Theoretical analysis of the optical rotational Doppler effect under atmospheric turbulence by mode decomposition

The optical rotational Doppler effect associated with orbital angular momentum provides a new means for rotational velocity detection.In this paper,we investigate the influence of atmospheric turbulence on the rotational Doppler effect.First,we deduce the generalized formula of the rotational Doppler shift in atmospheric turbulence by mode decomposition.It is found that the rotational Doppler signal frequency spectrum will be broadened,and the bandwidth is related to the turbulence intensity.In addition,as the propagation distance increases,the bandwidth also increases.And when C_(n)^(2)≤5×10^(-15)m^(-2/3)and 2z≤2 km,the rotational Doppler signal frequency spectrum width d and the spiral spectrum width d_(0)satisfy the relationship d=2d_(0-1).Finally,we analyze the influence of mode crosstalk on the rotational Doppler effect,and the results show that it destroys the symmetrical distribution of the rotational Doppler spectrum about 2l·Ω/2π.This theoretical model enables us to better understand the generation of the rotational Doppler frequency and may help us better analyze the influence of the complex atmospheric environment on the rotational Doppler frequency.

Propagation of the off-axis superposition of partially coherent beams through atmospheric turbulence

The propagation properties of the off-axis superposition of partially coherent beams through atmospheric turbulence and their beam quality in terms of the mean-squared beam width w（z） and the power in the bucket （PIB） are studied in detail, where the effects of partial coherence, off-axis beam superposition and atmospheric turbulence are considered. The analytical expressions for the intensity, the beam width and the PIB are derived, and illustrative examples are given numerically. It is shown that the maximum intensity/max and the PIB decrease and w（z） increases as the refraction index structure constant Cn^2 increases. Therefore, the turbulence results in a degradation of the beam quality. However, the resulting partially coherent beam with a smaller value of spatial correlation parameter γ and larger values of separate distance Xd and beam number M is less affected by the turbulence than that with a larger value of y and smaller values of Xd and M. The main results obtained in this paper are explained physically.

Scintillation of partially coherent Gaussian–Schell model beam propagation in slant atmospheric turbulence considering inner- and outer-scale effects

Based on the modified Rytov theory and the international telecommunication union-radio （ITU-R） slant atmospheric structure constant model, the uniform scintillation index of partially coherent Gaussian-Schell model （GSM） beam propa- gation in the slant path is derived from weak- to strong-turbulence regions considering inner- and outer-scale effects. The effects of wavelength of beams and inner- and outer-scale of turbulence on scintillation are analyzed numerically. Compar- ison between the scintillation of GSM beams under the von Karman spectrum and that of beams under the modified Hill spectrum is made. The results obtained show that the scintillation index obtained under the von Karman spectrum is smaller than that under the modified Hill spectrum. This study can find theory bases for the experiments of the partially coherent GSM beam propagation through atmospheric turbulence.

Effect of atmospheric turbulence on entangled orbital angular momentum three-qubit state

The entangled orbital angular momentum（OAM） three photons propagating in Kolmogorov weak turbulence are investigated. Here, the single phase screen model is used to study the entanglement evolution of OAM photons. The results indicate that the entangled OAM three-qubit state with higher OAM modes will be more robust against turbulence.Furthermore, it is found that the entangled OAM three-qubit state has a higher overall transmission for small OAM values.

Characteristics of a partially coherent Gaussian Schell-model beam propagating in slanted atmospheric turbulence

On the basis of the extended Huygens-Fresnel principle and the model of the refractive-index structure constant in the atmospheric turbulence proposed by the International Telecommunication Union-Radio Communication Sector,the characteristics of the partially coherent Gaussian Schell-model（GSM） beams propagating in slanted atmospheric turbulence are studied.Using the cross-spectral density function（CSDF）,we derive the expressions for the effective beam radius,the spreading angle,and the average intensity.The variance of the angle-of-arrival fluctuation and the wander effect of the GSM beam in the turbulence are calculated numerically.The influences of the coherence degree,the propagation distance,the propagation height,and the waist radius on the propagation characteristics of the partially coherent beams are discussed and compared with those of the fully coherent Gaussian beams.

Impact of atmospheric turbulence on coherent beam combining for laser weapon systems

The performance of a laser weapon system based on coherent beam combining(CBC)depends on its propagation properties in the atmosphere.In this study,an analytical model based on partial coherent beam combining(PCBC)for assumed coherence coefficients between beams in a CBC lattice was developed.The Kolmogorov model of atmospheric turbulence and the Hufnagel-Valley model of C^(2)_(n) dependence on atmospheric parameters were implemented.Novel simplified metrics were proposed to assess the CBC performance.Several beam profiles(super-Gaussian,truncated Gaussian,etc.)and geometries were analyzed in terms of maximal intensity in the far field.An approximate formula for PCBC efficiency dependent on the Fried radius was proposed.The results of CBC modeling were compared to those of the Gaussian beam propagation model in a turbulent atmosphere.The dependence of CBC performance on the C^(2)_(n) parameter,range,and elevation angle was analyzed.It could be concluded that the application of CBC for medium and long range propagation is impractical without an effective adaptive optics system.

Influences of Atmospheric Turbulence on Image Resolution of Airborne and Space-Borne Optical Remote Sensing System

A new way is proposed to evaluate the influence of atmospheric turbulence on image resolution of airborne and space-borne optical remote sensing system, which is called as arrival angle-method. Applying this method, some engineering examples are selected to analyze the turbulence influences on image resolution based on three different atmospheric turbulence models quantificationally, for the airborne remote sensing system, the resolution errors caused by the atmospheric turbulence are less than 1 cm, and for the space-borne remote sensing system, the errors are around 1 cm. The results are similar to that obtained by the previous Friedmethod. Compared with the Fried-method, the arrival angle-method is rather simple and can be easily used in engineering fields.

ATMOSPHERIC TURBULENCE STRUCTURE AND SPECTRAL CHARACTERISTICS AT NEAR SURFACE LAYER ON TROPICAL COASTS

By use of an observational experiment at the village of Tianwei, Haikou, Hainan province in 1990,characteristic turbulence values such as velocity component spectra and turbulence intensity are studied.The data were mostly obtained in cloudy condition, so that the stability parameter (L) and thermal flux (wt) did not vary diurnally while the turbulent energy and mean-temperature did. The basic characteristics of turbulence spectra are similar to those with fine weather, hems close to local isotropy in the inertial subrange. The velocity spectra agree with the law of "-2/3 th power"in Kolmogrov’s similarity theory. The relationship between turbulent intensity of components δi/U* (i=u,v,w) and stability Z/L is studied follow ins the Monim-Obukhov(M-O) similarity theory. It is shown that the two observe the law of "1/3 th power", though the turbulent intensity and energy are generally larger than those on the flat underlying topography.

BER Performance of FSO Communication System with Differential Signaling over Correlated Atmospheric Turbulence Fading

Free space optical(FSO) communication system with differential signaling possesses the advantage of requiring no channel state information and avoiding computational load or link throughput reduction compared to the systems with conventional receivers. In this work, we investigate bit error rate(BER) performance of this system over partially and fully correlated atmospheric turbulence fading. In order to conduct the above analysis, we obtain a probability density functions(PDF) of the channel fading on the differential signals and derive our instantaneous BER using differential signaling scheme. Based on these results, we develop two closed-form mathematical expressions for the average BER under fully correlated and partially correlated fading in the convergent infinite series confirmed by Cauchy’s ratio test. The accuracy of the derived BER expressions is demonstrated by the Monte Carlo simulations, and the analyses for the effects of the system parameters on the BER performance are provided.

Measurements of atmospheric turbulence parameters at Vainu Bappu Observatory using short-exposure CCD images

We report atmospheric turbulence parameters, namely atmospheric seeing, tilt-anisoplanatic angle(θ_0) and coherence time(Τ_0), measured under various sky conditions, at Vainu Bappu Observatory in Kavalur. Bursts of short exposure images of selected stars were recorded with a high-speed, frame-transfer CCD mounted on the Cassegrain focus of a newly commissioned 1.3 m telescope. The estimated median seeing is ≈ 1.85 " at wavelength of ～ 600 nm, the image motion correlation between different pairs of stars is ～44% for θ0≈ 36" and mean Τ_0 is ≈ 2.4 ms. This work was motivated by the design considerations and expected performance of an adaptive optics system that is currently being planned for the telescope.

Further analysis of scintillation index for a laser beam propagating through moderate-to-strong non-Kolmogorov turbulence based on generalized effective atmospheric spectral model

A new expression of the scintillation index （SI） for a Gaussian-beam wave propagating through moderate-to-strong non-Kolmogorov turbulence is derived, using a generalized effective atmospheric spectrum and the extended Rytov approx- imation theory. Finite inner and outer scale parameters and high wave number ＂bump＂ are considered in the spectrum with a generalized spectral power law in the range of 3-4, instead of the fixed classical Kolmogorov power law of 11/3. The obtained SI expression is then used to analyze the effects of the spectral power law and the inner scale and outer scale on SI under various non-Kolmogorov fluctuation conditions. These results will be useful in future investigations of optical wave propagation through atmospheric turbulence.

Simulation and fabrication of the atmospheric turbulence phase screen based on a fractal model

An atmospheric turbulence phase screen generated using a fractal method is introduced. It is etched onto fused silica and tested in the laboratory. The etched screen has relatively low cost, high resolution, and can be used in the broad waveband under severe temperature conditions. Our results are shown to agree well with the theory.

ATMOSPHERIC TURBULENCE INTENSITY AND DIFFUSION PARAMETER OVER COMPLICATED TOPOGRAPHY OF EASTERN GUANGDONG

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Propagation of partially coherent beams carrying an edge dislocation through atmospheric turbulence along a slant path

This paper derives the explicit expressions for the average intensity, beam width and angular spread of Gaussian Schell-model （GSM） beams with edge dislocation propagating through atmospheric turbulence along a slant path. The propagation of GSM beams with edge dislocation through horizontal atmospheric turbulence can be treated as a special case through a slant one. The propagation properties of GSM beams with edge dislocation through slant atmospheric turbulence are studied, where the influence of edge dislocation parameters including the slope p and off-axis distance d on the spreading of GSM beams with edge dislocation in atmospheric turbulence is stressed. It shows that the spreading of the intensity profile of GSM beams with edge dislocation along a slant path is smaller than that along a horizontal path in the long-distance atmospheric propagation. The larger the slope ｜p｜ and the smaller the off-axis distance ｜d｜ are, the less the beam-width spreading and angular spread of GSM beams with edge dislocation are affected by turbulence. The CSM beams with edge dislocation is less affected by turbulence than that of GSM beams without edge dislocation. The results are illustrated numerically and their validity is interpreted physically.

Basic Pattern in Atmospheric Turbulence Model

From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the projective Riccati equations are applied to solve these atmospheric turbulence models, where much more patterns are obtained, including solitary wave pattern, singular pattern, and so on.

Correcting Wavefront Distortion of Dual-Wavelength Beams Due to Atmospheric Turbulence with a Correction Coefficient

In order to improve the correction effect of the adaptive optical system in coherent optical communication, we investigate the relative distortion between the wavefronts of different wavelengths of the beams transmitted on the near-ground horizontal atmospheric turbulent links emitted by coherent optical communication system. And the situation is analyzed when the wavelength corresponding to the wavefront detected by the wavefront detector and the wavelength corrected by the deformed mirror are different, the influence of the wavelength factor on the adaptive optical system correction. We use a series of trigonometric functions and the Hankel transformation to derive the corrected residual variance and the Strehl ratio between the wavefront distortions of the wavelengths of the dual-wavelength combined beam in atmospheric turbulence. In relation to the parameters of the turbulent environment, the ensemble average of the wavefront difference corresponding to different wavelengths the derived is proposed as the coefficient to correct the dual-wavelength adaptive optical system. The results show that the statistic of the turbulence internal scale has a major influence on the difference between the wavefronts. By adding the correction coefficient, the signal light’s wavefront of the coherent optical communication system can be corrected more effectively by the dual-wavelength adaptive optical closure.

A new method of calculating the orbital angular momentum spectra of Laguerre-Gaussian beams in channels with atmospheric turbulence

Studying orbital angular momentum（OAM） spectra is important for analyzing crosstalk in free-space optical（FSO）communication systems. This work offers a new method of simplifying the expressions for the OAM spectra of Laguerre-Gaussian（LG） beams under both weak/medium and strong atmospheric turbulences. We propose fixing the radius to the extreme point of the intensity distribution, review the expression for the OAM spectrum under weak/medium turbulence,derive the OAM spectrum expression for an LG beam under strong turbulence, and simplify both of them to concise forms.Then, we investigate the accuracy of the simplified expressions through simulations. We find that the simplified expressions permit accurate calculation of the OAM spectrum for large transmitted OAM numbers under any type of turbulence. Finally,we use the simplified expressions to analytically address the broadening of the OAM spectrum caused by atmospheric turbulence. This work should contribute to the concise theoretical derivation of analytical expressions for OAM channel matrices for FSO-OAM communications and the analytical study of the laws governing OAM spectra.

Atmospheric Refractive Turbulence Effect on Diffraction-Limited Infrared Coherent Lidar

This paper, based on the Kavaya-Suni format, discusses the signal-to-noise ratio equation of the diffraction-limited coherent CO 2 lidar in detail, which is applied to atmospheric turbulence. The cumulative SNR and relative SNR, which are all affected by the nonlinear effects of the diffraction-limited Gaussian beam, atmospheric molecule and atmospheric turbulence, are simulated by microcomputer. Six instructions for the optimal design of IR CO 2 Coherent Lidar System, are provided.

Partially coherent Gaussian–Schell model pulse beam propagation in slant atmospheric turbulence

Based on the extended Huygens-Fresnel principle, a two-frequency, two-point cross-spectral density function of partially coherent Gaussian-Schell model pulse （GSMP） beam propagation in slant atmospheric turbulence is derived. Using the Markov approximation method and on the assumption that （w1 - w2）/（w1 ＋ w2） ≤ 1, the theory obtained is valid for turbulence of any strength and can be applied to narrow-band signals. The expressions for average beam intensity, the beam size, and the two-frequency complex degree of coherence of a GSMP beam are obtained. The numerical results are presented, and the effects of the frequency, initial pulse width, initial beam radius, zenith angle, and outer scales on the complex degree of coherence are discussed. This study provides a better understanding of the second-order statistics of a GSMP beam propagating through atmospheric turbulence in the space-frequency domain.

The Theoretical Model of Atmospheric Turbulence Spectrum in Surface Layer

It is shown that the slope of energy spectrum obtained from the velocity solution of Kdv-Burgers equation lies between -5/3 and -2 in the dilogarithmic coordinates paper. The spectrum is very close to one of Kolmogorov's isotropic turbulence and Frisch's intermittent turbulence in inertial region. In this paper, the Kdv-Burgers equation to describe atmospheric boundary layer turbulence is obtained. In the-equation, the 1 / Re corresponds to dissipative coefficient v, Ri1/2 to dispersive coefficient β, then (v/2β)2 corresponds to 1 /Re2 ·Ri. We prove that the wave number corresponding to maximum energy spectrum S(k) decreases with the decrease of stability (i.e., the increase of (v / 2β)2 in eddy-containing region. And the spectrim amplitude decreases with the increase of (v / 2β)2 (i.e., the decrease of stability). These results are consistent with actual turbulence spectrum of atmospheric surface layer from turbulence data.