Channel Capacity of Three Vortex Beams in Anisotropic Ocean Turbulence

Objective Due to the high data transmission rate, low energy consumption, and strong anti-interference ability, underwater wireless optical communication has been widely applied to underwater image transmission, underwater video transmission, underwater vehicles, underwater search and rescue, and other fields. As the vortex beams carry orbital angular momentum (OAM) and are orthogonal among different OAM modes, underwater optical communication can be conducted using the vortex beams. On one hand, in the atmospheric turbulent environment, the utilization of perfect vortex (PV) beams is proven to improve the channel capacity of optical communication system compared with Laguerre-Gauss (LG) and Bessel-Gauss (BG) beams. Meanwhile, it is unknown whether the channel capacity is still stronger than LG and BG beams when PV beams are adopted for optical communication in the ocean turbulent environment. On the other hand, most previous studies on the channel capacity of vortex beams in ocean turbulent environments have employed the power spectrum models of Nikishov or Elamassie, but both models are proposed under the assumption of infinite scale outside turbulence, which has certain limitations. Therefore, we explore the channel capacity of PV, LG, and BG beams transmitted in anisotropic ocean turbulence using the recently reported ocean turbulence power spectrum with finite outer scale. Our research is of great significance for implementing optical communication links and selecting light source parameters in the marine environment. Methods According to the Rytov approximation theory, the spatially coherent length of spherical wave propagation under anisotropic ocean turbulence is derived. OAM mode detection probability and channel capacity for PV, LG, and BG beam propagation in anisotropic ocean turbulence are calculated. Additionally, we simulate the channel capacity changes of PV, LG, and BG beams with beam radius, receiving aperture, transmission distance, number of transmitted OAM modes, turbulence inner and outer scales, turbulent energy dissipation rate, temperature variance dissipation rate, anisotropy factor, and temperature salinity contribution ratio. Results and Discussions The numerical simulation results of Fig. 2(a) -(c) show that the beam waist radius is an important factor limiting the channel capacity of PV, LG, and BG beams. When the transmission distance is less than 70 m and other parameters remain unchanged, PV or LG beams with a narrower waist radius (less than 4 mm) can obtain a larger channel capacity than that of BG beam. However, when the beam radius is larger (greater than 12 mm), the channel capacity of PV and LG beams is lower than that of BG beams. In addition, when the PV beam is less than 2 mm, the channel capacity is greater than those of LG and BG beams, and it is better for long-distance transmission. The numerical simulation results of Fig. 2(d) indicate that the channel capacity decreases and stabilizes with the rising receiving aperture. The numerical simulation results of Fig. 3(a) reveal that the channel capacity decreases with the increasing transmission distance. The numerical simulation results of Fig. 3(b) show that the channel capacity rises with the increase in the number of transmitted OAM modes. The numerical simulation results of Fig. 4(a) demonstrate that the channel capacity increases with the growing inner scale of turbulence. The numerical simulation results of Fig. 4(b) show that the channel capacity decreases only by a very low value with the increasing outer scale, and when the outer scale continues to grow, the channel capacity does not decrease and remains at a relatively stable value. The numerical simulation results of Fig. 4(c)-4(d) reveal that the channel capacity increases with the rising turbulent kinetic energy dispersion, and decreases with the increasing temperature variance dissipation rate. The numerical simulation results of Fig. 4(e) show that the channel capacity increases with the rising anisotropy factor, and those of Fig. 4(f) indicate that the channel capacity decreases with the increasing temperature salinity contribution ratio. Conclusions The beam radius has a great influence on the channel capacity of the three beams, and there is an optimal girdle size to make the channel capacity of the three beams peak, and the peak channel capacity of PV beam is greater than those of BG and LG beams. When the transmission distance is from 30 to 70 m, PV and LG beams with a smaller waist radius (less than 4 mm) can obtain a larger channel capacity than that of BG beam. However, the channel capacity of PV and LG beams with a larger waist radius (greater than 12 mm) is significantly lower than that of BG beam. Additionally, when the beam waist radius is less than 2 mm, the channel capacity of PV beam is greater than those of LG and BG beams, which indicates that PV beam with a narrow waist radius (less than 2 mm) can bring greater channel capacity to the communication system. In addition, the channel capacity of the three beams decreases with the increasing temperature variance dissipation rate, temperature salinity contribution ratio, and transmission distance. Meanwhile, it increases with the rising number of transmitted OAM modes, turbulent inner scale, turbulent kinetic energy dissipation rate, and anisotropic factor. Then, it decreases and eventually stabilizes as the aperture diameter of the receiver increases, but is very little affected by the turbulent outer scale.