Propagation In Turbulent Atmosphere Research Articles

Simulation Method for the Impact of Atmospheric Wind Speed on Optical Signals in Satellite–Ground Laser Communication Links

To analyze the intensity of atmospheric turbulence in a satellite–ground laser communication link, it is important to consider the effect of increased atmospheric turbulence caused by wind speed. Atmospheric turbulence causes a change in the refractive index, which negatively impacts the quality and focusing ability of the laser beam by altering its phase front. To simulate the changes in amplitude and phase characteristics of laser beam propagation in atmospheric turbulence caused by wind speed, a transverse translation phase screen is used. To better understand and address the influence of atmospheric wind speed on the phase of optical signals in satellite–ground laser communication links, this paper proposes a Monte Carlo simulation method. This method utilizes the spatial and temporal variations in the refractive index in the atmosphere and integrates the principles of optical signal propagation in the atmosphere to simulate changes in the phase of optical signals under different wind speed conditions. By analyzing the variations in the received optical signal’s power, the Monte Carlo method is employed to simulate phase screens and logarithmic amplitude screens. Additionally, it models the probability density of the statistical behavior of received optical signal’s fluctuations, as well as the time autocorrelation coefficient of optical signals. This paper, under the coupling condition in satellite–ground laser communication links, conducted a Monte Carlo simulation experiment to analyze the characteristics of the optical signal’s fluctuations in the link and discovered that atmospheric wind speed affects the shape of the power spectral density model of the received optical signal. Increasing wind speed leads to a decrease in the time autocorrelation coefficient of the received optical signal and affects the coupling efficiency. The paper then used a cubic spline interpolation fitting method to verify the models of the power spectral density and the autocorrelation time coefficient of the optical signal. This provides a theoretical foundation and practical guidance for the optimization of satellite–ground laser communication systems.

A Monte Carlo method for 3D radiative transfer equations with multifractional singular kernels

We propose in this work a Monte Carlo method for three dimensional scalar radiative transfer equations with non-integrable, space-dependent scattering kernels. Such kernels typically account for long-range statistical features, and arise for instance in the context of wave propagation in turbulent atmosphere, geophysics, and medical imaging in the peaked-forward regime. In contrast to the classical case where the scattering cross section is integrable, which results in a non-zero mean free time, the latter here vanishes. This creates numerical difficulties as standard Monte Carlo methods based on a naive regularization exhibit large jump intensities and an increased computational cost. We propose a method inspired by the finance literature based on a small jumps - large jumps decomposition, allowing us to treat the small jumps efficiently and reduce the computational burden. We demonstrate the performance of the approach with numerical simulations and provide a complete error analysis. The multifractional terminology refers to the fact that the high frequency contribution of the scattering operator is a fractional Laplace-Beltrami operator on the unit sphere with space-dependent index.

Second-order statistics of a Hermite-Gaussian correlated Schell-model beam carrying twisted phase propagation in turbulent atmosphere.

We investigate the second-order statistics of a twisted Hermite-Gaussian correlated Schell-model (THGCSM) beam propagation in turbulent atmosphere, including the spectral density, degree of coherence (DOC), root mean square (r.m.s.) beam wander and orbital angular momentum (OAM) flux density. Our results reveal that the atmospheric turbulence and the twist phase play a role in preventing the beam splitting during beam propagation. However, the two factors have opposite effects on the evolution of the DOC. The twist phase preserves the DOC profile invariant on propagation, whereas the turbulence degenerates the DOC. In addition, the influences of the beam parameters and the turbulence on the beam wander are also studied through numerical examples, which show that the beam wander can be reduced by modulating the initial parameters of the beam. Further, the behavior of the z-component OAM flux density in free space and in atmosphere is thoroughly examined. We show that the direction of the OAM flux density without the twist phase will be suddenly inversed at each point across the beam section in the turbulence. This inversion only depends on the initial beam width and the turbulence strength, and in turn, it offers an effective protocol to determine the turbulence strength by measuring the propagation distance where the direction of OAM flux density is inversed.

Wavefront reconstruction of vortex beam propagation in atmospheric turbulence based on deep learning

Wavefront distortion is one of the main challenges hampering the practical application of a vortex beam which carries orbital angular momentum. In this work, we propose a restoration method for wavefront distortion of the beam based on deep learning. The convolutional neural network model, which is capable of automatically learning the mapping relationship between optical field distribution of two kinds of vortex beams before and after the wavefront distortion, is well designed. After a large number of sample training, the CNN model possesses a good generalization ability to restore the distorted wavefront of the vortex beam by evaluating from mode purity, beam width and beam wander respectively under the conditions of different atmosphere turbulence, transmission distance and orbital angular momentum. Then, the experimental link is constructed to verify the effect of the model in the actual situation. The results show that the model proposed represents good robustness, which means the restored beam performs well in all indicators in different environments. The results provide a theoretical basis for the research of atmospheric turbulence suppression techniques of vortex optical communication.

Wavefront Reconstruction of Vortex Beam Propagation in Atmospheric Turbulence Based on Deep Learning

Wavefront Reconstruction of Vortex Beam Propagation in Atmospheric Turbulence Based on Deep Learning

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.

Electromagnetic phase coherence gratings for atmospheric applications.

We propose using electromagnetic phase coherence gratings (EMPCGs) for fine spatial segregation in polarimetric components of stationary beams on their propagation in atmospheric turbulence. Unlike for other beams, e.g., non-uniformly correlated EM beams, the off-axis shifts occurring in polarimetric components of EMPCGs are shown to be invariant with respect to the local turbulence strength. This effect may lead to implementation of novel techniques for direct energy, imaging, and wireless optical communication systems operating in the presence of turbulent air.

Propagation of a Hermite-cos-Gaussian correlated Schell-model beam in non-Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle, the cross-spectral density of a Hermite-cos-Gaussian correlated Schell-model (HcGCSM) beam propagating in non-Kolmogorov turbulence is derived in theory, and the intensity distribution and coherence properties of a HcGCSM beam propagation in atmospheric turbulence and free space are studied and compared by using numerical simulations. It is found that multiple beam spots of a HcGCSM beam propagation in atmospheric turbulence will combine with each other at the long distance, and the combination properties of multiple beam spots are related with initial beam parameters and strength of atmospheric turbulence. It is also found that spectral degree of coherence of a HcGCSM beam propagation in atmospheric turbulence will decrease faster than the beam propagation in free space as |r2−r1| increases

Numerical simulation of super-continuum laser propagation in turbulent atmosphere* *Project supported by the Director Fund of Advanced Laser Technology Laboratory of Anhui Province, China (Grant No. 20191002).

Considering the atmospheric extinction and turbulence effects, we investigate the propagation performances of super-continuum laser sources in atmospheric turbulence statistically by using the numerical simulation method, and the differences in propagation properties between the super-continuum (SC) laser and its pump laser are also analyzed. It is found that the propagation characteristics of super-continuum laser are almost similar to those of the pump laser. The degradation of source coherence degree may cause the relative beam spreading and scintillation indexes to decrease at different propagation distances or different turbulence strengths. The root-mean-square value of beam wandering is insensitive to the variation of source correlation length, and less aperture averaging occurs when the laser source becomes less coherent. Additionally, from the point of view of beam wandering, the SC laser has no advantage over the pump laser. Although the pump laser can bring about a bigger aperture average, the SC laser has a lower scintillation which may be due to the multiple wavelength homogenization effects on intensity fluctuations. This would be the most important virtue of the SC laser that can be utilized to improve the performance of laser engineering.

Comparison of propagation properties of circular edge dislocation beams and circular−linear edge dislocation beams

In this study, based on the extended Huygens–Fresnel principle, the propagation expressions of circular edge dislocation beams and circular–linear edge dislocation beams were obtained. The propagation properties of the two types of beam were compared in free space and atmospheric turbulence. The results show that, when circular–linear edge dislocation beams propagate in free space or atmospheric turbulence, because the linear edge dislocation is located in different beam locations, circular edge dislocation vanishes or evolves into a pair of optical vortices. However, when circular edge dislocation beams propagate in space, circular edge dislocation exists stably in free space propagation, while it evolves into a pair of optical vortices in atmospheric turbulence propagation. Therefore, the propagation properties of circular edge dislocation can be adjusted by adding linear edge dislocation when circular edge dislocation beams propagate through free space and atmospheric turbulence. This research can be useful for applications in optical communications.

Simulation of N-wave propagation in turbulent atmosphere using standard and wide-angle parabolic equations

Interest to the problem of sonic boom propagation in atmosphere is growing in recent decade due to the development of new generation of supersonic business jets. Important nonlinear wave effects occur in the last kilometer above the ground where sonic boom wave interacts with turbulence of the planetary boundary layer. Focusing and defocusing of the sonic boom on random inhomogeneities of sound speed lead to fluctuations of its peak overpressure and rise time, affecting the perceived loudness. Various one-way model equations of different complexity have been developed and actively used by the research community for analyzing wave propagation in turbulent atmosphere. The basic equation is the nonlinear parabolic equation of the Khokhlov-Zabolotskaya-Kuznetsov-type, which has limitation on diffraction angles. Improvement in accuracy of the diffraction term can be reached using wide-angle formulation. Here, the simulation results for N-wave propagation through homogeneous isotropic turbulence are compared for standard and wide-angle parabolic equations of scalar type. Turbulence wind velocity fluctuations are accounted via effective sound speed. The wide-angle model is based on split-step Pade approximation of the propagation operator. The importance of taking into account large diffraction angles for N-wave propagation in atmospheric turbulence is discussed. [Work supported by RSF-18-72-00196 and ANR-10-LABX-0060/ANR-16-IDEX-0005].

Improving system performance by using adaptive optics and aperture averaging for laser communications in oceanic turbulence.

We theoretically investigate the effectiveness of adaptive optics correction for Gaussian beams affected by oceanic turbulence. Action of an idealized adaptive optics system is modeled as a perfect removal of a certain number of Zernike modes from the aberrated wavefront. We focused on direct detection systems and we used the aperture-averaged scintillation as the main metric to evaluate optical system performances. We found that, similar to laser beam propagation in atmospheric turbulence, adaptive optics is very effective in improving the performance of laser communication links if an optimum aperture size is used. For the specific cases we analyzed in this study, scintillation was reduced by a factor of ∼7 when 15 modes were removed and when the aperture size of the transceiver was large enough to capture 4-5 speckles of the oceanic turbulence-affected beam.

Precision analysis of turbulence phase screens and their influence on the simulation of Gaussian beam propagation in turbulent atmosphere.

The slip-step method is widely used in simulating optical wave propagation in turbulent atmosphere, which treats propagation and phase perturbations caused by turbulence separately and in discrete steps along the propagation axis. The phase perturbations are represented by a series of phase screens, and hence, the precision of the phase screen concerns the accuracy of the simulation. In this paper, we first discuss the precision and computational performance of phase screens generated by the subharmonic complemented discrete Fourier transformation (DFT) (DFT-SH) method, three kinds of randomized spectral sampling techniques (sparse spectrum (SS) technique, sparse spectrum technique with uniform wave vectors (SU), randomized DFT technique), and optimization-based (OB) method; then, the simulations are implemented with the phase screens generated by these methods. Some statistical quantities of the received optical field are calculated, such as beam wander variance, long-term beam radius, short-term beam radius, and on-axis scintillation index. The statistical results show that the undersampling of phase screen in the low-frequency region causes underestimation of the values of beam wander variance, long-term beam radius, and focused beam on-axis scintillation index because these quantities are sensitive to the large-scale inhomogeneities. However, the undersampling does not affect the predicted values of the short-term beam radius and collimated beam on-axis scintillation index because these quantities are insensitive to the large-scale inhomogeneities.

Implementing Artificial Intelligence in Predicting Metrics for Characterizing Laser Propagation in Atmospheric Turbulence

The effects of a laser beam propagating through atmospheric turbulence are investigated using the phase screen approach. Turbulence effects are modeled by the Kolmogorov description of the energy cascade theory, and outer scale effect is implemented by the von Kármán refractive power spectral density. In this study, we analyze a plane wave propagating through varying atmospheric horizontal paths. An important consideration for the laser beam propagation of long distances is the random variations in the refractive index due to atmospheric turbulence. To characterize the random behavior, statistical analysis of the phase data and related metrics are examined at the output signal. We train three different machine learning algorithms in tensorflow library with the data at varying propagation lengths, outer scale lengths, and levels of turbulence intensity to predict statistical parameters that describe the atmospheric turbulence effects on laser propagation. tensorflow is an interface for demonstrating machine learning algorithms and an implementation for executing such algorithms on a wide variety of heterogeneous systems, ranging from mobile devices such as phones and tablets to large-scale distributed systems and thousands of computational devices such as GPU cards. The library contains a wide variety of algorithms including training and inference algorithms for deep neural network models. Therefore, it has been used for deploying machine learning systems in many fields including speech recognition, computer vision, natural language processing, and text mining.

Study on the Perturbation Characteristics of Two-Channel Laser Propagation in Atmospheric Turbulence

In order to study the influence factors of acquisition detection target information by lidar and understand the influence degree of each factor, the two-channel phase perturbation model and the two-channel eikonal variance model are derived in detail by using the geometrical optics method in this paper, and each factor is discussed in detail. The results show that the transmission distance is the main factor to affect the two-channel perturbation. With the increase of the transmission distance, the disturbing degree will gradually weaken. With the increase of transverse coordinates, the disturbing of two channels will also be weakened. In order to further weaken the disturbing degree, the feature dimension should be far larger than the wavelength, but far less than the transmission distance.

Mitigation of atmospheric turbulence with random light carrying OAM

The results of the laboratory experiments are presented for synthesis of the Im-Bessel correlated beams by a Spatial Light Modulator (SLM) and a Digital Micromirror Device (DMD) as well as for their interactions with atmospheric turbulence simulated by either an SLM or a mixed-air turbulent chamber. The synthesis procedure of these beams relies on the incoherent superposition of their coherent modes being Laguerre-Gaussian (LG) functions having a variable radial mode and a fixed azimuthal mode carrying the Orbital Angular Momentum (OAM). As a result of such construction the correlation functions of these random beams have separable phase carrying the OAM with the index inherited from the coherent modes. The coherence states of these beams are controlled by the distribution of weights of the coherent modes in superposition, varying from perfectly coherent to nearly incoherent. We explore the effects of the cycling rates of the SLM and the DMD used for source synthesis on the average intensity and the scintillation index of the generated beams having different OAM indices and coherence states after propagation in atmospheric turbulence. Our analysis indicates that for fairly incoherent beams with sufficiently large OAM index and high cycling rates the atmospheric turbulence can be efficiently mitigated.

Numerical simulation for echo characteristics of laser beams reflected by retro-reflectors in atmospheric turbulence

In this study, a split-step Fourier method (FFSM) was extended in the simulation of a double-passage laser propagation in atmospheric turbulence. The characteristics of the coherence length and intensity scintillation for the plane wave, spherical wave, and Gaussian beam reflected by the plane’s mirror and retro-reflector were numerically simulated and compared using a phase-screen approximation method. The properties of the echo waves from the mirror and retro-reflector, and that of the double-passage propagation without a target, were also presented. The results obtained in this study could be potentially used to detect the different characteristics of the echo fields of plane waves, spherical waves and Gaussian waves reflected by different targets, so as to obtain the target characteristics. In addition, the study results could also provide theoretical and technical guidance for the application of laser target detection and recognition.

Toward Defeating Diffraction and Randomness for Laser Beam Propagation in Turbulent Atmosphere

A large distance propagation in turbulent atmosphere results in disintegration of laser beam into speckles. We find that the most intense speckle approximately preserves both the Gaussian shape and the diameter of the initial collimated beam while loosing energy during propagation. One per 1000 of atmospheric realizations produces at 7km distance an intense speckle above 20\% of the initial power. Such optimal realizations create effective extended lenses focusing the intense speckle beyond the diffraction limit of vacuum propagation. Atmospheric realizations change every several milliseconds. We propose to use intense speckles to greatly increase the time-averaged power delivery to the target plane by triggering the pulsed laser operations only at times of optimal realizations. Resulting power delivery and laser irradiance at the intense speckles well exceeds both intensity of diffraction-limited beam and intensity averaged over typical realizations.

Propagation properties of rectangular Laguerre–Gaussian-correlated Schell-model beams in atmospheric turbulence

ABSTRACTBased on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function (WDF), the analytical expressions for the cross-spectral density (CSD) and the propagation factor of a rectangular Laguerre–Gaussian-correlated Schell-model (LGCSM) beam propagating in atmospheric turbulence are derived. The statistical properties, such as the average intensity, the spectral degree of coherence (SDOC) and the propagation factor, of a rectangular LGCSM beam in free space and atmospheric turbulence are comparatively analysed. It is illustrated that a rectangular LGCSM beam exhibits self-splitting and combing properties on propagation in atmospheric turbulence, and the self-splitting properties of such beam are closely related to its beam orders m and n, which is quite different from other self-splitting beams. In addition, the rectangular LGCSM beam has an advantage for reducing the turbulence-induced degradation compared with the conventional partially coherent beams.

Study on intensities, phases and orbital angular momentum of vortex beams in atmospheric turbulence using numerical simulation method

In this study, the characteristics of the Bessel-Gaussian (BG) and Laguerre–Gauss (LG)vortex beams propagation in atmospheric turbulence, including intensity, phase and orbital angular momentum (OAM), were numerically simulated, based on the Split-Step Fourier Method (SSFM) and Power Spectrum Inversion Method. Also, the propagation characteristics of the two beams in the free space and the atmospheric turbulence were compared. The results obtained showed that the equiphase lines of the LG and BG vortex beams propagation in atmospheric turbulence became arcs. However, the arcs of the LG vortex beam are discontinuous, those of the BG vortex beam are continuous. The OAM densities of the LG and BG vortex beams transferred from the ring to the center of beam with the increased propagation distance. The transmission quality and stability of the OAM of the BG beams were observed to be better than those of the LG beams.