Double-distance propagation of Gaussian beams passing through a tilted cat-eye optical lens in a turbulent atmosphere

By using the extended Huygens-Fresnel diffraction integral and the method of expanding the aperture function into a finite sum of complex Caussian functions, an approximate analytical formula of the double-distance propagation for Caussian beam passing through a tilted cat-eye optical lens and going back along the entrance way in a turbulent atmosphere has been derived. Through numerical calculation, the effects of incidence angle, propagation distance, and structure constant on the propagation properties of a Gaussian beam in a turbulent atmosphere are studied. It is found that the incidence angle creates an unsymmetrical average intensity distribution pattern, while the propagation distance and the structure constant can each create a smooth and symmetrical average intensity distribution pattern. The average intensity peak gradually deviates from the centre, and the central average intensity value decreases quickly with the increase in incidence angle, while a larger structure constant can bring the average intensity peak back to the centre.

Propagation of Gauss-Bessel beams in turbulent atmosphere

This paper studies the propagation properties of Gauss-Bessel beams in a turbulent atmosphere. Based on the extended Huygens-Fresnel principle, it derives the intensity distribution expression for such beams propagating in a turbulent atmosphere. Then the influence of turbulence and source beam parameters on the beam propagation is studied in great detail. It finds that the intensity distribution of Gauss-Bessel beams will change into Gaussian profile in a turbulent atmosphere, and that stronger turbulence and smaller topological charges will lead to a faster changing.

Effect of turbulent atmosphere on the on-axis average intensity of Pearcey–Gaussian beam

The propagation characteristics of the Pearcey–Gaussian（PG） beam in turbulent atmosphere are investigated in this paper.The Pearcey beam is a new kind of paraxial beam,based on the Pearcey function of catastrophe theory,which describes diffraction about a cusp caustic.By using the extended Huygens–Fresnel integral formula in the paraxial approximation and the Rytov theory,an analytical expression of axial intensity for the considered beam family is derived.Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors,including incident beam parameters and turbulence strengths.

Propagation of cylindrical vector beams in a turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the propagation of cylindrical vector beams in a turbulent atmosphere is investigated. The intensity distribution and the polarization degree of beams on propagation are studied. It is found that the beam profile has a Gaussian shape under the influence of the atmospheric turbulence, and the polarization distribution shows a dip in the cross section as the beam propagates in the turbulent atmosphere. It is also found that the beam profile and the polarization distribution are closely related to beam parameter and atmospheric turbulence.

Propagation properties of stochastic electromagnetic double-vortex beams in a turbulent atmosphere

Based on the extended Huygens-Fresnel principle, we study the propagation properties of stochastic electromagnetic double-vortex beams in a turbulent atmosphere. The result shows that the spreading of partially coherent double-vortex beams can be smaller than that of fully coherent ones. The degree of polarization of this kind of beam will experience change, which is dependent on the degree of polarization of the source plane, the atmospheric turbulence, topological charge, and the spatial coherence. The results may have applications in space optical communication.

Scintillation index of optical wave propagating in turbulent atmosphere

A concise expression of the scintillation index is proposed for a plane optical wave and a spherical optical wave both propagating in a turbulent atmosphere with a zero inner scale and a finite inner scale under an arbitrary fluctuation condition. The expression is based on both the results in the Rytov approximation under a weak fluctuation condition and the numerical results in a strong fluctuation regime. The maximum value of the scintillation index and its corresponding Rytov index are evaluated. These quantities are affected by the ratio of the turbulence inner scale to the Fresnel size.

Slant path average intensity of finite optical beam propagating in turbulent atmosphere

The average intensity of finite laser beam propagating through turbulent atmosphere is calculated from the extended Huygens Fresnel principle. Formulas are presented for the slant path average intensity from an arbitrarily truncated Gaussian beam. The new expressions are derived from the modified von Karman spectrum for refractive-index fluctuations, quadratic approximation of the structure function, and Gaussian approximation for the product of Gaussian function and Bessel function. It is shown that the form of average intensity is not a Gaussian function but a polynomial of the power of the binomial function, Gaussian function, and the incomplete gamma function. The results also show that the mean irradiance of a finite optical beam propagating in slant path turbulent atmosphere not only depends on the effective beam radius at the transmitting aperture plane, propagation distance, and long-term lateral coherence length of spherical wave, but also on the radius of emit aperture.

Wavefront dislocations of Gaussian beams nesting optical vortices in a turbulent atmosphere

A phase singularity of the light field created by interference of two Gaussian singular beams which propagate in a weak and near ground turbulent atmosphere is analyzed by the Rytov approximation and the short-term averaging method of the dislocation-position. We demonstrate that an edge or circular dislocation may be formed by both parallel and coaxial or noncoaxial collimated beams with different or equal beam-width interference. The edge or circular short-term wavefront dislocation of super position field depend on the atmospheric turbulence strength, beam propagation distance, amplitude ratio, dislocation of nesting vortices, and beam-width or beam-width ratio of the individual beams.

Propagation of Helmholtz-Gauss beams in weak turbulent atmosphere

Based on the Rytov approximation of light propagation in weak turbulent atmosphere, the closed-form expressions of field and average irradiance of each one of the four fundamental families of Helmholtz-Gauss （HzG） beams： cosine-Gauss beams, stationary Mathieu-Gauss beams, stationary parabolic-Gauss beams, and Bessel-Gauss beams, which are propagating in weak turbulent atmosphere, are obtained. The results show that the field and average irradiance can be written as the product of four factors： complex amplitude depending on the z-coordinate only, a Gaussian beam, a factor of complex phase perturbation induced by atmospheric turbulence, and a complex scaled version of the transverse shape of the non-diffracting beam. The effect of weak atmospheric turbulence on irradiance distribution of the HzG beam can be ignored.

Efficient turbulent compressible convection in the deep stellar atmosphere

We report on an application of gas-kinetic BGK scheme to the computation of turbulent compressible convection in the stellar interior. After incorporating the Sub-grid Scale （SGS） turbulence model into the BGK scheme, we tested the effects of numerical parameters on the quantitative relationships among the thermodynamic variables, their fluctuations and correlations in a very deep, initially gravity-stratified stellar atmosphere. Comparison indicates that the thermal properties and dynamic properties are dominated by different aspects of numerical models separately. An adjustable Deardorff constant in the SGS model cu, = 0.25 and an amplitude of artificial viscosity in the gas-kinetic BGK scheme C2 = 0 are appropriate for the current study. We also calculated the densityweighted auto- and cross-correlation functions in Xiong＇s turbulent stellar convection theory based on which the gradient type of models of the non-local transport and the anisotropy of the turbulence were preliminarily studied. No universal relations or constant parameters were found for these models.

Quantum polarization fluctuations of partially coherent dark hollow beams in non-Kolmogorov turbulence atmosphere

Non-classical polarization properties of dark hollow beams propagating through non-Kolmogorov turbulence are studied. The analytic equation for the polarization degree of the quantization partially coherent dark hollow beams is obtained.It is found that the polarization fluctuations of the quantization partially coherent dark hollow beams are dependent on the turbulence factors and beam parameters with the detection photon numbers. Furthermore, an investigation of the changes in the on-axis propagation point and off-axis propagation point shows that the polarization degree of the quantization partially coherent dark hollow beams presents oscillation for a short propagation distance and gradually returns to zero for a sufficiently long distance.

Diffraction deep neural network-based classification for vector vortex beams

The vector vortex beam(VVB)has attracted significant attention due to its intrinsic diversity of information and has found great applications in both classical and quantum communications.However,a VVB is unavoidably affected by atmospheric turbulence(AT)when it propagates through the free-space optical communication environment,which results in detection errors at the receiver.In this paper,we propose a VVB classification scheme to detect VVBs with continuously changing polarization states under AT,where a diffractive deep neural network(DDNN)is designed and trained to classify the intensity distribution of the input distorted VVBs,and the horizontal direction of polarization of the input distorted beam is adopted as the feature for the classification through the DDNN.The numerical simulations and experimental results demonstrate that the proposed scheme has high accuracy in classification tasks.The energy distribution percentage remains above 95%from weak to medium AT,and the classification accuracy can remain above 95%for various strengths of turbulence.It has a faster convergence and better accuracy than that based on a convolutional neural network.

Mitigation of time-series InSAR turbulent atmospheric phase noise: A review

Synthetic Aperture Radar(SAR)interferometry is one of the most powerful remote sensing tools for ground deformation detection.However,tropospheric delay greatly limits the measurement accuracy of the InSAR technique.While vertically stratified tropospheric delays have been extensively investigated and well tackled,turbulent tropospheric phase noise still remains an intractable issue.In recent years,great efforts have been made to reduce the influence of turbulent atmospheric delay.This contribution is intended to provide a systematic review of the progress achieved in this field.First,it introduces the physical characteristics of atmospheric signals in interferograms.Then,a review of the main mitigation algorithms proposed in the literature is provided.In addition,the strengths and weaknesses of each approach are analyzed to provide guidance for choosing a suitable method accordingly.Finally,sug-gestions for resolving the challenging issues and an outlook for future research are given.

Site-testing at Muztagh-ata site Ⅲ:temperature inversion in surface-layer atmosphere

In this article,we present detailed seasonal,monthly and daily statistics of temperature difference in the surface layer at the Muztagh-ata site based on the temperature measurements at two heights of 2 m and6 m.We find that temperature inversion occurs frequently at our site during nighttime,especially during the cold season.Strong temperature inversion always represents stable atmospheric turbulence,which is crucial for an optical observatory.By analyzing the behavior of temperature inversion and its correlation with wind and cloud amount,one conclusion can be made that radiation inversion is the main reason for the existence of temperature inversion in the surface-layer at the Muztagh-ata site.

Influence of moderate-to-strong anisotropic non-Kolmogorov turbulence on intensity fluctuations of a Gaussian–Schell model beam in marine atmosphere

The scintillation index（SI） of a Gaussian–Schell model（GSM） beam in a moderate-to-strong anisotropic nonKolmogorov turbulent atmosphere is developed based on the extended Rytov theory. The on-axis SI in a marine atmosphere is higher than that in a terrestrial atmosphere, but the off-axis SI exhibits the opposite trend. The on-axis SI first increases and then begins to decrease and saturate as the turbulence strength increases. Turbulence inner and outer scales have different effects on the on-axis SI in different turbulent fluctuation regions. The anisotropy characteristic of atmospheric turbulence leads to the decline in the on-axis SI, and the rise in the off-axis SI. The on-axis SI can be lowered by increasing the anisotropy of turbulence, wavelength, and source partial coherence before entering the saturation attenuation region. The developed model may be useful for evaluating ship-to-ship/shore free-space optical communication system performance.

Transport of particles in an atmospheric turbulent boundary layer

A program incorporating the parallel code of large eddy simulation （LES） and particle transportation model is developed to simulate the motion of particles in an atmospheric turbulent boundary layer （ATBL）. A model of particles of 100-micrometer order coupling with large scale ATBL is proposed. Two typical cases are studied, one focuses on the evolution of particle profile in the ATBL and the landing displacement of particles, whereas the other on the motion of particle stream.

Effects of Turbulent Dispersion of Atmospheric Balance Motions of Planetary Boundary Layer

New Reynolds' mean momentum equations including both turbulent viscosity and dispersion are used to analyze atmospheric balance motions of the planetary boundary layer. It is pointed out that turbulent dispersion with r 0 will increase depth of Ekman layer, reduce wind velocity in Ekman layer and produce a more satisfactory Ekman spiral lines fit the observed wind hodograph. The wind profile in the surface layer including tur-bulent dispersion is still logarithmic but the von Karman constant k is replaced by k1 = 1 -2/k, the wind increasesa little more rapidly with height.

Power and Cross-Spectra for the Turbulent Atmospheric Motion and Transports in the Domain of Wave Number Frequency Space: Theoretical Aspects

The study of large-scale atmospheric turbulence and transport processes is of vital importance in the general circulation of the atmosphere. The governing equations of the power and cross-spectra for the atmospheric motion and transports in the domain of wave number frequency space have been derived. The contributions of the nonlinear interactions of the atmospheric waves in velocity and temperature fields to the conversion of kinetic and potential energies and to the meridional transports of angular momentum and sensible heat in the atmosphere have been discussed.

A Novel Non-Equidifferent Optical APPM Mapping Scheme for Strong Turbulent Atmospheric Channel

An optical Amplitude and Pulse Position Modulation(APPM) mapping scheme for strong turbulent atmospheric channel is proposed to optimize Bit Error Rate(BER) performance.In this scheme,a nonequidifferent amplitude series is designed based on quantitative BER analysis of the specific A×M APPM demapping procedures containing time slot selection and amplitude decision in selected time slot,which are different from traditional ones.Simulation results of 4×4,4×8 and 4×16 APPM show 4,3.4 and 6.9 d B SNR gain against traditional APPM scheme respectively.Thus significant BER performance improvement is achieved which helps to enhance reliability of freespace optical communication systems.

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.