Anisotropic non-Kolmogorov Turbulence Research Articles

Propagation characteristics of the vortex beam array through anisotropic non-Kolmogorov maritime atmospheric turbulence

This study employs the power spectrum inversion method to generate the phase screens of atmospheric turbulence over the sea, the theoretical model of the vortex beam array emitted by a focusing system through anisotropic non-Kolmogorov maritime atmospheric turbulence was built. The propagation characteristics of the vortex beam array were investigated theoretically and compared to those of the Gaussian beam array. The results show that the vortex beam array is less affected by turbulence and exhibits stronger resistance to the turbulence. On this basis, using the evaluation parameters including the relative beam width and the beam wander, the influences of various parameters of the vortex beam array and atmospheric turbulence, such as topological charge, beamlet width, number of beamlets, anisotropy factor, and power law, on its propagation characteristics through anisotropic non-Kolmogorov maritime atmospheric turbulence were studied extensively. The results can provide a useful reference for the applications of the vortex beam array in optical communication through the maritime atmosphere.

Performance of HQAM/XQAM Laser Communication System in Anisotropic Non-Kolmogorov Ground–HAP–Satellite Uplink

Satellite laser communication can achieve high-speed, high-precision, and high-security broadband communication without being constrained by the electromagnetic spectrum, which has attracted attention. So, this paper proposes the use of a high-altitude platform (HAP) under anisotropic non-Kolmogorov turbulence to improve the communication performance of the system. Cross quadrature amplitude modulation (XQAM) and hexagon quadrature amplitude modulation (HQAM) are applied to the ground–HAP–satellite (G-H-S) laser communication system. Considering the combined effects of uplink light intensity scintillation, beam wander, and the angle of arrival fluctuation, the G-H-S system’s bit error rate (BER) closure expression is derived under the EW distribution. Simultaneously, the relationship between the G-H-S system’s signal-to-noise ratio (SNR) and BER under different anisotropic factor u values is simulated and compared with the traditional ground–satellite (G-S) system. The results show that the communication performance of the G-H-S system with HQAM modulation is better. In addition, the effects of the zenith angle, receiving aperture, transmitter beam radius, and beam divergence angle on the BER performance of the system are also studied. Finally, the correctness of the analysis results is verified via Monte Carlo simulation. This research will benefit the design and optimization of satellite laser communication systems.

Performance of rectangular QAM/FSO communication systems in the anisotropic non-Kolmogorov ground-to-satellite uplink

Quadrature amplitude modulation (QAM) is an exciting technology to accomplish a high communication data rate without increasing the system bandwidth, which can undoubtedly greatly improve the performance of free-space optical (FSO) communication systems. With the increase of experimental and theoretical results about atmospheric turbulence, scientists have confirmed that the anisotropy and non-Kolmogorov property cannot be ignored for atmospheric turbulence. In this paper, utilizing the new anisotropic non-Kolmogorov (ANK) turbulence spectrum models for the satellite links that are applicable to both vertical and slant links, we derive the average bit error rate (BER) expression of rectangular QAM for a Gaussian-beam transmission through the weak ANK ground-to-satellite uplink under the influences of both scintillation and beam wander. Numerical results display that, when the zenith angle is less than a certain angle, the average BER of the ground-to-satellite uplink decays with the enhancement of the anisotropic factor, but while the zenith angle is greater than the certain angle, the contrary trend will occur. Our work will benefit the design optimization of QAM/FSO communication systems in ANK satellite links.

Performance of a free-space optical communication system employing receive diversity techniques in anisotropic atmospheric non-Kolmogorov turbulence

In this paper, bit error rate (BER) performance of a free-space optical communication (FSOC) system operating in anisotropic non-Kolmogorov weak turbulence is investigated together with the spatial diversity techniques. The spatial diversity techniques are implemented as maximum ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) and applied to the receiver. The propagating beam is the Gaussian beam wave, and the modulation scheme is binary phase-shift keying (BPSK). Results are obtained for various parameters such as the anisotropy factor, non-Kolmogorov power law exponent, photodetector responsivity, equivalent load resistor, electronic bandwidth, Gaussian beam radius, wavelength, propagation distance, and turbulence structure constant. It is found that the spatial diversity technique used at the receiver causes significant improvement in the performance of an FSOC system under the conditions of anisotropic non-Kolmogorov atmospheric turbulence. It is also observed that BER performance improves as the atmospheric turbulence becomes more anisotropic. Among the spatial diversity techniques, SC is inferior to EGC and EGC is inferior to MRC in terms of BER performance.

Backscatter amplification effect in a non-Kolmogorov anisotropic turbulent medium

The paper presents a tool for numerical simulation of the backscatter amplification effect associated with double-pass propagation of laser radiation passing through an anisotropic non-Kolmogorov turbulence. It is shown that for variety of power-law exponents of refractive-index fluctuations, all other conditions being equal, the value of amplification factor also changes: the amplification factor increases when the fluctuation spectrum becomes more and more low-frequency. For the anisotropic medium, the two-dimensional distribution of the amplification factor allows remotely determining the spatial orientation of anisotropic inhomogeneities in a randomly inhomogeneous medium.

Is the Anisotropic Tilt Angle Necessary in the Turbulence Spectrum of Refractive-Index Fluctuations?

With the deepening of atmospheric turbulence research, scientists have discovered that the anisotropy of turbulence cells cannot be ignored. The anisotropic non-Kolmogorov turbulence model is more in line with the actual situation of atmospheric turbulence. However, the recent experimental results of Korotkova et al. and Beason et al. display that the turbulence cell has an anisotropic tilt angle, that is, the long axis of the turbulence cell may not be horizontal to the ground but has a certain angle with the ground. Therefore, it is urgent to analyze whether the anisotropic tilt angle is necessary in the turbulence spectrum. In this study, we develop the anisotropic non-Kolmogorov turbulence spectra for the horizontal and vertical links in the presence of the anisotropic tilt angle. Then, based on these spectra, the analytical expressions of the scintillation index for the horizontal and vertical links are derived under weak fluctuation condition. The results indicate that the anisotropic tilt angle is necessary in the vertical link but not in the horizontal link.

Spatial Property of Optical Wave Propagation through Anisotropic Atmospheric Turbulence

For the free-space optical (FSO) communication system, the spatial coherence of a laser beam is influenced obviously as it propagates through the atmosphere. This loss of spatial coherence limits the degree to which the laser beam is collimated or focused, resulting in a significant decrease in the power level of optical communication and radar systems. In this work, the analytic expressions of wave structure function for plane and spherical wave propagation through anisotropic non-Kolmogorov turbulence in a horizontal path are derived. Moreover, the new expressions for spatial coherence radius are obtained considering different scales of atmospheric turbulence. Using the newly obtained expressions for the spatial coherent radius, the effects of the inner scales and the outer scales of the turbulence, the power law exponent, and the anisotropic factor are analyzed. The analytical simulation results show that the wave structure functions are greatly influenced by the power law exponent α , the anisotropic factor ζ , the turbulence strength σ ~ R 2 , and the turbulence scales. Moreover, the spatial coherence radiuses are also significantly affected by the anisotropic factor ζ and the turbulence strength σ ~ R 2 , while they are gently influenced by the power law exponent α and the inner scales of the optical waves.

Anisotropic Non-Kolmogorov Turbulence Spectrum with Anisotropic Tilt Angle

With the in-depth study of atmospheric turbulence, scholars have identified that the anisotropy of turbulence cells should not be forgotten. The anisotropic non-Kolmogorov turbulence model can better characterize the actual situation of atmospheric turbulence. However, the results of recent experiments by Wang et al. and Beason et al. demonstrate that the turbulence cell has an anisotropic tilt angle, i.e., the long axis of turbulence cell may not be horizontal to the ground but has a certain angle with the ground. In this paper, we derive the anisotropic non-Kolmogorov turbulence spectra for the horizontal and satellite links with anisotropic tilt angle. Then by use of these spectra, the analytical expressions of scintillation index in the horizontal and satellite links are derived for the weak fluctuation condition. The calculation results display that the scintillation index for the horizontal and satellite links vary with the changes of anisotropic tilt angle and azimuth angle. Therefore, the anisotropic tilt angle is indispensable in the horizontal and satellite links.

Probability density function of fiber-coupling efficiency and temporal power spectrum of irradiance fluctuations in the anisotropic non-Kolmogorov satellite-to-ground downlink

As many related experimental and theoretical results are identified, scholars have found that the anisotropy of turbulence cells is indispensable in the atmospheric turbulence. In this paper, based on a new anisotropic non-Kolmogorov turbulence spectrum for the satellite links that is applicable to both vertical and slant links, the probability density function of fiber-coupling efficiency and the temporal power spectrum of irradiance fluctuations for a plane wave propagating through the weak anisotropic non-Kolmogorov satellite-to-ground downlink are developed. The results show that when the zenith angle is greater than a certain angle, the probability density function of fiber-coupling efficiency shifts to the side with smaller coupling efficiency with the rising of anisotropic factor, and the temporal power spectrum of irradiance fluctuations and the absolute value of power exponent at high frequencies increase with the growing of anisotropic factor and power law, but while the zenith angle is less than the certain angle, the opposite trend will appear. It is anticipated that this work will benefit the understanding of laser beam transmission in anisotropic non-Kolmogorov satellite links and provide the theoretical basis for the design and parameter optimization of satellite optical communication systems based on fiber-coupling.

Turbulence spectrum model and fiber-coupling efficiency in the anisotropic non-Kolmogorov satellite-to-ground downlink

Increasing experimental and theoretical results have confirmed that the anisotropy of turbulence cells cannot be ignored in the atmospheric turbulence. The satellite-to-ground downlink is the important part of satellite optical communication network, so the anisotropic non-Kolmogorov turbulence spectrum model for the satellite links needs to be established urgently. However, the previously derived turbulence spectrum model for the satellite links is only applicable to vertical links. In this paper, considering the ellipsoid hypothesis of turbulence cell, we derive a new anisotropic non-Kolmogorov turbulence spectrum for the satellite links that is applicable to both vertical and slant links. Then based on this spectrum, the fiber-coupling efficiency for a Gaussian-beam propagating through the weak-to-strong anisotropic non-Kolmogorov satellite-to-ground downlink is developed. The results show that when the zenith angle is greater than a certain angle, the coupling efficiency decreases with the rising of anisotropic factor, but while the zenith angle is less than the certain angle, the opposite trend will appear. It is anticipated that this work will benefit the understanding of laser beam transmission in the anisotropic non-Kolmogorov satellite links and provide the theoretical basis for the design and parameter optimization of satellite optical communication systems based on fiber-coupling.

Statistical properties of partially coherent vector beams propagating through anisotropic atmospheric turbulence

Statistical properties of partially coherent vector beams propagating through anisotropic non-Kolmogorov atmospheric turbulence have attracted a large quantity of interest in recent years. Here, we show that the partially coherent vector Gaussian Schell-model (PCVGSM) beams for different initial correlation lengths will appear splitting phenomenon in turbulence, and the distribution of degree of coherence gradually evolves into circularly symmetric distribution with increasing propagation distance. We find that the distribution of degree of polarization of PCVGSM beam displays four petals pattern. It can also be found that the PCVGSM beam still keeps linearly polarized through turbulence without initial phase difference. In spite of this, it will gradually evolve into an elliptically polarized beam in turbulence by controlling the initial correlation lengths and the correlation coefficient. Our results are of great significance to detect and image for atmospheric lidar.

A novel idea: Calculating anisotropic turbulence only by Kolmogorov structure constant [formula omitted] and power law [formula omitted

As stated in the present research, the anisotropic non-Kolmogorov turbulence model is more in line with the actual turbulence. However, anisotropic factor is vital for the accuracy of calculations, and measuring it precisely is a challenging task. In this paper, utilizing three modeling approaches, we derive four different equivalence formulas between the anisotropic non-Kolmogorov and the Kolmogorov structure constants, and apply them to the extant anisotropic results. It is found that the anisotropic factor is eliminated and the anisotropic turbulence can be predicted only by Kolmogorov structure constant and power law.

BER performance of M-ary pulse position modulated communication systems in anisotropic non-Kolmogorov turbulent atmosphere

We investigated the effect of anisotropic non-Kolmogorov atmospheric turbulence on the performance of the optical wireless systems when M-ary Pulse Position Modulation (PPM) is applied to a Gaussian beam. The performance of the optical wireless systems that use avalanche photodetector at the receiver is evaluated in terms of the bit error rate (BER). The effects of the parameters, such as the anisotropy factors in x–y directions, modulation order, data bit rate, equivalent load resistor, photodetector quantum efficiency, non-Kolmogorov turbulence power law exponent, beam source size, link length, photodetector gain and structure constant on BER of the M-ary PPM Gaussian beam propagating in anisotropic non-Kolmogorov atmospheric turbulence, are examined.

Beam wander of partially coherent twisted elliptical vortex beam in turbulence

Based on the generalized Huygens–Fresnel theorem, the characteristics of beam wander in partially coherent elliptical vortex beams in anisotropic non-Kolmogorov turbulence are studied. Considering not only the vortex phase but also the twisted phase modulation in the partially coherent beams, the study of twisted phase modulation is carried out based on the content of the partially coherent elliptical vortex beam in order to research the relationship between the beam wander and the twisted phase modulation factor. It is found that twisted phase modulation and coherent modulation have a saturation region, and outside the saturation region, the twisted phase modulation can restrain the beam wander effectively.

Fiber-coupling efficiency of a Gaussian-beam in anisotropic non-Kolmogorov turbulence in the presence of random angular jitter

Increasing experimental evidence and theoretical results verify that the non-Kolmogorov property and anisotropy are both exhibited in the atmospheric turbulence. In the actual laser communication link, random angular jitter and bias error are important components that affect the laser communication performance. Therefore, in this study, we develop the fiber-coupling efficiency for a Gaussian-beam propagating horizontally through weak-to-strong anisotropic non-Kolmogorov turbulence in the presence of random angular jitter and bias error. The effects of anisotropic factors, power law, random angular jitter, and bias error, on the fiber-coupling efficiency are then evaluated. This study will be beneficial for the optimization of free-space optical communication systems and will enhance the understanding of optical wave propagation in anisotropic non-Kolmogorov link.

Temporal Frequency Spread of Plane Wave Propagation through Moderate to Strong Turbulence

In this study, we derive new expressions for the atmospheric-brought on frequency unfold of plane waves propagating thru slight to strong turbulence in a horizontal direction based on the modified anisotropic non-Kolmogorov electricity spectrum as antagonistic to conventional Kolmogorov electricity spectrum. The energy regulation price varies from three to 4 instead of the traditional Kolmogorov power law price; the general amplitude price differs from the conventional Kolmogorov regular cost 0.033. these new expressions are based on slight to robust fluctuation vicinity and anisotropic non-Kolmogorov turbulence. The simulation results show that temporal frequency unfold will decrease even as the anisotropic component   2  is increasing

Average channel capacity in anisotropic atmospheric non-Kolmogorov turbulent medium

The average channel capacity of a free space optical (FSO) communication system running an intensity modulated Gaussian beam is examined in anisotropic non-Kolmogorov atmospheric weak turbulence based on Rytov variance. Results are obtained by employing the log-normal distribution of irradiance fluctuations corresponding to weak turbulence regime. Our results show that average channel capacity increases together with the increase in anisotropy factor in x and y direction, non-Kolmogorov power law exponent, quantum efficiency of photo detector, Gaussian beam source size and the inner scale length. However, the average channel capacity is found to decrease when turbulence strength, link length and noise variance increase.

The analysis of anisotropic the non-Kolmogorov turbulence effect on asymmetrical Gaussian beam propagation in a marine atmosphere

The variations of the scintillation index of an asymmetrical Gaussian beam are investigated when the beam propagates in anisotropic non-Kolmogorov marine atmospheric turbulence. The results indicate that the scintillation decreases when the anisotropy factors in both x and y directions increase. Increases in the beam asymmetry ratio and the inner scale length increase the scintillation index level. The scintillations are found to increase as the propagation distance and structure constant increase, and as the wavelength decreases. Being valid for any asymmetry and anisotropic factor, for small values of the power law exponent, of non-Kolmogorov marine atmospheric turbulence, the scintillation index tends to increase proportionally with . However, as is further increased, the scintillation index starts to decrease after reaching a peak value. Larger anisotropy in the non-Kolmogorov marine turbulence is found to be preferable since the scintillation index is found to decrease at large anisotropic factors.

Effect of anisotropic non-Kolmogorov turbulence on the evolution behavior of Gaussian Schell-model vortex beams

Abstract The effect of anisotropic non-Kolmogorov turbulence on the evolution behavior of average intensity and coherent vortices for Gaussian Schell-model (GSM) vortex beams is investigated. Based on the extended Huygens–Fresnel principle and power spectrum of the anisotropic non-Kolmogorov turbulence, the analytical expressions for the cross-spectral density and average intensity of GSM vortex beams propagating through anisotropic non-Kolmogorov turbulence are obtained. The evolution behavior of intensity and coherent vortices for GSM vortex beams in anisotropic non-Kolmogorov turbulence has been discussed in detail by numerical simulation. The results shown that the evolution behavior of coherent vortices and intensity profile depends on the effective anisotropic factor, generalized exponent factor and structure constant of anisotropic non-Kolmogorov turbulence, as well as the beam parameters, such as beam waist, wave length and correlation length.

Twisted partially coherent array sources and their transmission in anisotropic turbulence.

A new class of twisted Schell-model array correlated sources are introduced based on Mercer's expansion. It turns out that such sources can be expressed as superposition of fully coherent Laguerre-Gaussian modes, and the twistable condition is established. Furthermore, on the basis of a stretched coordinate system and a quadratic approximation, analytical expressions for the mutual coherence function of an anisotropic non-Kolmogorov turbulence and the cross-spectral density of a twisted Gaussian Schell-model array beam are rigorously derived. Due to the presence of the twist phase, the beam spot and the degree of coherence rotate as they propagate, but their rotation centers are different. It is shown that the anisotropy of turbulence causes an anisotropic beam spreading in the horizontal and vertical directions. However, impressing a twist phase on source beams can significantly inhibit this effect. For an anticipated atmospheric channel condition, a comprehensive selection of initial optical signal parameters, receiver aperture size and receiver capability, etc., is necessary. Our work is helpful for exploring new forms of twistable sources, and promotes guidance on optimization of partial coherent beam applications.