Weak non-Kolmogorov Turbulence Research Articles

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.

An Empirical Model of Angle-of-Arrival Variance for a Gaussian Wave Propagation through Non-Kolmogorov Turbulence

This paper proposes an empirical model of the angle-of-arrival (AOA) variance for a Gaussian wave propagating through the weak non-Kolmogorov turbulence. The proposed model is approximately expressed as the linear weighted average between the AOA variances of the plane and spherical waves. The Monte Carlo method is applied to validate the proposed model. The numerical simulations indicate that, under the geometrical optics approximation, the AOA variance for a Gaussian wave is insensitive to the change of the diffraction parameter and can be closely approximated by a simple linear relationship in the refraction parameter. These two properties ensure the validity of the empirical model.

Self-recovery effect of orbital angular momentum mode of circular beam in weak non-Kolmogorov turbulence.

It is generally true that the orbital angular momentum (OAM) mode persistently degenerate when a vortex beam propagates in the atmospheric turbulence. Here, however, we unveil an interesting self-recovery effect of OAM mode of the circular beam (CiB) in weak non-Kolmogorov turbulence. We show that the CiB displays the self-focusing effect and has clear focus in the weak non-Kolmogorov turbulence if we choose proper complex parameters, and the detection probability of the original OAM mode reaches the maximum at the focus. Our study proposes a method to alleviate the turbulent effects on OAM-based communication.

Irradiance Scintillation Index for a Gaussian Beam Based on the Generalized Modified Atmospheric Spectrum with Aperture Averaged

This paper investigates the aperture-averaged irradiance scintillation index of a Gaussian beam propagating through a horizontal path in weak non-Kolmogorov turbulence. Mathematical expressions are obtained based on the generalized modified atmospheric spectrum, which includes the spectral power law value of non-Kolmogorov turbulence, the finite inner and outer scales of turbulence, and other optical parameters of the Gaussian beam. The numerical results are conducted to analyze the influences of optical parameters on the aperture-averaged irradiance scintillation index for different Gaussian beams. This paper also examines the effects of the irradiance scintillation on the performance of the point-to-point optical wireless communication system with intensity modulation/direct detection scheme.

Temporal power spectra of angle of arrival fluctuations for optical waves propagating through moderate-to-strong non-Kolmogorov refractive turbulence

The temporal statistical property of angle of arrival (AOA) fluctuations is investigated in detail both analytically and numerically. New analytic expressions for the temporal power spectra of AOA fluctuations are derived with the extended Rytov theory for both plane and spherical waves propagating through moderate-to-strong (or strong) non-Kolmogorov atmospheric turbulence. They cover a more wide range of turbulence strength, and can reduce correctly to previously published analytic expressions for the weak non-Kolmogorov turbulence case. The final results indicate that, as turbulence strength increases up to moderate-to-strong (or strong) turbulence regime, the expressions derived in this work deviates from those obtained via the Rytov theory and the discrepancy increases with the increased turbulence strength. These results are useful for the understanding the potential impact of derivations from the standard non-Kolmogorov spectrum.

Influence of asymmetry turbulence cells on the angle of arrival fluctuations of optical waves in anisotropic non-Kolmogorov turbulence.

Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. Very recent analyses of angle of arrival (AOA) fluctuations of an optical wave in anisotropic non-Kolmogorov turbulence have adopted the assumption that the propagation path was in the z-direction with circular symmetry of turbulence cells maintained in the orthogonal xy-plane throughout the path, and one single anisotropy factor was adopted in the orthogonal xy-plane to parameterize the asymmetry of turbulence cells or eddies in both horizontal and vertical directions. In this work, the circular symmetry assumption of turbulence cells or eddies in the orthogonal xy-plane is no longer required, and two anisotropy parameters are introduced in the orthogonal xy-plane to investigate the AOA fluctuations. In addition, 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. With the Rytov approximation theory, new theoretical models for the variance of AOA fluctuations are developed for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. When the two anisotropic parameters are equal to each other, they reduce correctly to the recently published results (the circular symmetry assumption of turbulence cells or eddies in the orthogonal xy-plane was adopted). Furthermore, when these two anisotropic parameters equal one, they reduce correctly to the previously published analytic expressions for the cases of optical wave propagation through weak isotropic non-Kolmogorov turbulence.

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.

Influence of moderate-to-strong non-Kolmogorov turbulence on the imaging system by atmospheric turbulence MTF

The atmospheric turbulence modulation transfer function (MTF) which describes the degrading effect of atmospheric turbulence on imaging system is investigated theoretically for plane and spherical waves propagating through moderate-to-strong non-Kolmogorov turbulence. In the investigation, the effective non-Kolmogorov spectral model is adopted, and it modifies the conventional non-Kolmogorov spectral model with a modified frequency filter function. The new expressions cover a more wide range of non-Kolmogorov turbulence strength, and reduce correctly to previously published analytic expressions for both weak non-Kolmogorov turbulence and moderate-to-strong (or strong) Kolmogorov turbulence cases. Numerical calculations show that the MTF model derived in this work deviates from those obtained with the Rytov theory as turbulence strength increases up to moderate-to-strong (or strong) non-Kolmogorov turbulence regime.

Effects of non-Kolmogorov turbulence on the orbital angular momentum of Hankel–Bessel–Schell beams

Abstract We model the effects of the turbulence on the spread and crosstalk of the spiral spectrum of the orbital angular momentum (OAM) states for Hankel–Bessel–Schell (HBS) beams in paraxial and weak non-Kolmogorov turbulence channel. Our results show that HBS beam is a better light source which has the ability to weaken turbulence spreading of the beams and can mitigate the effects of turbulence on the detection probability of the signal OAM state due to its nondiffraction property. The detection probability of the signal OAM state for HBS beams in the non-Kolmogorov turbulence decreases with the increase of propagation distance, the generalized refractive-index structure parameters, OAM quantum number and non-Kolmogorov turbulence-parameters and with the decrease of the source spatial coherence and the wavelength of the beams. The crosstalk probability is symmetrical and has an opposite trend of the detection probability of the signal OAM state for HBS beams, and the spatial incoherence of the source increases the crosstalk effect of atmospheric turbulence among the OAM states and the spread of the spiral spectrum. Our results also show that increasing the values of non-Kolmogorov parameter and quantum number l0, will increase the spread of the spiral spectrum of the OAM states for HBS beams.

Cross beam scintillations in non-Kolmogorov medium

For the collimated and focused cross beams, the on-axis scintillation index is evaluated when these beams propagate in weak non-Kolmogorov turbulence. In the limiting cases, our solution correctly reduces to the known Gaussian beam scintillations in Kolmogorov turbulence. For both the collimated and the focused cross beams, large power law exponent of the non-Kolmogorov turbulence is found to result in larger scintillations. Evaluating at a fixed power law exponent, the scintillation index of the collimated (focused) cross beam is higher (lower) than the collimated (focused) Gaussian beam scintillation index. When the asymmetry of the collimated (focused) cross beam increases, the scintillations increase (decrease). At a given cross beam configuration, change in the turbulence parameters varies the scintillations in the same manner for all power law exponent values.

Influence of atmospheric turbulence on the transmission of orbital angular momentum for Whittaker-Gaussian laser beams.

We analyze the effects of turbulence on the detection probability spectrum and the mode weight of the orbital angular momentum (OAM) for Whittaker-Gaussian (WG) laser beams in weak non-Kolmogorov turbulence channels. Our numerical results show that WG beam is a better light source for mitigating the effects of turbulence with several adjustable parameters. The real parameters of WG beams γ and W0, which have significant effects on the mode weight, have no influence on the detection probability spectrum. Larger signal OAM quantum number, shorter wavelength, smaller beamwidth and coherence length will lead to the lower detection probability of the signal OAM mode.

Rytov variance equivalence through extended atmospheric turbulence and an arbitrary thickness phase screen in non-Kolmogorov turbulence

An arbitrary thickness phase screen model can describe scintillation index for Gaussian beam propagating through a phase screen more accurate than thin phase screen model. To describing actual scintillation index for Gaussian beam propagating through an extended medium using a phase screen in weak non-Kolmogorov turbulence, the scintillation index and Rytov variance for arbitrary thickness phase screen model are derived. Specially, the ratio of the Rytov variances for a phase screen and extended random media is found under the assumption of equivalence in scintillation index of the two cases. The theoretical results show that the normalized Rytov variance varies with the power law of the turbulence spectrum, the relative thickness of the phase screen, the position of the phase screen, the transmitter beam parameters and the radial position at output plane. The influences of these variables are also simulated. These results will be applied to simulation of adaptive optics and laser communication.

Theoretical expressions of temporal power spectra of irradiance fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

The temporal power spectra of irradiance fluctuations reflect the frequency distribution of temporal statistical property of irradiance fluctuation. In this paper, new analytical expressions of the temporal power spectral models of irradiance fluctuations are developed for optical waves propagating through weak non-Kolmogorov turbulence with horizontal path. They are derived with the general modified atmospheric spectral model, and they consider the finite turbulence inner and outer scales, and have a general spectral power law value in the range of 3 to 4 instead of the standard power law value of 11/3. Numerical calculations are conducted to analyze the influence of non-Kolmogorov weak turbulence on the temporal power spectra of irradiance fluctuations.

Scintillation and BER for optimum sinusoidal Gaussian beams in weak non-Kolmogorov turbulence

The scintillation index and the average bit error rate (BER) are evaluated for the optimum sinusoidal Gaussian beams in weak non-Kolmogorov turbulence. The beam parameters that minimize the scintillation index and the average BER are stated and such beams are denoted as the optimum beams. For the collimated Gaussian, cos- and cosh-Gaussian beams, the scintillations increase as the power law exponent, α increases. Cos- and cosh-Gaussian beams that have larger absolute displacement parameters are found to exhibit larger scintillations especially at small α. Larger focal length and larger source size of cos-Gaussian beams induce reduction in the scintillations. When the propagation distance is large, the power law exponent is small and the source size is large, the scintillations of the optimum beams tend to decrease. Small power law exponent and large source size reduce the average BER. The optimum beam is shown to exhibit the smallest average BER for any α.

Analysis of the temporal power spectral models of angel of arrival fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

New analytical expressions for the temporal power spectral models of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through weak non-Kolmogorov turbulence. They consider the finite turbulence inner and outer scales, and have a general power law value in the range of 3–4 instead of the standard power law value of 11/3. The results derived in this work can reduce correctly to the previously published analytic expressions for the case of plane and spherical waves propagation through Kolmogorov turbulence case. These results are useful for the understanding the potential impact of derivations from the standard Kolmogorov spectrum.

Analytical expressions for the angle of arrival fluctuations for optical waves’ propagation through moderate-to-strong non-Kolmogorov refractive turbulence

The effects of moderate-to-strong non-Kolmogorov turbulence on the angle of arrival (AOA) fluctuations for plane and spherical waves are investigated in detail both analytically and numerically. New analytical expressions for the variance of AOA fluctuations are derived for moderate-to-strong non-Kolmogorov turbulence. The new expressions cover a wider range of non-Kolmogorov turbulence strength and reduce correctly to previously published analytic expressions for the cases of plane and spherical wave propagation through both weak non-Kolmogorov turbulence and moderate-to-strong Kolmogorov turbulence cases. The final results indicate that, as turbulence strength becomes greater, the expressions developed with the Rytov theory deviate from those given in this work. This deviation becomes greater with stronger turbulence, up to moderate-to-strong turbulence strengths. Furthermore, general spectral power law has significant influence on the variance of AOA fluctuations in non-Kolmogorov turbulence. These results are useful for understanding the potential impact of deviations from the standard Kolmogorv spectrum.

Irradiance scintillation considering finite turbulence inner scale for optical wave propagating through weak non-Kolmogorov turbulence

The turbulence inner scale plays an important role in investigating the irradiance scintillation index for optical wave propagating through atmospheric turbulence. However, previous expressions of the irradiance scintillation index, which were derived based on the general non-Kolmogorov spectral model, did not consider the influences of finite turbulence inner scale. In this study, based on the generalized exponential spectral model for non-Kolmogorov atmospheric turbulence, theoretical expressions of the irradiance scintillation index are derived for plane and spherical optical waves propagating through weak turbulence. The new expressions have considered the influences of the finite turbulence inner scale and the receiver aperture on the irradiance scintillation index. Numerical simulations are performed to analyze these parameters’ influences.

Analysis of optical waves propagating through moderate-to-strong non-Kolmogorov turbulence

The turbulence effect models derived with the Rytov theory method cannot be applied in the analysis of moderate-to-strong non-Kolmogorov turbulence. In this work, new expressions of the temporal power spectra of irradiance fluctuations are derived theoretically for optical waves propagating through moderate-to-strong non-Kolmogorov turbulence. They are developed under Andrews' assumption that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations of the optical wave. A wide range of turbulence strength is considered instead of a limited range for weak non-Kolmogorov turbulence. These expressions have general spectral power law values in the range 3 to 4 instead of the standard power law value of 11/3 for Kolmogorov turbulence. Calculations are performed to analyze turbulence strength and turbulence spectral power law's variations on the final expressions.

Analysis of angle-of-arrival fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

Theoretical expressions of the variance of angle-of-arrival (AOA) fluctuations are derived for plane and spherical optical waves propagating through weak non-Kolmogorov turbulence, and the generalized modified atmospheric spectral model which considers physically the influence of turbulence inner and outer scales is adopted. The new theoretical expressions relate the variance of AOA fluctuations to the receiver aperture, general spectral power law, finite turbulence inner and outer scales, and the optical wavelength. Numerical calculations show that these parameters produce ignorable effects on the AOA fluctuations for weak non-Kolmogorov turbulence.

Analysis of non-Kolmogorov weak turbulence effects on infrared imaging by atmospheric turbulence MTF

The atmospheric turbulence modulation transfer functions (MTF) can be used to describe the degrading effects of atmospheric turbulence on an optical imaging system. In this study, new expressions of long exposure atmospheric turbulence MTF are derived with the generalized atmospheric spectral model for optical waves propagating through non-Kolmogorov weak turbulence with horizontal path. They consider the finite turbulence inner and outer scales, and have a general spectral power law value in the range of 3 to 4 instead of the standard power law value of 11/3. Numerical calculations are conducted to analyze the influence of non-Kolmogorov weak turbulence on the infrared imaging in term of atmospheric turbulence MTF, and results show that the non-Kolmogorov weak turbulence produces less effect on the far infrared imaging.