non-Kolmogorov Turbulence Research Articles

Influence of anisotropic turbulence on the long-range imaging system by the MTF model

Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. In this paper, new analytic expressions for the anisotropic non-Kolmogorov turbulence modulation transfer function (MTF) based on Rytov approximation theory have been derived for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. Compared with the previously published results where the turbulence inner and outer scales were set separately to zero and infinite for calculation convenience, the concept of anisotropy at different turbulence cell scales and finite turbulence inner and outer scales are introduced to study the MTF models. Also, deviations from the classic 11/3 spectral power law behavior for Kolmogorov turbulence are allowed by assuming spectral power law value variations between 3 and 4. To reduce the complexity and calculation time of the analytic results, the asymptotic-fit expressions are also derived and they fit well with the closed-form ones. Calculations are performed to analyze the anisotropic non-Kolmogorov turbulence’s influence on the long-range imaging system.

Characterization of Pseudo-Random-Phase-Plate as a Kolmogorov/non-Kolmogorov turbulence simulator using statistical parameters and the phase structure function

A He-Ne laser lasing at 633 nm is used as source in Mach-Zehnder and Michelson’s interferometric geometries separately, for characterizing a Pseudo-Random-Phase-Plate (PRPP), which presents atmospheric turbulence like conditions to a light beam passing through it. Two methods are employed for the same. The first method involves a comparison of the retrieved phase profiles of sections of PRPP (used as object in one of the arms of Mach-Zehnder Interferometer) with those of numerically generated Kolmogorov phase screens, using statistical parameters commonly used for characterizing optically rough surfaces. The second method uses the phase profiles obtained in Mach-Zehnder (single passage through the object, PRPP) and Michelson’s (double passage through the object, PRPP) interferometric geometries separately for calculating phase structure function, D φ (r). Through both the methods, we try to determine whether the PRPP presents a Kolmogorov or non-Kolmogorov turbulence regime at 633 nm wavelength. A comparison of the two methods shows that the phase structure function analysis provides a better method for such a characterization.

Sensitivity of neutrinos to the supernova turbulence power spectrum: Point source statistics

The neutrinos emitted from the proto-neutron star created in a core-collapse supernova must run through a significant amount of turbulence before exiting the star. Turbulence can modify the flavor evolution of the neutrinos imprinting itself upon the signal detected here at Earth. The turbulence effect upon individual neutrinos, and the correlation between pairs of neutrinos, might exhibit sensitivity to the power spectrum of the turbulence and recent analysis of the turbulence in a two-dimensional hydrodynamical simulation of a core-collapse supernova indicates the power spectrum may not be the Kolmogorov 5/3 inverse power law as has been previously assumed. In this paper we study the effect of non-Kolmogorov turbulence power spectra upon neutrinos from a point source as a function of neutrino energy and turbulence amplitude at a fixed post-bounce epoch. We find the two effects of turbulence upon the neutrinos - the distorted phase effect and the stimulated transitions - both possess strong and weak limits in which dependence upon the power spectrum is absent or evident respectively. Since neutrinos of a given energy will exhibit these two effects at different epochs of the supernova each with evolving strength, we find there is sensitivity to the power spectrum present in the neutrino burst signal from a Galactic supernova.

Wave structure function and long-exposure MTF for laser beam propagation through non-Kolmogorov turbulence

Abstract The degrading effects of atmospheric turbulence on an imaging system can be characterized by the atmospheric modulation transfer function (MTF). In this paper, we derived analytically a new expression for the wave structure function (WSF) of a Gaussian-beam based on the weak fluctuation theory. We assumed the beam-wave is propagating through a horizontal path experiencing isotropic and homogeneous non-Kolmogorov atmospheric turbulence where the power spectrum has a generalized spectral power-law exponent which varies between 3 and 4 instead of the fixed classical Kolmogorov power-law exponent of 11/3. Using the WSF, we derived mathematical expressions for the spatial coherence radius and the long-exposure turbulence MTF of the Gaussian-beam wave. These new expressions were used to analyze the influence of power-law variations and beam sizes on the WSF and quality of imaging systems. The simulation results show that different exponent values produce varying effects on both WSF and imaging systems.

Fiber coupling efficiency for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.

Nowadays it has been accepted that the Kolmogorov model is not the only possible turbulent one in the atmosphere, which has been confirmed by the increasing experimental evidence and some results of theoretical investigation. This has prompted the scientist community to study optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, using the method of effective beam parameters and a non-Kolmogorov power spectrum which has a more general power law instead of standard Kolmogorov power law value 11/3 and a more general amplitude factor instead of constant value 0.033, the fiber coupling efficiency for a Gaussian-beam wave has been derived for a horizontal path in both weak and strong fluctuation regimes. And then the influence of spectral power law variations on the fiber coupling efficiency has been analyzed. It is anticipated that this work is helpful to the investigations of atmospheric turbulence and optical wave propagation in the atmospheric turbulence.

Propagation of Partially Coherent Elegant Hermite-Cosh-Gaussian Beam in Non-Kolmogorov Turbulence**Supported by the National Basic Research Program of China under Grant No 2015CB921000, and the Fundamental Research Funds of Shandong University under Grant No 2014TB018.

Based on the extended Huygens—Fresnel integral, analytical propagation expressions for the rms beam width and angular of partially coherent elegant Hermite cosh Gaussian beam (EHChGB) in non-Kolmogorov turbulence are derived. The effects of exponent value, inner and outer scales of non-Kolmogorov turbulence on partially coherent EHChGB are investigated quantitatively.

Analysis of temporal power spectra for optical waves propagating through weak anisotropic non-Kolmogorov turbulence

Analytic expressions for the temporal power spectra of irradiance fluctuations and angle of arrival (AOA) fluctuations are derived for optical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. In the derivation, the anisotropic non-Kolmogorov spectrum is adopted, which adopts the assumption of circular symmetry in the orthogonal plane throughout the path and the same degree of anisotropy along the propagation direction for all the turbulence cells. The final expressions consider simultaneously the anisotropic factor and general spectral power law values. When the anisotropic factor equals one (corresponding to the isotropic turbulence), the derived temporal power spectral models have good consistency with the known results for the isotropic turbulence. Numerical calculations show that the increased anisotropic factor alleviates the atmospheric turbulence's influence on the final expressions.

SLM-based laboratory simulations of Kolmogorov and non-Kolmogorov anisotropic turbulence.

In this paper, we present a laboratory setup to simulate anisotropic, non-Kolmogorov turbulence. A sequence of numerical phase screens that incorporate the turbulence characteristics were applied to a spatial light modulator placed in the path of a laser beam with a Gaussian intensity profile and the resulting far-field intensity patterns were recorded by a CCD camera. The values of scintillation at the position of the maximum intensity were extracted from the images and compared with theoretical values. Our experimental results show a trend that is in agreement with known theoretical expressions; however, the turbulence rescaling due to anisotropy shows some discrepancy with theory and requires more investigation.

Splitting and combining properties of an elegant Hermite-Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence.

Elegant Hermite-Gaussian correlated Schell-model (EHGCSM) beam was introduced in theory and generated in experiment just recently [Phys. Rev. A 91, 013823 (2015)]. In this paper, we study the propagation properties of an EHGCSM beam in turbulent atmosphere with the help of the extended Huygens-Fresnel integral. Analytical expressions for the cross-spectral density and the propagation factors of an EHGCSM beam propagating in turbulent atmosphere are derived. The statistical properties, such as the spectral intensity, the spectral degree of coherence and the propagation factors, of an EHGCSM beam in Kolmogorov and non-Kolmogorov turbulence are illustrated numerically. It is found that an EHGCSM beam exhibits splitting and combing properties in turbulent atmosphere, and an EHGCSM beam with large mode orders is less affected by turbulence than an EHGCSM beam with small mode orders or a Gaussian Schell-model beam or a Gaussian beam, which will be useful in free-space optical communications.

Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence

The analytical expressions for the spectral degree of coherence, the effective radius of curvature and the propagation factor of the Bessel-Gaussian Schell-model (BGSM) beam in turbulent atmosphere are derived based on the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function (WDF). The evolution properties of BGSM beams propagating in non-Kolmogorov turbulence are investigated by a set of numerical examples. It is demonstrated that the spectral degree of coherence of the BGSM beam evolves into Gaussian profile twice with the increasing of the propagation distance. The turbulence-induced degradation can be remarkably reduced by using the BGSM beam with the proper source parameters. The effects that the generalized refractive-index structure constant, outer and inner scales, and the spectral index of spatial power spectrum of atmospheric turbulence have on the evolution properties of BGSM beams are also discussed in detail.

Classification of coherent vortices creation and distance of topological charge conservation in non-Kolmogorov atmospheric turbulence.

The analytical expressions for the cross-spectral density function of partially coherent sinh-Gaussian (ShG) vortex beams propagating through free space and non-Kolmogorov atmospheric turbulence are derived, and used to study the classification of coherent vortices creation and distance of topological charge conservation. With the increment of the general structure constant and the waist width, as well as the decrement of the general exponent, the inner scale of turbulence and spatial correlation length, the distance of topological charge conservation will decrease, whereas the outer scale of turbulence and the Sh-part parameter have no effect on the distance of topological charge conservation. According to the creation, the coherent vortices are grouped into three classes: the first is the inherent coherent vortices of the vortex beams, the second is created by the vortex beams when propagating through free space, and the third is created by the atmospheric turbulence inducing the vortex beams.

Temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.

In the past decades, both the increasing experimental evidence and some results of theoretical investigation on non-Kolmogorov turbulence have been reported. This has prompted the study of optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, based on the thin phase screen model and a non-Kolmogorov power spectrum which owns a generalized power law instead of standard Kolmogorov power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave is derived in the weak fluctuation regime for a horizontal path. The analytic expressions are obtained and then used to analyze the influence of spectral power law variations on the temporal power spectrum of irradiance fluctuations.

Beam wander of partially coherent array beams through non-Kolmogorov turbulence.

Based on the theory of second moments and non-Kolmogorov spectrum, the beam wander theory is extend to non-Kolmogorov turbulence, the general analytical expression of beam wander in non-Kolmogorov turbulence is derived. Beam wander depends on the non-Kolmogorov turbulence parameters and the initial second moments of the laser beam at the input plane. Taking the Gaussian Schell model array beams as an example, the effects of the generalized exponent parameter, inner scale, and outer scale of non-Kolmogorov turbulence and the beam separation distance, beam number, and coherence degree on the beam wander are studied in detail. It has been shown that the beam wander varies non-monotonically with increasing generalized exponent parameter of the turbulence. Furthermore, it increases as the inner scale decreases or outer scale increases, and decreases as the beam separation distance and beam number increase and the coherence of the beam becomes weaker. Our results also indicate that the beam wander could be reduced by adjusting the beam parameters appropriately.

Effects of non-Kolmogorov turbulence on the spiral spectrum of Hypergeometric-Gaussian laser beams.

We study the effects of non-Kolmogorov turbulence on the orbital angular momentum (OAM) of Hypergeometric-Gaussian (HyGG) beams in a paraxial atmospheric link. The received power and crosstalk power of OAM states of the HyGG beams are established. It is found that the hollowness parameter of the HyGG beams plays an important role in the received power and crosstalk power. The larger values of hollowness parameter give rise to the higher received power and lower crosstalk power. The results also show that the smaller OAM quantum number and longer wavelength of the launch beam may lead to the higher received power and lower crosstalk power.

Inner scale effect on scintillation index of flat-topped beam in non-Kolmogorov weak turbulence.

A simpler generalized expression of irradiance fluctuation for flat-topped beams is presented based on the Born and Rytov perturbation methods. The theoretical expression of the on-axis scintillation index in non-Kolmogorov weak atmospheric optics links is developed using the generalized von Kármán spectrum model, and using the equivalent structure constant that is different for all power-law exponents. The effect of the inner scale on the on-axis scintillation index is examined comprehensively. It is observed that flat-topped beams happen to possess smaller scintillation indices at larger inner scale. The effects of the power law, flat-topped order, source size of the fundamental Gaussian beam, propagation distance, and wavelength are also analyzed.

Anisotropic non-Kolmogorov turbulence phase screens with variable orientation.

We describe a modification to fast Fourier transform (FFT)-based, subharmonic, phase screen generation techniques that accounts for non-Kolmogorov and anisotropic turbulence. Our model also allows for the angle of anisotropy to vary in the plane orthogonal to the direction of propagation. In addition, turbulence strength in our model is specified via a characteristic length equivalent to the Fried parameter in isotropic, Kolmogorov turbulence. Incorporating this feature enables comparison between propagating scenarios with differing anisotropies and power-law exponents to the standard Kolmogorov, isotropic model. We show that the accuracy of this technique is comparable to other FFT-based subharmonic methods up to three-dimensional spectral power-law exponents around 3.9.

Analysis of angle of arrival fluctuations for optical waves' propagation through weak anisotropic non-Kolmogorov turbulence.

Analytical expressions for the variance of angle of arrival (AOA) fluctuations based on the Rytov approximation theory are derived for plane and spherical waves' propagation through weak anisotropic non-Kolmogorov turbulence atmosphere. The anisotropic spectrum model based on the assumption of circular symmetry in the orthogonal plane throughout the path is adopted and it includes the same degree of anisotropy along the direction of propagation for all the turbulence cells size in the inertial sub-range. The derived expressions consider a single anisotropic coefficient describing the turbulence anisotropic property and a general spectral power law value in the range 3 to 4. They reduce correctly to the previously published analytic expressions for the cases of plane and spherical waves' propagation through weak isotropic non-Kolmogorov turbulence for the special case of anisotropic factor equaling one. To reduce the complexity of the analytical results, the asymptotic-fit expressions are also derived and they fit well with the close-form ones. These results are useful for understanding the potential impact of deviations from the standard isotropic non-Kolmogorov turbulence atmosphere.

Accurate measurements of Optical Turbulence with Sonic- anemometers

The minimization of optical turbulence in and around the dome is key to reach optimum performance on large telescopes equipped with adaptive optics. We present the method and preliminary results of in-situ measurements of optical measurements made using sonic-anemometers. We show the impact of correcting the raw data for aliasing, path averaging, pulse sequence delays and Taylors’ hypothesis. Finally, we highlight the occurrence of non-Kolmogorov turbulence which complicates the quantitative impact of the measurements on the telescope's resolution.

Single and double passage interferometric analysis of Pseudo-Random-Phase-Plates

In this paper, we analyze the phase introduced by two Pseudo-Random-Phase-Plates (PRPPs) in the path of a propagating beam, when the PRPPs are inserted as objects (either individually or in-a-combination) in one of the arms of well-known Mach–Zehnder and Michelson's interferometers. A He–Ne laser lasing at 633nm is used as a source for this purpose. We find that both the PRPPs under consideration behave like non-Kolmogorov turbulence simulators, when introduced individually or jointly. We also notice an interesting phenomenon that the nature of turbulence depends upon the number of passages the beam travels through these PRPPs. More specifically, we witness the tendency of approaching towards Kolmogorov turbulence regime on increasing the number of passages through the given PRPP or PRPPs-in-a-combination.

Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beams through non-Kolmogorov turbulence.

Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian (PCESHG) vortex beams through non-Kolmogorov atmospheric turbulence, including the spectral degree of polarization and evolution behavior of coherent vortices and average intensity are investigated in detail by using the extended Huygens-Fresnel principle and the spatial power spectrum of the refractive index of non-Kolmogorov turbulence. It is shown that the motion, creation and annihilation of the coherent vortices of PCESHG vortex beams in non-Kolmogorov turbulence may appear with the increasing propagation distance, and the distance for the conservation of the topological charge depends on the turbulence parameters and beam parameters. In additions, the evolution behavior of coherent vortices, average intensity and spectral degree of polarization vary significantly for different values of the generalized exponent parameter and the generalized refractive-index structure parameter of non-Kolmogorov turbulence, and the beam parameters as well as the propagation distance.