transport gradually dominates, the intensity rise rate of LGB increases with the topological charge. At an AL of 10, the intensity uprate of the LGB is 1.20, 1.33 and 1.70 for topological charges L=8, 16 and 24, respectively [Fig. 6(a)]. Regarding the effect of turbulence, the simulation results show that the light intensity attenuation caused by turbulence is affected by the concentration of suspended particles. The effect of turbulence on light intensity attenuation is more significant at lower particle concentrations (smaller AL). For example, at an AL of 1, the energy attenuation of GB due to strong turbulence is about 3.93 dB; when the particle concentration increases (AL increases), the effect of turbulence on the attenuation of light intensity decreases significantly. At an AL of 10, the energy attenuation of GB by strong turbulence is only about 0.44 dB [Fig. 6(b) ‒ (d)]. The experimental results are in agreement with the simulation results. In the flume experiment, the AL value is varied by adjusting the concentration of magnesium hydroxide powder and hot water is injected with a pump to simulate turbulence, and the results show that LGBs with high topological charge have higher intensity uprate in high turbidity water. At an AL of 9.9, the intensity uprate of LGBs with topological charges L=8, 16 and 24 is 1.16, 1.31 and 1.61, respectively [Fig. 8(a)]. Then the turbulence-induced attenuation is investigated under different attenuation lengths. The experimental results are consistent with the simulation results, showing that this attenuation is greater at lower AL and decreases as the AL increases [Fig. 8(b)‒(d)]. Finally, we conduct probing experiments, and the results show that LGBs with larger topological charges exhibit performance advantages over GBs. As the AL increases, the difference in transmission characteristics between LGB and GB grows. This trend is consistent with the previous experimental results. Conclusions During underwater transmission, lasers are subjected to a combination of factors such as absorption by particles, scattering, and turbulence, leading to unfavorable effects such as energy attenuation and scintillation, which seriously affect the transmission performance. Compared with GB, LGB shows better underwater transmission capabilities. In order to quantify the transmission performance of LGB in underwater complex environments, this paper proposes an electric-field Monte Carlo-based model, which combines the GLMT and the ocean refractive index power spectrum to analyze the scattering characteristics of GB and LGB under the combined effect of particle scattering and turbulence. With this model, the effects of different attenuation lengths and turbulence intensity on the transmission of underwater vortex laser beams can be analyzed. The simulation and experimental results show: when the attenuation length is small, the photon transmission is mainly dominated by the ballistic form, where the intensity enhancement of the LGB is small, and the intensity loss difference between the GB and the LGB is not significant; while when the attenuation length increases, the multiple scattering effect gradually takes the dominant position, significantly raising the intensity enhancement of the LGB and enlarging the loss difference between the GB and the LGB. In addition, at low attenuation length, the light intensity attenuation caused by turbulence is more significant; while under high attenuation length, the particle concentration becomes the main influencing factor, and the light intensity attenuation caused by turbulence is relatively weaker. The experimental validation and simulation results show that the two are in good agreement, thus confirming the effectiveness of the proposed semi-analytical electric field Monte Carlo method. The method is able to accurately identify the specific effects of scattered particles and turbulence on the LGB long-range propagation performance. The results show that the LGB is expected to realize a more stable transmission over longer distances compared to the GB in application scenarios such as ocean remote sensing and underwater communication.