Average Channel Capacity of Hypergeometric Gaussian Beams in Absorbing Anisotropic Ocean Turbulence
Objective We aim to investigate the transmission and communication characteristics of the Hypergeometric-Gaussian(HyGG)beam,which exhibits pseudo-nondiffraction,self-focusing,and self-reconstruction characteristics.These properties are expected to enhance the channel capacity of underwater optical communication(UWOC)systems based on orbital angular momentum(OAM).While there is growing interest in the transmission of the HyGG beam through turbulent media,recent research on its performance in underwater channels remains limited.The team led by Shengmei Zhao explores the spiral phase spectrum evolution of the HyGG beam based on the Nikishov oceanic turbulence power spectrum.However,the Nikishov spectrum exhibits a singularity at zero spatial wave number,and the absorption effects of seawater and anisotropic impacts on the transmission of HyGG beam OAM modes have not been adequately addressed.Furthermore,the existing study investigates the OAM detection probability evolution of the HyGG beam only within less than 0.1 times the Rayleigh distance,failing to fully demonstrate its transmission advantages.Thus,it is essential to introduce a new oceanic turbulence power spectrum and conduct theoretical research on the long-distance transmission and communication performance of the HyGG beam in an absorbent and anisotropic oceanic turbulence channel.This research provides a vital reference for designing and improving practical underwater wireless optical communication systems.Methods To further investigate the transmission and communication characteristics of the HyGG beam in underwater channels,we introduce a newly proposed oceanic turbulence power spectrum.We comprehensively consider the effects of seawater absorption and anisotropy.Based on the Rytov turbulence approximation theory and the new oceanic turbulence power spectrum,we derive the analytical expression of the OAM spiral phase spectrum for the HyGG beam under absorptive and anisotropic oceanic turbulence.Subsequently,using the established average channel capacity model,we analyze in detail the influence of the HyGG beam parameters,seawater channel parameters,and communication system parameters on the average channel capacity during long-distance transmission.Results and Discussions The influence of oceanic turbulence leads to an increase in spiral wavefront distortion with increasing transmission distance.The vortex beam with OAM mode number gradually disperses its energy into neighboring OAM modes.After transmitting 200 m,the OAM detection probability of the HyGG beam is approximately 20％higher than that of the Gaussian vortex(GV)beam and 10％higher than that of the Laguerre-Gaussian(LG)beam.This is due to the stronger self-focusing ability of the HyGG beam,which results in smaller beam broadening in oceanic channels and fewer turbulent cells with varying refractive indices.Consequently,the HyGG beam exhibits reduced wavefront distortion and higher purity of OAM signal modes during transmission in oceanic channels(Fig.3).For practical applications,selecting the appropriate p value of the HyGG beam according to different communication distances effectively enhances system performance(Fig.4).The average channel capacity of the HyGG beam decreases with increasing l0,favoring larger p values for higher average channel capacity due to faster divergence of the HyGG beam with larger l0 values(Fig.5).To mitigate the effects of seawater absorption in long-distance UWOC,we recommend the HyGG beam in the 410-490 nm range.Additionally,selecting the appropriate initial waist radius of the HyGG beam according to actual underwater communication distance requirements maximizes average channel capacity(Fig.6).The average channel capacity of the HyGG beam increases with increasing turbulence scale and decreases with increasing outer scale.Furthermore,the channel capacity increases with the anisotropy parameter,benefiting transmission and communication in seawater(Fig.7).The average channel capacity decreases with increasing root mean square temperature dissipation rate xT and temperature-salinity gradient ratio w,and increases with the kinetic energy dissipation rate ε.Higher values of w,Xt,or lower values ofε,increase oceanic turbulence intensity,exacerbating wavefront distortion and deteriorating transmission and communication performance of the HyGG beam in oceanic channels(Fig.8).At 50 m,the average channel capacity of the HyGG beam is nearly independent of the size of the receiving aperture.With increasing transmission distance,the average channel capacity initially increases and then decreases with larger receiving aperture size,stabilizing at Ra=3 mm with a peak value.These phenomena can be explained as follows:1)at shorter transmission distances,optical signal energy attenuation and inter-mode crosstalk are minimal,and the received optical power significantly exceeds system noise power N0,thus channel capacity is primarily determined by OAM signal mode power and crosstalk power,with little influence from varying the receiving aperture size;2)Although reducing the receiving aperture size can enhance OAM detection probability,longer distances and smaller receiving apertures also result in greater power loss.When received optical power approaches N0,average channel capacity is primarily influenced by received optical power(Fig.10).Conclusions We derive analytical expressions for the OAM detection probability and average channel capacity of the HyGG beam in absorptive anisotropic oceanic channels based on the Rytov approximation and generalized Huygens-Fresnel principle.Our analysis covers the intensity distribution of the HyGG beam in turbulence-free channels and extensively studies the influence of source parameters,channel environmental parameters,and communication system parameters on the transmission and communication quality of the HyGG beam.The results indicate that the self-focusing ability of the HyGG beam increases with the hollowness parameter.The influence of oceanic turbulence on the HyGG beam increases with transmission distance,temperature variance dissipation rate,turbulence inner scale,and OAM mode number,while it decreases with kinetic energy dissipation rate,turbulence outer scale,and anisotropy parameter.The system's average channel capacity increases with higher transmit power and OAM channel number.The trend of the communication system error rate is opposite that of average channel capacity.For different communication link lengths,optimal values for HyGG beam wavelength,waist radius,hollowness parameter,and receiving aperture values exist to maximize the system's average channel capacity.Additionally,due to its self-focusing characteristics,the HyGG beam with hollowness parameter p＞0 demonstrates superior transmission and communication performance over LG and GV beams in long-distance transmission.Therefore,The HyGG beam exhibits strong resistance to turbulence and attenuation.
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