Anisotropic Atmospheric Turbulence Research Articles

Anisotropic atmospheric turbulence and partially coherent self-focusing vortex beams for wireless optical communication

It is generally believed that employing partially coherent light for wireless optical communication can improve the communication performance. In this paper, we show that whether the partial coherence contributes positively or negatively depends on the turbulence strength of the link. For illustration, partially coherent self-focusing vortex (PCSFV) beams propagating via anisotropic atmospheric turbulence at different altitudes are investigated. It is shown that lower coherence improves focusing and helps the signal receiving only for low-altitude and strong turbulence. There is an altitude related to the critical turbulence strength of the turbulence at which the communication performance is almost independent of the initial coherence of the beam. Besides, we focus on the channel capacity as well as the bit error rate (BER) for a high-altitude link. The results show that stronger anisotropy and larger inner scale parameters lead to higher average channel capacity with lower BER. By adjusting the beam waist or receiving aperture size, the communication performance can be further maximized. Our study represents the pioneering effort to assess the different impacts of the initial partial coherence on the receiving probability and validate the potential applications of PCSFV beams in wireless optical communications.

Modulation effect of focusing mirror on beam propagation through anisotropic turbulence

In this study, we modulated the Bessel-Gaussian (BG) beam using a focusing mirror to enhance the performance of wireless optical communication (WOC) while considering the angles between turbulence cells and the transmitted direction when beams propagate through anisotropic atmospheric turbulence along a slant path. Numerical results reveal that when the BG beam is modulated by a focusing mirror with a focusing length of 1 km, the detection probability of orbital angular momentum (OAM) is increased by 9.06% compared with the unmodulated BG beam when the OAM quantum number is 1. Simultaneously, this modulation method effectively reduces the bit error rate and enhances the channel capacity in OAM-based WOC. Furthermore, we observed that the smaller the OAM number, the better the effect of the modulation. Through our analysis, we identified that the most significant distortions in OAM mode propagation occur at the exponential parameter approximately 3.1 in the modified von Karman spectrum. Moreover, we demonstrated that the effects of the anisotropic tilt angle can not be negligible for beams through a slant path. Therefore, the modulation of the focusing mirror, in combination with a well-designed propagation direction that takes appropriate angles into account, can significantly improve the overall quality and performance of optical communication systems.

Propagation properties of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam through anisotropic atmospheric turbulence.

Using the extended Huygens-Fresnel principle and the Rytov approximation, the analytical formula for the propagation of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam (PCEShVB) in anisotropic atmospheric turbulence has been theoretically derived. Detailed studies have been conducted on the evolution characteristics of the average intensity, the degree of coherence (DOC), and the degree of polarization (DOP) of the beam in turbulence. The results show that during propagation, the intensity distribution of the beam will exhibit a spiral structure, and the overall distribution of the light spots will rotate in a direction related to the sign of the topological charge. The DOC distribution of PCEShVB will display a pattern reminiscent of beam interference fringes with an increase in propagation distance, with the number of "interference fringes" greatly impacted by the hyperbolic sine parameter. Furthermore, PCEShVB with a large initial coherent length and hyperbolic sine parameter will increase the degree of separation of the spots and yield a large DOP. Finally, for the validation of the theoretical findings, the random phase screen method was employed to simulate the propagation of PCEShVB through anisotropic atmospheric turbulence. The studies revealed a consistent alignment between the simulation results and the theoretical predictions.

Crosstalk characteristics of orbital angular momentum of focused perfect vortex beam in atmospheric turbulence

The perfect optical vortex beam (POV) is a special kind of vortex beam, whose radius is independent of its orbital angular momentum (OAM) mode, but the atmospheric turbulence (AT) causes crosstalk between different topological charges, which is a serious challenge in OAM-based communication system. We establish a theoretical model with a turbulence suppression effect for deriving the spiral spectrum of a focused perfect optical vortex beam (FPOV) after propagation through anisotropic AT. Through numerical analysis, we simulate the behavior of FPOV under different turbulence and beam parameters to better understand the effect of the received probability and its corresponding modal crosstalk under various conditions. In addition, the simulation of AT uses the multi-phase screen method to verify the theoretical results. The results show that the changes in topological charge, wavelength, receiving aperture, beam waist, and hollow radius all have an influence on the received probability. Also, some strategies for selecting turbulence parameters to reduce modal crosstalk in anisotropic AT are also discussed. The focus would reduce the effect of turbulent aberrations on the signal OAM mode received probability, and the FPOV provided better performance than the POV, which may be useful in OAM-based free space optical communication.

Partially coherent anomalous vortex beam in anisotropic turbulence

Propagation properties of a partially coherent anomalous vortex beam (PCAVB) through the anisotropic turbulent atmosphere are studied. Based on the generalized anisotropic von-Karman spectrum and Rytov approximation, the mathematical expressions of mode probability, energy content, and spiral spectrum of the PCAVB are obtained. The effects of anisotropic turbulence and source parameters on the PCAVB’s signal orbital angular momentum (OAM) modal crosstalk are investigated. According to numerical findings, the transmission performance of the PCAVB can be improved by increasing the anisotropy coefficient, the beam order, the partial coherence length of the beam source, or reducing the OAM mode. In some instances, the PCAVB also shows stronger resistance to turbulence than the partially coherent Laguerre-Gaussian beam (PCLGB). This research may be helpful for constructing optical vortex communication systems as well as for comprehending the optical transmission mechanism in turbulent fluids.

Propagation of Lorentz-Gaussian elliptical multi-Gaussian correlated Schell-Model beam in anisotropic turbulence

The beam spreading, spectral degree of coherence and evolution behavior of the intensity profile of partially coherent Lorentz-Gaussian elliptical multi-Gaussian correlation Schell-Model beam propagating in anisotropic atmospheric turbulence are studied. The analytical expressions of cross-spectral density function, as well as root mean square (rms) beam width, are derived based on the extended Huygens-Fresnel principle and the relationship of Lorentz distribution and Hermitian Gaussian function. With the increases of propagation distance, the elliptical beam will first evolve into Gaussian beam and then change back to elliptical beam. In anisotropic atmospheric turbulence, the influence of the inner scale of turbulence on the spectral degree of coherence and rms beam width are obviously greater than that of the outer scale. For Lorentz-Gaussian elliptical multi-Gaussian correlated Schell-Model beams, better propagation performance was found in anisotropic atmospheric turbulence with larger anisotropic factor and smaller inner scale.

Evolution Properties of a Partially Coherent Twisted Laguerre-Gaussian Pulsed Beam Propagating through Anisotropic Atmospheric Turbulence

Analytical expressions for the cross-spectral density matrix of a partially coherent twisted Laguerre-Gaussian pulsed (PCTLGP) beam in anisotropic atmospheric turbulence are derived based on the extended Huygens–Fresnel principle. Numerical results indicate that the atmospheric turbulence induces the degeneration of the spectral intensity distribution of the PCTLGP beam, and the PCTLGP beam also shows different evolution properties on propagation in weaker turbulence and stronger turbulence. The PCTLGP beam with a negative twisted factor exhibits an advantage over the Laguerre-Gaussian pulsed beam for reducing the atmospheric turbulence-induced degeneration, and this advantage is further strengthened with increasing the topological charge, mode order and absolute value of the twisted factor. In addition, we also find that the pulse duration will affect the spectral intensity of the PCTLGP beam in turbulence. This kind of beam will show potential application value in free-space optical communications and remote sensing.

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.

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.

Propagation characteristics of partially coherent twisted Laguerre-Gaussian beam in atmospheric turbulence with anisotropy

Analytical formulas for average intensity of partially coherent twisted Laguerre-Gaussian beam (PCTLGB) propagating through anisotropic atmospheric turbulence are derived based on the extended Huygens–Fresnel principle. Our results indicate that PCTLGB gradually evolves from dark hollow distribution to flat-topped distribution and finally degenerates to Gaussian distribution both in free space and atmospheric turbulence. We also find that the effect of atmospheric turbulence on propagation characteristics for PCTLGB can be effectively reduced by adjusting twisted factor, topological charge and beam order. An important result is that PCTLGB has stronger anti-turbulence ability when vortex phase and twisted phase have the same chirality, and it can resist atmospheric turbulence more effectively than the beam without twisted phase under the same conditions. Our results will be useful in free space optical communication, lidar detection and imaging.

Properties of an electromagnetic twisted Gaussian Schell-model array beam propagating in anisotropic atmosphere turbulence

The effect of anisotropic atmosphere turbulence on propagation characteristics of an electromagnetic twisted Gaussian Schell-model array (EM TGSMA) beam is investigated. An analytical expression for the cross-spectral density function of such beam propagating through anisotropic turbulent atmosphere is derived and used to explore the evolutionary behavior of the spectral intensity, degree of polarization (DOP) and degree of coherence (DOC). An example illustrates the fact that twisted strength and anisotropic turbulent factors have an important impact on the behavior of spectral density, DOC and DOP, in particular. The rotation angle of the array beams can also be controlled by adjusting twisted strength. Furthermore, strong anisotropic turbulence was also found to cause significant mergence of the array beams. Our results might be beneficial for free-space communications of the partially coherent beams endowed with twist.

Spatial Property of Optical Wave Propagation through Anisotropic Atmospheric Turbulence

For the free-space optical (FSO) communication system, the spatial coherence of a laser beam is influenced obviously as it propagates through the atmosphere. This loss of spatial coherence limits the degree to which the laser beam is collimated or focused, resulting in a significant decrease in the power level of optical communication and radar systems. In this work, the analytic expressions of wave structure function for plane and spherical wave propagation through anisotropic non-Kolmogorov turbulence in a horizontal path are derived. Moreover, the new expressions for spatial coherence radius are obtained considering different scales of atmospheric turbulence. Using the newly obtained expressions for the spatial coherent radius, the effects of the inner scales and the outer scales of the turbulence, the power law exponent, and the anisotropic factor are analyzed. The analytical simulation results show that the wave structure functions are greatly influenced by the power law exponent α , the anisotropic factor ζ , the turbulence strength σ ~ R 2 , and the turbulence scales. Moreover, the spatial coherence radiuses are also significantly affected by the anisotropic factor ζ and the turbulence strength σ ~ R 2 , while they are gently influenced by the power law exponent α and the inner scales of the optical waves.

Evolution properties of partially coherent radially polarized Laguerre–Gaussian vortex beams in an anisotropic turbulent atmosphere

Analytical formulas for the cross-spectral density matrix of a partially coherent radially polarized Laguerre-Gaussian vortex (PCRPLGV) beam in anisotropic atmospheric turbulence are derived based on the extended Huygens-Fresnel principle. The evolution laws of statistical properties of a PCRPLGV beam in turbulence, such as the average intensity, degree of coherence (DOC) and degree of polarization (DOP), are investigated in detail. It is found that the atmospheric turbulence induces degeneration of the intensity distribution of a PCRPLGV beam on propagation, and some new properties, such as self-shaping and self-rotating, will appear on propagation due to vortex phase. In addition, in order to verify our theoretical results, we combined the complex screen method and multi-phase screens method to simulate the propagation of PCRPLGV beam in atmospheric turbulence. And the studies indicate that the simulation results are consistent with the theoretical predictions. Our results will be useful in some potential applications, such lidar detection, remote sensing and free-space optical communications.

Reducing orbital angular momentum modes crosstalk of Bessel Gaussian beams in anisotropic atmospheric turbulence with Localized Wave

Rytov theory is employed to analyze the spiral spectrum and orbital angular momentum (OAM) crosstalk effects of partially coherent Bessel Gaussian localized wave (BGLW) in the completely weak to strong anisotropic atmospheric turbulence channel. Propagation quality of OAM mode carried by BGLW is superior to that of the traditional Bessel Gaussian (BG) beam in the turbulence, which provide a good choice for OAM based optical communication. Atmospheric turbulence grows up with the increase of Reynolds number, the effects of the atmospheric turbulence parameters (anisotropy parameters, power spectrum index and refractive index structure constant) on the OAM modal detection probability also enhance. The influence of atmospheric turbulence can be reduced by increasing the half pulse width of the input pulse and wavelength of BGLW. The research results provide a theoretical basis for the performance evaluations and parameters optimization of practical OAM based optical communication technology.

Propagation factor of partially coherent radially polarized vortex beams in anisotropic turbulent atmosphere.

We skillfully combined the cosine theorem with the second moment theory and the Wigner distribution function and derived the analytical expressions of the propagation factor (M2-factor) of a partially coherent radially polarized vortex beam (PCRPVB) in atmospheric turbulence. Then, we comparatively studied the propagation factors of a PCRPVB and a partially coherent electromagnetic vortex beam (PCEVB) in atmospheric turbulence. The results show that a PCRPVB has a smaller value of a relative M2-factor than a PCEVB, which means that a PCRPVB has a stronger ability to resist atmospheric turbulence than a PCEVB. To confirm our theoretical studies, the hyperbolic fitting method is combined with the random phase screen (RPS) to simulate the M2-factor of a PCRPVB and a PCEVB through atmospheric turbulence. The study results indicate that the theoretical values agree well with the simulated values. Our results may find applications in free-space optical communications and remote sensing.

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.

Recording optical vortices in azo polymer films by applying holographic method

In this paper the optical vortices with topological charge <i>q</i> = –1, 1, 2, 4 are recorded in azo polymer films by using holographic technology. The forked holographic gratings formed by the Gaussian beam and optical vortex beam are recorded in the sample films, the original forked holographic grating and the recording rate are analyzed. The vortex beam is reconstructed by illuminating the sample film with a reference beam, and the recording quality is analyzed. Also the erasability and durability of the sample are tested. The experimental results show that the recording rates of vortex beams with different topological charges are relatively uniform, which means that the optical vortices with different topological charges can be recorded at the same speed. The forked holographic grating of the high-order optical vortex splits in the recording process due to the disturbances, such as anisotropic nonlinear light, atmospheric turbulence, and background light field. However, the split vortex beam still maintains a stable ring structure. The reconstructed optical vortex and the original optical vortex are highly consistent in morphology, and the interference fringes of the reconstructed optical vortices are highly consistent with the original vortex holographic gratings, indicating that the topological charge information in the optical vortices can be effectively recorded and read out. The recorded information can be erased by heating the sample to about 97 ℃, and new information can be re-recorded after cooling. There appears no fatigue in the sample after the information has been erased 100 times and good durability is still retained. Optical vortices theoretically have infinite states of topological charges, based on which great success is achieved in optical communication and information encoding. Therefore, storing and reading information of topological charges in optical vortices may have potential applications in optical information storage.

Propagation of orbital angular momentum modes carried by hollow vortex Gaussian beams in anisotropic atmospheric turbulence.

We establish the propagation model of orbital angular momentum (OAM) modes carried by hollow vortex Gaussian (hvG) beams propagating in anisotropic atmospheric turbulence. Effects of light source parameters and atmospheric conditions on the OAM mode propagation performance are investigated in detail. The findings indicate the hvG beam with a smaller OAM quantum number, a larger beam order, or a longer source wavelength has more robust resistance to atmospheric turbulence interference. The waist width of the light source has different influences on the OAM mode propagation at different propagation distances. Atmospheric turbulences with larger values of anisotropy, inner-scale factor, non-Kolmogorov power spectrum index, and altitude are favorable for the OAM mode propagation. These research results are conducive to optimizing the design of light sources and space wireless communication systems with hvG beams.

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.

Effect of the Zenith Angle on Optical Wave Propagation in Anisotropic Non-Kolmogorov Atmospheric Turbulence: A New Experiment-Based Model

The spectral properties of the structural function of atmospheric turbulence can differ in the vertical and horizontal directions. Taking into account the influence of this anisotropy on the signal along the direction of propagation at an angle y, to the horizon, can be useful in modeling and interpreting the results of measurements. Usually when modeling the propagation of an electromagnetic signal in the anisotropic turbulent atmosphere, the effective anisotropic parameter η is introduced. In the latter case, the dependence of the wave vector is given by the expression k = √ηk <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> +k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , where k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> is a vertical component of k, and k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> is horizontal. However, the spectral index of the structural function, α, remains constant and independent of y. Here, we consider the structural function of atmospheric turbulence with dependence on the propagation angle y. The existing experimental data show that the spectral index α is a function of height and y. The dependence of the α parameter on y is introduced, and it is determined from the experimental measurements of atmospheric turbulent spectra. As an example of using the proposed approach, we present the results of calculations of the log-amplitude variance and propagation of a Gaussian beam through the anisotropic turbulent atmosphere.