Anisotropic Oceanic Turbulence Research Articles

Performance analysis of Sinh and Cosh Gaussian vortex beam in vertical underwater optical communication

The performance analysis of Sinh Gaussian vortex beam (ShGvB) and Cosh Gaussian vortex beam (ChGvB) in oceanic turbulence is established by employing an anisotropic spatial power spectrum that considers the influence of the ocean depth to mimic the actual oceanic conditions. Since the salinity and temperature variations along depth are not linear, the actual data of temperature and salinity measured from the tropical region of the ocean is used for the current study. The propagation properties of the ShGvB are studied by deriving the cross-spectral density of the beam, and the average intensity of the beam is plotted over depth and studied in both isotropic and anisotropic oceanic turbulence systems. The analysis of the beam spot radius shows that the beam degrades faster in anisotropic media than in isotropic media. Quantitative estimation of the detection probability, channel capacity and bit error rate (BER) have been made to evaluate the beam's performance for vertical underwater optical communication. The BER may be improved by enlarging the detector aperture radius and signal-to-noise ratio. The ShGvB performs effectively in vertical underwater optical communication compared to the ChGvB.

Scintillation index for the optical wave in the vertical oceanic link with anisotropic tilt angle.

The influence of the ocean depth and anisotropic tilt angle on vertical underwater wireless optical communication (UWOC) systems is considered in this study. We propose a power spectrum model of oceanic turbulence with an anisotropic tilt angle for the first time. Thereafter, the expression of the scintillation index is derived for a spherical wave propagating over anisotropic oceanic turbulence in the vertical link. In addition, considering the temperature and salinity, relevant data of the Atlantic and Pacific oceans at different depths are selected to study further the effect of ocean depth on the scintillation index. The results indicate that the scintillation index strongly depends on the ocean depth and anisotropic tilt angle. Moreover, the scintillation index is also related to other parameters, such as temperature and salinity, kinematic viscosity, the anisotropic factor, optical wavelength, and propagation distance. The presented results can be beneficial in designing optical wireless communication systems in the ocean environment.

Scintillation Index for Spherical Wave Propagation in Anisotropic Weak Oceanic Turbulence with Aperture Averaging under the Effect of Inner Scale and Outer Scale

Due to the advantages of high transmission rate, lower power consumption, high security, etc., underwater wireless optical communication (UWOC) has been widely studied and considered as a potential technique for underwater communication. However, its performance is severely degraded by oceanic turbulence due to refractive index fluctuations, which is caused by the change of inhomogeneous ocean environment. Within our derived spatial power spectrum model under anisotropic oceanic turbulence, we conducted a detailed investigation for a spherical wave propagating in weak anisotropic turbulence in this paper. Based on the derived oceanic spectrum, we proposed a scintillation index model for spherical wave in anisotropic oceanic turbulence considering the aperture averaging effect at non-zero inner scale and limited outer scale. Besides, we analyze the aperture averaging scintillation index under the influence of channel parameters such as inner and outer scales. Simulation results reveal that the scintillation index increases with the increase of the outer scale, while the inner scale induces an opposite trend on the scintillation index. Moreover, the inner scale exhibits a larger impact than the outer scale on the UWOC system over weak oceanic turbulence.

Research on the influence of anisotropic ocean on the capacity of vortex Hankel–Bessel beam

Vortex optical communication is a method to improve the spectral efficiency of underwater wireless optical communication. However, facing the complex marine environment, the turbulence effect in the offshore area is a big challenge to vortex optical communication. Oceanic turbulence will influence the transmission performance of the vortex beam. After turbulent transmission, crosstalk will inevitably occur between different topological modes. This paper studies the degree of crosstalk of Hankel–Bessel (HB) vortex light in different oceanic turbulences. By establishing a mathematical model of anisotropic oceanic turbulence, the main focus is on average temperature dissipation rate, turbulent energy dissipation rate, and temperature-salinity balance parameters. The influence of different turbulence parameters on the propagation of HB vortex light is discussed, and the degree of influence of the above parameters on the channel capacity of the orbital angular momentum HB (OAM-HB) optical communication system is studied. Simulation experiments show that anisotropic oceanic turbulence will cause energy migration in different topological models and cause significant decreases in channel capacity. We observed the capacity of HB vortex beams and compared the communication effects of Laguerre–Gaussian and HB vortex beams in anisotropic ocean turbulence. The communication performance of OAM-HB light in anisotropic turbulent is better than that in an isotropic one. The research results of the transmission characteristics of the vortex HB light underwater show that the OAM-HB underwater communication is worthy of further study.

Effect of oceanic turbulence with anisotropy on the propagation of multi-sinc Schell-model beams

Using the extended Huygens-Fresnel principle, the expressions for the cross-spectral density function of both the circular and square multi-sinc Schell-model (MSSM) beams propagating in an anisotropic oceanic turbulent medium have been derived respectively. Based on the expression, the effects of the oceanic turbulence parameters and the anisotropic factor on the intensity and coherence properties of such beams are explored explicitly. By comparative analysis with the case in free space, it is shown that the adjustable multi-ring and square lattice intensity structures of the MSSM beam in ocean are shaped to be circular flat-topped, square flat-topped or Gaussian-like due to different strength of turbulence. The unique intensity patterns can be maintained for a relatively long propagation distance as the anisotropic factor increases. Furthermore, it is found that the turbulent parameters including the salinity and temperature contribution factor, rate of dissipation of turbulent kinetic energy and rate of dissipation of the mean squared temperature have less impacts on the propagation behaviors of the MSSM beam in anisotropic oceanic turbulence in comparison to the corresponding isotropic case. The results presented here have potential applications in oceanic optical telecommunication links.

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

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.

Multi-Gaussian correlated Hankel-Bessel beam properties in anisotropic oceanic turbulence.

We introduce the model of a multi-Gaussian correlated Hankel-Bessel (MGCHB) beam generated by a multi-Gaussian Shell-model source and investigate the properties of the beam in anisotropic oceanic turbulence. Under Rytov approximation, the detection probability of the MGCHB beam and the channel capacity with MGCHB beams are derived; both the influence of oceanic turbulence and initial beam parameters on them are discussed by numerical simulations. The results show that the increase of the dissipation rate of kinetic energy per unit mass of fluid, the anisotropic coefficient, and the inner scale factor, as well as the decrease of the dissipation rate of mean-squared temperature and the temperature-salinity contribution ratio, can significantly improve the detection probability and the channel capacity. The results also indicate that the MGCHB beam is a better candidate than an Airy vortex beam for mitigating the influence of oceanic turbulence. Furthermore, smaller topological charge and larger orbital angular momentum modes number are beneficial to improve the detection probability and channel capacity, respectively. Moreover, the performance of the MGCHB beam with longer wavelength, smaller beam index, and larger transverse coherence width is conducive to enhancing the transmission quality through oceanic turbulence.

Propagation characteristics of autofocusing Airy beam with power exponential phase vortex in weak anisotropic oceanic turbulence

In the paper, we present the analytical expression of propagation characteristics of the autofocusing Airy beam (AAB) with power-exponent-phase beam carrying orbital angular momentum (OAM) mode (named AAB-PEPV), in weak anisotropic oceanic turbulence. We discuss the influence of the weak oceanic turbulence on the detection probability of the AAB-PEPV beams with different power phases and wavelengths. The results show that the AAB-PEPV beam has a higher detection probability when the anisotropic ocean turbulence has a larger unit mass fluid dynamic energy dissipation rate, a larger internal ratio factor and a higher anisotropy factor. At the same time, the detection probability decreases with the temperature change dissipation rate, the temperature and salinity contribution to the refractive index spectrum. Additionally, for a larger power exponential phase and a longer wavelength, the AAB-PEPV beam has a better anti-interference performance in the underwater channel.

Propagation characteristics of the perfect vortex beam in anisotropic oceanic turbulence.

The propagation model of orbital angular momentum (OAM) modes carried by the perfect vortex (pv) beam through anisotropic oceanic turbulence links is established and the factors influencing the OAM propagation are discussed. The findings show that the self-focusing property of pv beams is beneficial to the propagation of OAM modes: a smaller topological charge, a smaller initial radius, and an optimized half-ring width can alleviate degrading effects of turbulence on the pv beam. Additionally, the pv beam with a longer wavelength is more resistant to turbulent interference. The oceanic conditions with a higher dissipation rate of kinetic energy per unit mass of seawater, larger values of anisotropy and inner-scale factor, a smaller temperature-salinity contribution ratio, or a lower mean-squared temperature dissipation rate can improve the signal mode detection probability. The results are expected to further optimize the design of OAM-based underwater wireless communication systems.

Outage probability and channel capacity of an optical spherical wave propagating through anisotropic weak-to-strong oceanic turbulence with Málaga distribution.

The influence of anisotropic weak-to-strong oceanic turbulence on the performance of underwater optical communication (UWOC) systems is investigated in this paper. The Málaga distribution fading model is used to model the statistical distribution of a spherical wave propagating through anisotropic oceanic turbulence, which is a versatile model of weak-to-strong turbulence. First, the scintillation index for a spherical wave propagating in oceanic turbulence is formulated, and closed-form expressions for the outage probability and average channel capacity of the UWOC systems are then proposed in terms of Meijer's G function. The simulation results demonstrate that both the outage probability and the average channel capacity strongly depend on the parameters of oceanic turbulence, such as the ratio of temperature to the contribution of salinity to the refractive index spectrum, the rate of dissipation of kinetic energy per unit mass of fluid, and the rate of dissipation of mean-squared temperature; they are also related to system parameters such as wavelength and aperture diameter. Numerical results are provided to verify the accuracy of our proposed expressions for outage probability and average channel capacity, and perfect agreement is observed.

Statistical properties of twisted Gaussian Schell-model array beams in anisotropic ocean

The effect of anisotropic oceanic turbulence on propagation characteristics of twist Gaussian Schell-model array beams is investigated. The analytical expression for the cross-spectral density function of such beam propagating through turbulent ocean is derived and used to explore the evolution behavior of the spectral intensity and the degree of coherence. An example illustrates the fact that, the most important oceanic effect is destroying the far zone lattice-like beam profile, and the beam shape eventually converges into Gaussian profile. Besides, after passing through the turbulence at sufficiently large distances from the source, the twist phase modulation of the second-order statistical properties is shown to be suppressed by the turbulence fluctuation, the spectral intensity evolves in the same way with different twist strength, and so is the case for the degree of coherence. The impacts, which arise from the source coherence and the turbulence parameters on beam characteristics are analyzed in detail.

SNR advantage of anisotropy in oceanic optical wireless communications links.

Signal-to-noise ratio (SNR) of an optical wireless communication (OWC) link that operates in anisotropic oceanic turbulence is evaluated. To find the SNR advantage of the anisotropy in the oceanic turbulent medium, SNR in anisotropic oceanic turbulence is normalized by the SNR in isotropic oceanic turbulence. The dB values of this normalized SNR are examined versus the oceanic turbulence parameters of the ratio of temperature to salinity contributions to the refractive index spectrum, the rate of dissipation of mean-squared temperature, the rate of dissipation of kinetic energy per unit mass of fluid at various oceanic anisotropic factors, the avalanche multiplication factors, the radii of receiver aperture, link lengths, and detector responsivity values. It is found that as the oceanic turbulence becomes more anisotropic, at any link parameter, the SNR of the OWC link becomes advantageous over the isotropic counterpart.

Anisotropy effect on performance of PPM optical wireless oceanic communication links

The performance, quantified by the bit-error-rate (BER), of M-ary pulse position modulated (PPM) optical wireless oceanic communication (OWOC) link is investigated when such a link operates in anisotropic weak oceanic turbulence. For this purpose, formulations of the average received power and the scintillation index of collimated Gaussian optical beam detected by a point detector are developed for anisotropic weak oceanic turbulence, which in turn are employed in the BER expression of the PPM OWOC links. BER is evaluated under various turbulence parameters of anisotropic oceanic turbulence, M of M-ary PPM, data bit rate, average current gain of avalanche photodiode (APD). For any investigated parameter, it is found that the BER performance of M-ary PPM OWOC links is improved as the ocean becomes more anisotropic.

Structure parameter of anisotropic atmospheric turbulence expressed in terms of anisotropic factors and oceanic turbulence parameters.

The structure parameter of the anisotropic atmospheric turbulence is expressed in terms of atmospheric, oceanic anisotropic factors in x and y directions, and the oceanic turbulence parameters, which are the wavelength, the link length, the ratio of temperature to salinity contributions to the refractive index spectrum, the rate of dissipation of mean-squared temperature, and the rate of dissipation of kinetic energy per unit mass of fluid. For the purpose of expressing the structure parameter of the anisotropic atmospheric turbulence in terms of atmospheric, oceanic anisotropic factors and the oceanic turbulence parameters, the spherical wave scintillation indices that are found in weak anisotropic atmospheric turbulence and in weak oceanic turbulence are equated to each other. We aim to utilize the structure parameter expressed in this paper in the evaluations of various physical entities such as the average intensity, scintillation index, and beam spread in anisotropic oceanic turbulence by exploiting the existing solutions for the same physical entities in anisotropic atmospheric turbulence. Use of this structure parameter will help us to obtain the anisotropic oceanic turbulence results easily because such results will be found by just inserting the structure parameter expressed in this paper to the already reported corresponding results of anisotropic atmospheric turbulence.

Influence of anisotropic turbulence on the Second-order statistics of a general-type partially coherent beam in the ocean

We investigate detailedly evolution properties of the angular spread and propagation factor (M2-factor) of a general-type partially coherent beam with Schell-model correlator in anisotropic oceanic turbulence. According to the extended Huygens–Fresnel principle, analytical expressions for the second-order moments of Wigner distribution function (WDF) in anisotropic oceanic turbulence are derived. In order to measure the resistance of a general partially coherent beam to effects of anisotropic oceanic turbulence, we introduce deviation percentage of the normalized angular spread and M2-factor respectively between the general-type partially coherent beam and conventional Gaussian Schell-model (GSM) beam. Numerical results show that influence of anisotropy on the angular spread and M2-factor is less for a general-type partially coherent beam than a conventional GSM beam in oceanic turbulence. Besides, the initial beam parameters have a significant effect on the angular spread and M2-factor of a general-type partially coherent beam. Our results may be useful for underwater communication.

Effects of anisotropic oceanic turbulence on the power of the bandwidth-limited OAM mode of partially coherent modified Bessel correlated vortex beams.

We study the impacts of anisotropic turbulence on the bandwidth-limited orbital angular momentum (OAM) mode of partially coherent modified Bessel correlated beam propagation in oceanic turbulence. In a paraxial link, a power model of the bandwidth-limited OAM mode is established. We find that small-scale eddies of turbulence are an important factor that affects the power of the bandwidth-limited OAM mode transfer in a region of strong salinity fluctuation. By choosing the mode carrying lower OAM quantum number, we can transfer OAM information more efficiently, and by utilizing OAM modes with large energy level difference between modes, one can achieve multichannel communication.

Effect of anisotropy on the M2-factor and angular spreading of partially coherent Hermite-Gaussian beam propagating in anisotropic oceanic turbulence

Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function (WDF), the analytical expressions for the normalized propagation factor (M2-factor) and normalized angular spreading of partially coherent Hermite-Gaussian (PCHG) beam through anisotropic oceanic turbulence have been derived. Our numerical results show that anisotropic factors have larger effect on the oceanic turbulent intensity T than that of isotropic factors. In addition, the normalized M2-factor and normalized angular spreading of PCHG beam propagating in anisotropic oceanic turbulence apparently increases with the propagation distance, and that of PCHG beam increases slower with smaller anisotropic factorμx, μy or larger beam order m. Besides, we also found that initial beam parameters λ, σ0, w0 and oceanic turbulence parameters ε, w, XT andν have different influence on normalized M2-factor and normalized angular spreading of a PCHG beam propagating in anisotropic oceanic turbulence, which can improve the performance of optical communication in anisotropic oceanic turbulence where a PCHG beam is used.

Influence of oceanic turbulence on propagation of Airy vortex beam carrying orbital angular momentum

With Rytov approximation theory, we derive the analytic expression of detection probability of Airy vortex beam carrying orbital angular momentum (OAM) through an anisotropic weak oceanic turbulence. We investigate the influences of turbulence parameters and beam parameters on the propagation properties of Airy-OAM beam. The numerical simulation results show that the anisotropic oceanic turbulence with a lower dissipation rate of temperature variance, smaller ratio of temperature and salinity contributions to the refractive index spectrum, larger dissipation rate of kinetic energy per unit mass of fluid, bigger inner scale factor, higher anisotropic coefficient causes the larger detection probability of Airy-OAM beam. Moreover, the Airy-OAM beam with a smaller topological charge, larger main ring radius and longer wavelength, has strong resistance to oceanic turbulent interference. Additionally, the detection probability decreases with the increase of receiving aperture size. In comparison with Laguerre-Gaussian-OAM beam, Airy-OAM beam has more anti-interference to turbulence when its topological charge is larger than 5 due to its non-diffraction and self-healing characteristics. The results are useful for underwater optical communication link using Airy-OAM beam.

New model of the fiber coupling efficiency of a partially coherent Gaussian beam in an ocean to fiber link

The fiber coupling efficiency between the turbulent ocean to fiber of a partially coherent Gaussian beam propagating through the weak to strong anisotropic oceanic turbulence is studied. We derive the expression of new model of the fiber coupling efficiency for the partially coherent Gaussian beam. The numerical analyses reveal that larger inner scale and anisotropic factor, weaker oceanic turbulence strength, and smaller temperature-salinity contribution ratio will lead to a higher coupling efficiency; a longer wavelength, an suitable aperture diameter of the coupling lens, an optimum focal length and beam size, and a higher coherent degree will improve the fiber coupling efficiency. Our fiber coupling efficiency is higher than the previous fiber coupling efficiency.

Effects of anisotropic oceanic turbulence on the propagation of the OAM mode of a partially coherent modified Bessel correlated vortex beam

ABSTRACTWe have studied the impacts of anisotropic turbulence on the orbital angular momentum (OAM) mode of a partially coherent modified Bessel correlated vortex beam propagation in an oceanic channel. In the weak turbulence paraxial channel, a new model of the probability density of OAM modes has been established. Effects of specific parameters of the oceanic turbulence on it have been studied, it is shown that there is an optimizing receiving aperture diameter in the specific interval of the ratio of temperature and salinity , which can reduce the effect of on the normalized energy weight of OAM modes and the reception of fluctuation signal. The effect of oceanic turbulence with higher anisotropy on the OAM signal is weaker than the turbulence possessing lower anisotropy. We can choose the mode carrying lower OAM quantum number to transfer information more efficiently, and we can utilize the OAM mode with large energy level difference between modes and so on to reduce mode interference and enhance the information capacity of optical communication links.