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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Non-Gaussian statistics of partially coherent light in atmospheric turbulence

We derive theoretically and verify experimentally a concise general expression for the normalized intensity correlations(IC)of partially coherent light in a weak atmospheric turbulence in the fast detector measurement regime.The derived relation reveals that the medium turbulence acts,in general,as an additional noise source enhancing the IC of partially coherent beams.The maximum of the beam IC is,in general,enhanced,causing the fields to exhibit super-Gaussian statistics.On the other hand,the relation indicates that turbulence-induced noise is negligible for sufficiently low coherence light,which reveals the condition for the turbulence-free correlation imaging.

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.