non-Kolmogorov Atmospheric Turbulence Research Articles

Average capacity and bit error rate of vortex gamma beams propagating in non-Kolmogorov atmospheric turbulence.

In recent years, free-space optical communication based on various vortex beams has gained significant attention due to its high channel capacity and low bit error rate (BER). To investigate a novel type of vortex beam (termed as gamma beam) and its application in free-space optical communication (FSO), a comprehensive analysis of its transmission performance in weak-to-strong non-Kolmogorov turbulence has been conducted for the first time. Based on the extended Rytov method, the propagation behaviors of the gamma beam via weak-to-strong non-Kolmogorov turbulent atmosphere is explored, revealing that gamma beams may outperform LG beams and HyGG beams in certain short links. Numerical calculations are performed to analyze the effects of transmission distance, rms beam radius, receiver aperture, and other parameters on the average capacity and BER. Our results are potentially significant for free-space optical communication based on orbital angular momentum.

Propagation of perfect Laguerre–Gaussian entangled states in non-Kolmogorov atmospheric turbulence

We investigate the impacts of backward scattering (BS) of non-Kolmogorov turbulence on the entangled perfect Laguerre–Gaussian (PLG) beams. The explicit expressions for PLG quantum entanglement and quantum coherence are derived in the BS case. We find that the introduction of BS reduces the entanglement and coherence, disrupts the initial decay characteristics, and induces the revival of entanglement and coherence, in which sense turbulence may possess a non-Markovian (memory) effect. As the OAM number increases, the non-Markovian feature increases logarithmically. In addition, the universal decay of entanglement and coherence and the non-Kolmogorov effects are also explored.

Unveiling detection probability for multi-Gaussian correlated anomalous vortex modes in maritime atmospheric turbulence

In this study, we employ the Rytov approximation to investigate the detection probability of orbital angular momentum (OAM) in multi-Gaussian correlated anomalous vortex (MGCAV) beams under non-Kolmogorov maritime atmospheric turbulence. Our results demonstrate that the OAM detection probability of a MGCAV beam is influenced by various factors, including beam parameters and the characteristics of maritime atmospheric turbulence. Specifically, an increase in propagation distance, beam order, and beam index, or a decrease in inner scale, spatial coherence width, and non-Kolmogorov parameter, leads to a decrease in the OAM detection probability. The phase characteristics of partially coherent vortex modes are affected by both atmospheric turbulence phase and initial random phase, resulting in reduced robustness compared to fully coherent vortex modes. Furthermore, a comparative analysis between Gaussian–Schell correlated anomalous vortex (GSCAV) beams and MGCAV beams reveals the superior resilience of GSCAV beams in mitigating the impact of maritime atmospheric turbulence. Moreover, specific combinations of beam order, topological charge, and beam waist, or the optimal beam width, yield maximum OAM detection probability or minimum scintillation. These findings provide valuable insights applicable to optical communication, particularly in scenarios above sea and ocean levels.

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.

Impacts of low-order aberrations on capacity of orbital-angular-momentum quantum states

We use Hypergeometric Gaussian-II (HyGG-II) modes to investigate the impacts of non-Kolmogorov atmospheric turbulence on the Holevo channel capacity of a quantum communication scheme. The capacity of HyGG-II modes can be higher than that of Laguerre–Gaussian modes via modulating the hollowness parameter. The influences of low-order turbulence aberrations including tilt, defocus, astigmatism, and coma on the capacity are also explored. Generally, tilt aberration dominates among all low-order aberrations and defocus and astigmatism aberrations are always negligible. By contrast, the effect of coma aberration can be enhanced to be non-negligible when the turbulence strength or the channel zenith angle is enhanced. We also show that only the total and tilt aberrations are sensitive to the non-Kolmogorov power-law exponent. Our results may contribute to the quantum optical communication as well as aberration compensation in turbulent channels utilizing the novel family of vortex beams.

Channel capacity and quantum entanglement of autofocusing hypergeometric-Gaussian beams through non-Kolmogorov turbulence

We establish propagation models for distributing autofocusing hypergeometric-Gaussian (HyGG) beams via non-Kolmogorov atmospheric turbulence in the single-photon and biphoton cases. Analytical expressions of the channel capacity and entanglement are employed to explore the communication performance in turbulence. It can be demonstrated that in the single-photon case, a lower hollowness parameter and larger topological charge could contribute to the anti-interference ability of HyGG beams. Such an anti-interference ability could be affected by the autofocusing distance more severely for beams with larger topological charges. In addition, the channel capacity of beams at a certain distance decays rapidly at first before it grows steadily with the increase in the power-law exponent of the non-Kolmogorov spectrum. For the biphoton case, the higher hollowness parameter, larger power-law exponent of the non-Kolmogorov spectrum and larger topological charge make HyGG beams maintain a high concurrence at longer distances. We believe that our results could serve as a reference for improving the quality of orbital-angular-momentum communication of HyGG beams via atmospheric turbulence.

Angle-of-Arrival Fluctuations and Adaptive Optics Correction in Non-Kolmogorov Turbulent Atmosphere

In this study, angle-of-arrival (AOA) fluctuations of plane and spherical waves propagating through a non-Kolmogorov turbulent atmosphere are examined. Moreover, the effects of adaptive optics compensation are investigated. Here, the terms non-Kolmogorov turbulence spectrum and generalized power-law are used in the sense that the refractive index spectrum is allowed to differ from the classical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa ^{-11/3}$ </tex-math></inline-formula> power law. The AOA variance observed with a circular aperture and various adaptive-optics correction methods is analyzed for plane and spherical waves propagating through non-Kolmogorov turbulence. Results are obtained depending on the power-law exponent, the aperture size, the optical wavenumber, and various combinations of adaptive optics correction methods.

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.

Quantum coherence of thermal biphoton orbital angular momentum state and its distribution in non-Kolmogorov atmospheric turbulence.

Quantum coherence has been considered as a resource for quantum information process in recent years. Sharing the quantum resource distantly is a precondition for quantum communication. In this paper, we explore the quantum coherence properties of the prepared state starting from initially incoherent thermal light source. It is shown that the quantum coherence is directly proportional to the dimension of Hilbert space and therefore employ the orbital angular momentum (OAM) to encode resources. The distribution of biphoton thermal OAM state via the one-sided noisy channel (non-Kolmogorov turbulent atmosphere) is then investigated. It is found that the prepared OAM state can have large amount of quantum coherence, which is maximized when the thermal source is completely incoherent. The turbulence effects on quantum coherence are studied and compared to those on the fidelity and quantum channel capacity. Contrasting to the monotonic decay, the dynamics of coherence displays a peak during the propagation and the mechanism behind is presented. Finally, the dynamics of quantum thermal state can be more robust than that of Bell-like pure state since more interference can be induced. We believe our results is of importance to OAM quantum communication using quantum coherence as a resource.

Orbital angular momentum evolution of twisted multi-Gaussian Schell model beams in anisotropic turbulence

Twist phase is an unconventional phase that allows a partially coherent beam to carry orbital angular momentum (OAM). In this work, based on the Mercer’s expansion and the nonnegativity of the cross-spectral density function, we obtain a twistable condition for the multi-Gaussian Schell model (MGSM) correlation structure. The expression of an elliptical twisted multi-Gaussian Schell model (TMGSM) beam through non-Kolmogorov anisotropic atmospheric turbulence is rigorously derived, and its spectral density and OAM variation in anisotropic turbulence are studied in detail. The results show that the spectral density and OAM flux density distributions rotate with increasing transmission distance, and increasing the multi-Gaussian modulus and twist factor can significantly suppress the negative effects of atmospheric turbulence. The difference of turbulence anisotropy, beam modulus, and coherence length can affect the distribution of OAM. Furthermore, the twist phase affects both the OAM distribution and magnitude. Our work is helpful for exploring new forms of OAM sources, and promote the application of free-space optical communications.

Secrecy outage probability analysis in a free-space optical system based on partially coherent beams through anisotropic non-Kolmogorov turbulent atmosphere

In this paper, the secrecy outage probability of a partially coherent beam free-space optical communication system considering the combined effect of anisotropic non-Kolmogorov strong turbulent atmosphere and the eavesdropper’s position is investigated. The Fisher–Snedecor distribution is chosen to model the atmospheric turbulence because it is not only suitable for weak to strong turbulence conditions but is also mathematically simple. Based on the fading channel model and the generalized pointing error model, we derive analytical expressions for the lower bounded secrecy outage probability. Also, we obtain asymptotic closed-form expression at a high signal-to-noise regime. The obtained expressions are corroborated by Monte Carlo simulations. The calculation results based on the analytical expressions show that increasing the source coherence parameter makes the secrecy interruption probability performance first better and then worse for a given condition, and an optimal value is observed. The anisotropic coefficient and power law have a positive effect on the secrecy outage probability of the free-space optical communication system. Under the given conditions, the performance of the secrecy outage probability is significantly improved by the divergent beam, although the increased spot size at the receiver makes it easier for eavesdroppers to tap the link. The secrecy outage probability performance deteriorates as the vertical component of Bob, the jitter variance, and the refractive index structure constant increase.

Wander of a Gaussian-Beam Wave Propagating through Kolmogorov and Non-Kolmogorov Turbulence along Laser-Satellite Communication Uplink

It is accepted that there exists two kinds of atmospheric turbulence in the Earth’s aerosphere—Kolmogorov and non-Kolmogorov turbulence; therefore, it is important to research their combined impacts on laser-satellite communications. In this paper, the exponential power spectra of refractive-index fluctuations for non-Kolmogorov turbulence in the free troposphere and stratosphere are proposed, respectively. Based on these two spectra, using the Markov approximation, beam wander displacement variances of a Gaussian-beam wave are derived, respectively, which are valid under weak turbulent fluctuations condition. On this basis, using a three-layer altitude-dependent turbulent spectrum model for vertical/slant path, the combined influence of a three-layer atmospheric turbulence on wander of a Gaussian-beam wave as the carrier wave in laser-satellite communication is studied. This three-layer spectrum is more accurate than a two-layer model. Moreover, the variations of beam wander displacement with beam radius, zenith angles, and nominal value of the refractive-index structure parameter on the ground are estimated. The theory of optical wave propagation through non-Kolmogorov atmospheric turbulence is further enriched and a theoretical model of a three-layer atmospheric turbulence beam wander for a satellite-ground laser communication uplink is established.

A Survey of Structure of Atmospheric Turbulence in Atmosphere and Related Turbulent Effects

The Earth’s atmosphere is the living environment in which we live and cannot escape. Atmospheric turbulence is a typical random inhomogeneous medium, which causes random fluctuations of both the amplitude and phase of optical wave propagating through it. Currently, it is widely accepted that there exists two kinds of turbulence in the aerosphere: one is Kolmogorov turbulence, and the other is non-Kolmogorov turbulence, which have been confirmed by both increasing experimental evidence and theoretical investigations. The results of atmospheric measurements have shown that the structure of atmospheric turbulence in the Earth’s atmosphere is composed of Kolmogorov turbulence at lower levels and non-Kolmogorov turbulence at higher levels. Since the time of Newton, people began to study optical wave propagation in atmospheric turbulence. In the early stage, optical wave propagation in Kolmogorov atmospheric turbulence was mainly studied and then optical wave propagation in non-Kolmogorov atmospheric turbulence was also studied. After more than half a century of efforts, the study of optical wave propagation in atmospheric turbulence has made great progress, and the theoretical results are also used to guide practical applications. On this basis, we summarize the development status and latest progress of propagation theory in atmospheric turbulence, mainly including propagation theory in conventional Kolmogorov turbulence and one in non-Kolmogorov atmospheric turbulence. In addition, the combined influence of Kolmogorov and non-Kolmogorov turbulence in Earth’s atmosphere on optical wave propagation is also summarized. This timely summary is very necessary and is of great significance for various applications and development in the aerospace field, where the Earth’s atmosphere is one part of many links.

Adaptive optics compensation of M-ary pulse position modulated communication systems in anisotropic non-Kolmogorov turbulent atmosphere

Adaptive optics compensation effect on the performance of an optical wireless communication system (OWC) employing M-ary pulse position modulation (PPM) scheme in anisotropic non-Kolmogorov turbulent atmosphere is investigated. Avalanche photodetector (APD) is used at the receiver side and log-normal channel that models the weak turbulence conditions is utilized. Anisotropy, generally resulting in better performance in OWC systems operating in the turbulent medium, combined with the adaptive optics applications will enhance the bit-error-rate (BER) of the OWC systems significantly. Results are obtained depending on various parameters for both the turbulent atmosphere and the receiver. Our work gives OWC system designers a perspective to optimize their design.

Signal-to-noise ratio with adaptive optics compensation in non-Kolmogorov weak turbulent atmosphere

This study investigates the average signal-to-noise ratio ⟨ SNR ⟩ at the shot-noise limited receiver of an optical wireless communication system (OWC) that uses collimated Gaussian beam with adaptive optics correction in non-Kolmogorov weak turbulent atmosphere. ⟨ SNR ⟩ and the variation in the percentage ⟨ SNR ⟩ are calculated and the results are presented against various adaptive optics correction modes, non-Kolmogorov power-law exponent, receiver aperture size, Gaussian beam source size, photodetector quantum efficiency, electronic bandwidth, link length, and turbulence strength. Adaptive optics correction is analyzed for tilt, defocus, astigmatism, coma and trefoil modes and their variations. The effects of adaptive optics compensation are examined that cause an increase in SNR, hence improve the performance of an OWC system using collimated Gaussian beam and operating in the non-Kolmogorov weak turbulent atmosphere.

Spiral spectrum of high-order elliptic Gaussian vortex beams in a non-Kolmogorov turbulent atmosphere.

In a free space optical communication system based on vortex beams, the effects of spread and crosstalk caused by atmospheric turbulence should not be ignored. The orbital angular momentum (OAM) spectrum of the signal based on elliptic Gaussian beam (EGB) after propagation through non-Kolmogorov turbulent atmosphere are deduced, and a theoretical model of the spiral spectrum of EGB propagating through turbulent atmosphere is obtained. Numerically calculated OAM modes detection and crosstalk probability under different ellipticity parameters. The results show that the ellipticity parameter has a significant impact on the OAM spectral distribution of EGB and the transmission characteristics after turbulent atmosphere. The selection of appropriate ellipticity parameter can correspondingly reduce the degradation and crosstalk caused by turbulent atmosphere. We also compared a Laguerre-Gaussian beam (LGB) with EGB and pointed out the advantages and limitations of these two kinds of beams. The research results may be useful in the field of short distance optical communication and OAM-based multiplex communication.

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.

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.

Outer-Scale Effect of a Gaussian-Beam Wave Propagated Through Non-Kolmogorov Turbulent Atmosphere on the Beam Wander

To date, it is a common knowledge that there exists two kinds of turbulence in Earth’s aerosphere, the Kolmogorov turbulence and the non-Kolmogorov turbulence, which has been confirmed by both increasing experimental evidences and some results of theoretical investigations. Therefore, it is necessary to further develop theory of optical wave propagation through the atmospheric turbulence, namely, to study the propagation of laser beams in the non-Kolmogorov turbulence before analyzing the joint influence of the Kolmogorov turbulence and the non-Kolmogorov turbulence on satellite laser communication. Also it is well known that the beam wander results in the performance degradation of satellite laser communication systems and exert an influence on the achievement and stability of its links. In this paper, considering a non-Kolmogorov generalized exponential power spectrum of refractive-index fluctuations, we derive the variances of beam wander for a Gaussian-beam wave in weak turbulence for a horizonal path. This spectrum includes the inner and outer scales with a generalized power law; thus, we also analyze the effect of spectral power law and outer scale variations on the beam wander. It is important to note that the expression for the beam wander variance obtained is concise closed form and independent on the optical wavelength.

Twisted rectangular Laguerre–Gaussian correlated sources in anisotropic turbulent atmosphere

The ability to impress twist phase on random sources has led to new insights into coherence theory as well as important applications in optical tweezers and optical communications. In the paper, a new class of twisted sources named rectangular Laguerre–Gaussian correlated (TRLGC) fields is introduced based on a superposition of a mutually incoherent, tilted and displaced partially coherent beams. The analytical expressions for the cross-spectral density and the second-order moments of a TRLGC beam propagating through anisotropic non-Kolmogorov turbulent atmosphere are derived. The evolution characteristics of a TRLGC beam such as the spectral intensity, the spectral degree of coherence, and the beam quality are investigated in detail. It is shown that higher values of twist factor can significantly suppress the anisotropic beam spreading induced by the anisotropy of turbulence. Moreover, owing to the twist phase and higher-order coherence parameter, the anti-turbulence capability of partially coherent beams is further enhanced. For anticipated atmospheric communication channel conditions, a comprehensive selection of initial beam parameters, receiver aperture size and receiver capability, etc., is very important. Our work is helpful for exploring new forms of twistable sources and enriches potential applications of novel partially coherent beams in free space optical communications.