non-Kolmogorov Turbulence Research Articles

Science and technology of atmospheric effects on optical engineering: Progress in 3rd quinquennium of 21st century

Brief introduction with remarks is given for recent work in optical properties of turbulent and turbid atmospheres and their effects on optical engineering. Emphasis about turbulence investigation is paid on spatial structure characteristics of optical turbulence, turbulence profiling with lidar technology, and turbulence prediction based on mesoscale atmospheric model. Discussion of turbid atmosphere study is focused on light scattering by non-spherical aerosol particles, high resolution atmospheric transmittance from solar radiation measurement, total sky imaging with high spectral resolution, and the modulation transfer function of a turbid medium. Key points about light propagation through turbulence include non-Kolmogorov turbulence effects, probability distribution models of scintillation, and combined beam propagation. Atmospheric effects on quantum communication are discussed, and statistical characteristics of atmospheric effects on optical engineering are introduced.

Evolution of orbital angular momentum mode of the autofocusing Hypergeometric-Gaussian beams through moderate-to-strong anisotropic non-Kolmogorov turbulence

In order to investigate the evolution of mode probability density (MPD) and received power of orbital angular momentum (OAM) mode carried by autofocusing Hypergeometric-Gaussian (HyGG) beams in moderate-to-strong anisotropic non-Kolmogorov turbulence, the corresponding expressions of the spatial coherence radius and spiral spectrum of HyGG beams are achieved. Results show that the autofocusing property of HyGG beams has a significant impact on the propagation of the MPD. Smaller topological charge, Shorter wavelength, higher values of hollowness parameters and wider beam waist shrink to a narrower width of the MPD and maintain the characteristic of diffraction-free with a longer transmission distance. Moreover, smaller outer-scale, larger inner-scale, larger non-Kolmogorov parameter and larger anisotropic coefficient make the received power of OAM suffer less turbulence.

Intensity of vortex modes carried by Lommel beam in weak-to-strong non-Kolmogorov turbulence.

We investigate the atmospheric turbulence effects on the propagation of vortex modes carried by Lommel beam. The analytic expression of the received signal and crosstalk mode intensity is derived based on the weak-to-strong non-Kolmogorov turbulence theory. The simulation results show that turbulence with small non-Kolmogorov spectrum parameter, small inner-scale factor and large outer-scale factor is more likely to induce modal crosstalk. With the increment of turbulence strength, the crosstalk spreads from adjacent modes to peripheral modes. The received signal intensity can be improved by use of Lommel beam with small asymmetry parameter, low orbital angular momentum quantum number and long wavelength. The results are helpful to the design of orbital angular momentum based free-space optical communication link.

Differential piston phase variance in non-Kolmogorov atmospheres.

We derive a generalized expression for the differential piston phase variance in non-Kolmogorov turbulence. Specifically, our result applies in the case where index of refraction is described by a power-law medium with an exponent between 0 and 1. Kolmogorov assumptions of homogeneity and isotropy are maintained. After some development, our expression is derived using the Mellin-transform techniques and may be generalized to other forms for the three-dimensional index of refraction turbulence power spectrum. This analytical result has two regions of convergence. The separation between these regions is defined by a characteristic time given as the ratio of the mean wind speed and aperture size. By evaluating this expression, we find the differential piston phase variance exhibits a power-law behavior roughly proportional to that of the medium. In addition, we find that piston phase variance decreases with increase in aperture size. We also find that the differential piston phase variance is independent of aperture size as the power law approaches unity.

Effect of aberration correction on beam wander of electromagnetic multi-Gaussian shell-model beams in anisotropic turbulence

The influences of source parameters, non-Kolmogorov and anisotropic turbulence on the beam spreading and beam wander of electromagnetic Multi-Gaussian Shell-model (EMGSM) beams in the atmosphere with aberration correction were analyzed. Zernike tilt aberration correction method had more effect on beam spreading compared to beam wander. Increasing the anisotropic property of turbulence could degrade both beam spreading and beam wander. EMGSM beams with larger beam order, wavelength could better mitigate the turbulence effects than GSM beams, which could be adopted as a better light source with several adjustable parameters to lower scintillation and beam wander in free-space optical communication.

Kurtosis parameter K of arbitrary electromagnetic beams propagating through non-Kolmogorov turbulence

General analytical formulae for the kurtosis parameters K (K parameters) of the arbitrary electromagnetic (AE) beams propagating through non-Kolmogorov turbulence are derived, and according to the unified theory of polarization and coherence, the effect of degree of polarization (DOP) of an electromagnetic beam on the K parameter is studied. The analytical formulae can be given by the second-order moments and fourth-order moments of the Wigner distribution function for AE beams at source plane, the two turbulence quantities relating to the spatial power spectrum, and the propagation distance. Our results can also be extended to the arbitrary beams and the arbitrary spatial power spectra of Kolmogorov turbulence or non-Kolmogorov turbulence. Taking the stochastic electromagnetic Gaussian Schell-model (SEGSM) beam as an example, the numerical examples indicate that the K parameters of a SEGSM beam in non-Kolmogorov turbulence depend on propagation distance, the beam parameters and turbulence parameters. The K parameter of a SEGM beam is more sensitive to effect of turbulence with smaller inner scale and generalized exponent parameter. A non-polarized light has the strongest ability of resisting turbulence (ART), however, a fully polarized SEGSM beam has the poorest ART.

Karhunen–Loeve functions for non-Kolmogorov turbulence

ABSTRACTKarhunen–Loeve functions for the case of non-Kolmogorov turbulence are calculated. The calculations are performed using the covariance matrix of Zernike coefficients which is derived in analytical form. It is shown that the Karhunen–Loeve expansion is more efficient than the Zernike one for simulations of high-order, turbulence-induced phase distortions.

Effects of inner and outer scale on the modulation transfer function for a Gaussian wave propagating through anisotropic non-Kolmogorov turbulence

Both experimental results and empirical research have shown that the atmospheric turbulence can present the anisotropic property not only at a few meters above the ground but also at high altitudes of up to several kilometers. This paper investigates the modulation transfer function of a Gaussian beam propagating along a horizontal path in weak anisotropic non-Kolmogorov turbulence. Mathematical expressions are obtained based on the generalized exponential spectrum for anisotropic turbulence, which includes the spectral power law value, the finite inner and outer scales of turbulence, the anisotropic factor, and other essential optical parameters of the Gaussian beam. The numerical results indicate that the atmospheric turbulence would produce less negative effects on the wireless optical communication system with an increase in the anisotropic factor.

Laboratory simulation of non-Kolmogorov turbulence based on a liquid crystal spatial light modulator

An experimental platform was built for the atmospheric turbulence simulation upon a liquid crystal spatial light modulator. The phase-only spatial light modulator is driven by a series of dynamic phase screens that have non-Kolmogorov turbulence characteristics. After passing through the simulated non-Kolmogorov turbulence, the angle-of-arrival (AoA) and light intensity of the laser beam were analyzed statistically. The variation trends of the AoA fluctuation and the scintillation index exhibited by the experimental results are in accordance with the theoretical predictions. Although there was some divergence between the experiments and theory that needs to be improved further, the experimental data demonstrate the feasibility of using the platform to simulate the turbulence influence on laser communication in the lab.

Polarization properties of Square Multi-Gaussian Schell-Model beam propagating through non-Kolmogorov turbulence

In this paper, analytical expressions for elements of the cross-spectral density matrix of Square Multi-Gaussian Schell-Model (SMGSM) beam, propagating in non-Kolmogorov turbulence, are derived based on the extended Huygens Fresnel integral. Polarization properties of the SMGSM beam are studied in detail based on the derived expressions. It is interesting to find that, apart from keeping the square flat shape of intensity distribution, polarization properties of the SMGSM beam, such as degree of polarization, the orientation angle and degree of ellipticity for the polarization ellipse also form square plateau distributions in the same areas as that of intensity distribution, and can preserve relatively long distance in atmospheric turbulence. This novel characteristic can be used for coherent light free space communications, polarization remote sensing and imaging in atmosphere.

Propagation factor of electromagnetic concentric rings Schell-model beams in non-Kolmogorov turbulence**Project supported by the National Basic Research Program of China (Grant No. 2013CBA01702), the National Natural Science Foundation of China (Grant Nos. 61377016, 11104049, 10974039, 61575055, and 61575053), the Fundamental Research Funds for the Central Universities, China (Grant No. HIT.BRETIII.201406), and the Program for New Century Excellent Talents in University,

We derive an analytical expression for the propagation factor (known as M2-factor) of electromagnetic concentric rings Schell-model (EM CRSM) beams in non-Kolmogorov turbulence by utilizing the extended Huygens–Fresnel diffraction integral formula and the second-order moments of the Wigner distribution function (WDF). Our results show that the EM CRSM beam has advantage over the scalar CRSM beam for reducing the turbulence-induced degradation under suitable conditions. The EM CRSM beam with multi-rings far-fields in free space is less affected by the turbulence than the one with dark-hollow far-fields or the electromagnetic Gaussian Schell-model (EGSM) beam. The dependence of the M2-factor on the beam parameters and the turbulence are investigated in detail.

Simulating non-Kolmogorov turbulence phase screens based on equivalent structure constant and its influence on simulations of beam propagation

Gaussian distribution is used to describe the power law along the propagation path and phase screen of the non-Kolmogorov turbulence is proposed based on the equivalent refractive-index structure constants. Various simulations of Gaussian beam propagation in Kolmogorov and non-Kolmogorov turbulence are used for telling the difference between isotropic and anisotropic turbulence. The results imply that the non-Kolmogorov turbulence makes a great influence on the simulations via power law in spectrum and the number of phase screens. Furthermore, the influence is mainly reflected in light intensity and beam drift. Statistics suggest that when Gaussian beam propagate through single phase screen of non-Kolmogorov, maximum and uniformity of light intensity increase first and then decrease with power law, and beam drift firstly increases and then to stabilize. When Gaussian beam propagate through multiple phase screens, relative errors of beam drift decrease with the number of phase screens. And scintillation indices in non-Kolmogorov turbulence is larger than that in Kolmogorov turbulence when the number is small. When the number is big, the scintillation indices in non-Kolmogorov turbulence is smaller than that in Kolmogorov turbulence. The results shown in this paper demonstrate the effect of the non-Kolmogorov turbulence on laser atmospheric transmissions. Thus, this paper suggests a possible direction of the improvement of the laser transmission accuracy over a long distance through the atmosphere.

Change in the state of polarization of Gaussian Schell-model beam propagating through non-Kolmogorov turbulence

Abstract Analysis of effect of source parameters and the turbulence on the state of polarization of Gaussian Schell-model beam (GSM) is carried out based on the non-Kolmogorov power spectrum. The results show that selecting the appropriate source parameters can increase the length of the state of polarization remaining unchanged (hereafter referred to as an L p ), which means improving the effective transmission distance under the polarization modulation. Several GSM beams with different parameters are numerically calculated to verify the conclusion. These results provide a light source design and are helpful to the free space optical communication.

部分相干反常椭圆空心高斯光束在非Kolmogorov湍流中的光束漂移

部分相干反常椭圆空心高斯光束在非Kolmogorov湍流中的光束漂移

Linearization theory of small scale thermal blooming effect in non-Kolmogorov turbulent atmosphere

High energy laser beams propagating in the atmosphere are subjected to a variety of effects, such as the absorption and scattering of molecule and aerosol, atmospheric turbulence effects, thermal blooming effects, and the interaction between turbulence and thermal blooming. In general, these atmospheric propagation effects degrade laser beam quality and reduce the beam power concentration at the target. With adaptive optics compensation, the beam quality can be modified. But small-scale perturbation has developed and the phase compensation becomes unstable in some conditions. The performance of adaptive-optics system is degraded, which effects can be well explained by small-scale linear theory of thermal blooming. However previous theoretical studies of small-scale thermal blooming focused on the Kolmogorov turbulence. In the past decade, experimental evidence has shown significant deviations from Kolmogorov model in certain portions of the atmosphere. An generalized power-law of non-Kolmogorov turbulence model has been introduced, which becomes quite popular in the optical propagation community. Numerous theoretical and developmental efforts have been made based on non-Kolmogorov turbulence model in recent years. Thus it is very meaningful and imperative to explore the theoretical mechanism of high energy laser phase compensation with non-Kolmogorov turbulence.In this study, the Strehl ratio of the thermal blooming phase compensation is generalized with the non-Kolmogorov turbulence spectrum, and the analytical expression is obtained based on the linear theory of small-scale thermal blooming. The influence of the turbulence spectrum on the phase compensation of the high energy laser is analyzed. The results show that the turbulence spectrum has an important influence on the phase compensation of turbulent thermal blooming effect. Under the same turbulence Fresnel number condition, the compensation effect is worse when the spectral index is closer to 3 and the compensation effect is better when the spectral index is close to 4. Under the same atmospheric coherence length condition or under the same turbulence refractive index constant condition, the Strehl ratio decreases with the increase of the thermal blooming effect when the spectral index is close to 3 and the decline rate of the Strehl ratio is slower when the turbulence spectrum index is close to 4. This is because as the turbulence spectrum exponent increases, the logarithmic amplitude fluctuation slows down due to the interaction between turbulence and thermal blooming. These theoretical results can provide some scientific bases and theoretical guidance for the practical applications of high energy laser transmission.

Effects of inner and outer scale on beam spreading for a Gaussian wave propagating through anisotropic non-Kolmogorov turbulence

Effects of inner and outer scale on beam spreading for a Gaussian wave propagating through anisotropic non-Kolmogorov turbulence

Correlation singularities of a partially coherent radially polarized beam in non-Kolmogorov turbulence

We have investigated the correlation singularities of a partially coherent radially polarized beam propagating through non-Kolmogorov turbulence. An analytical expression for the radius of a ring dislocation is derived. It is shown that the dependence of the radius of a ring dislocation on spatial coherence width in non-Kolmogorov turbulence is quite different from that in free space. The relation between spatial coherence width and beam width affects the change trends of the radius of a ring dislocation versus spatial coherence width. For different value ranges of the power law, the change of the radius of a ring dislocation with power law has an opposite trend. It is also found that the propagation distance plays an important role in determining the change of the radius of a ring dislocation. Our results will be useful in measuring the statistical properties of a random medium or a random field.

Beam wander and M2-factor of partially coherent electromagnetic hollow Gaussian beam propagating through non-Kolmogorov turbulence

Propagation formulae for M2-factor and beam wander of partially coherent electromagnetic hollow Gaussian (PCEHG) beam in non-Kolmogorov turbulence are derived based on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function. Our results indicate that the normalized M2-factors of PCEHG beam with larger beam order, waist width, inner scale of turbulence, the generalized exponent parameter, and smaller transverse coherent widths, outer scale of turbulence, the generalized structure parameter are less affected by the turbulence. The root mean square beam wander and relative beam wander are more obvious for PCEHG beam with smaller beam order, larger inner and outer scales of turbulence, exponent parameter, transverse coherent widths, and the generalized structure parameter. What is more, the beam wander properties of PCEHG beam in non-Kolmogorov turbulence are very different from M2-factor and spreading properties of beam in turbulence.

Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence

A new ring Airy Gaussian (RAiG) vortex beam generation method by coherent combination of Gaussian beam array has been proposed. To validate the feasibility of this method, the propagation properties of the RAiG vortex beam and the coherent combining beam in vacuum have been studied and analyzed. From the comparisons of the intensity distributions and phase patterns along the propagation path, we can conclude that the coherent combining beam has the same properties as those of the ideal RAiG vortex beam. So this method can be used to obtain RAiG vortex beam in practice. Then the general analytical expression of the root-mean-square (RMS) beam width of the RAiG vortex beam, which is appropriately generated by coherent combining method, through anisotropic non-Kolmogorov turbulence has been derived. The influence of anisotropic turbulence on RMS beam width of the generated RAiG vortex beam has been numerically calculated. This generation method has good appropriation to the ideal RAiG vortex beam and is very useful for deriving the analytical expression of propagation properties through a random media. The conclusions are useful in practical applications, such as laser communication and remote sensing systems.

Scintillations of higher order laser beams in anisotropic atmospheric turbulence.

The scintillation index of higher order laser beams is examined when such beams propagate in anisotropic atmospheric turbulence. Anisotropy is introduced through non-Kolmogorov atmospheric turbulence. The scintillation index results are obtained by employing the Rytov method solution; thus the results are valid for weak anisotropic atmospheric turbulence and for horizontal links. Variations in the scintillations are shown for various higher order laser modes against the changes in the optical source size, power law exponent of anisotropic non-Kolmogorov spectrum, anisotropic factors, and link length. Our results can be used in the design of optical wireless communication systems used between airplanes.