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 Gaussian functions, an approximate analytical formula of the double-distance propagation for Gaussian 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.     

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 Presnel 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.     

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 vert pvert and the smaller the off-axis distance vert dvert are, the less the beam-width spreading and angular spread of GSM beams with edge dislocation are affected by turbulence. The GSM 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.     

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.     

Propagation of phase-locked truncated Gaussian beam array in turbulent atmosphere

Truncation manipulation is a simple but effective way to improve the intensity distribution properties of the phase-locked Gaussian beam array at the receiving plane. In this paper, the analytical expression for the propagation of the phase-locked truncated Gaussian beam array in a turbulent atmosphere is obtained based on the extended Huygens--Fresnel principle. Power in the diffraction-limited bucket is introduced as the beam quality factor to evaluate the influence of different truncation parameters. The dependence of optimal truncation ratio on the number of beamlets, the intensity of turbulence, propagation distance and laser wavelength is calculated and discussed. It is revealed that the optimal truncation ratio is larger for the laser array that contains more lasers, and the optimal truncation ratio will shift to a larger value with an increase in propagation distance and decrease in intensity of atmosphere turbulence. The optimal truncation ratio is independent of laser wavelength.     

Propagation of bright femtosecond pulses in a nonlinear optical fibre with the third- and fourth-order dispersions

We solve the generalized nonlinear Schr\"{o}dinger equation describing the propagation of femtosecond pulses in a nonlinear optical fibre with higher-order dispersions by using the direct approach to perturbation for bright solitons, and discuss the combined effects of the third- and fourth-order dispersions on velocity, temporal intensity distribution and peak intensity of femtosecond pulses. It is noticeable that the combined effects of the third- and fourth-order dispersions on an initial propagated soliton can partially compensate each other, which seems to be significant for the stability controlling of soliton propagation features.     

Propagation of cylindrical vector beams in a turbulent atmosphere

<正>Based on the extended Huygens-Presnel 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.     

A unique circular path of moving single bubble sonoluminescence in water

Based on a quasi-adiabatic model,the parameters of the bubble interior for a moving single bubble sonoluminescence (m-SBSL) in water are calculated.By using a complete form of the hydrodynamic force,a unique circular path for the m-SBSL in water is obtained.The effect of the ambient pressure variation on the bubble trajectory is also investigated.It is concluded that as the ambient pressure increases,the bubble moves along a circular path with a larger radius and all bubble parameters,such as gas pressure,interior temperature and light intensity,increase.A comparison is made between the parameters of the moving bubble in water and those in N-methylformamide.With fluid viscosity increasing,the circular path changes into an elliptic form and the light intensity increases.     

Paraxial propagation of cosh-Airy vortex beams in chiral medium

Propagation dynamics of the cosh-Airy vortex(CAiV) beams in a chiral medium is investigated analytically with Huygens–Fresnel diffraction integral formula. The results show that the CAiV beams are split into the left circularly polarized vortex(LCPV) beams and the right circularly polarized vortex(RCPV) beams with different propagation trajectories in the chiral medium. We mainly investigate the effect of the cosh parameter on the propagation process of the CAiV beams.The propagation characteristics, including intensity distribution, propagation trajectory, peak intensity, main lobe's intensity, Poynting vector, and angular momentum are discussed in detail. We find that the cosh parameter affects the intensity distribution of the CAiV beams but not its propagation trajectory. As the cosh parameter increases, the distribution areas of the LCPV and RCPV beams become wider, and the side lobe's intensity and peak intensity become larger. Besides, the main lobe's intensity of the LCPV and RCPV beams increase with the increase of the cosh parameter at a farther propagation distance, which is confirmed by the variation trend of the Poynting vector. It is significant that we can vary the cosh parameter to control the intensity distribution, main lobe's intensity, and peak intensity of the CAiV beams without changing the propagation trajectory. Our results may provide some support for applications of the CAiV beams in optical micromanipulation.     

Light propagation characteristics of turbulent plasma sheath surrounding the hypersonic aerocraft

The characteristics of light propagation through turbulent plasma sheath surrounding the hypersonic aircraft have been studied.The turbulent flow fields around a hypersonic aircraft are given by using the Navier–Stokes(NS) equations and k–ε turbulence model.Based on the distribution of flow field, refractive index and density of the plasma sheath for a blunt cone are discussed with different flight velocities and altitudes.The refractive index is mainly influenced by the electrons in the turbulent plasma sheath.The influence of different velocities and altitudes on the features of light propagation in the turbulent plasma sheath is analyzed.The results show that as the flight speed increases or the flight altitude decreases,the refractive index fluctuation becomes larger.It is also found that the refractive index fluctuation varies with the incident wavelength.This study shows how the characteristics of an optical beam propagating through plasma sheath are affected by the incident wavelength, flight velocities, and altitudes.     

Performance of distributed array receivers for optical-wave propagation in the slant path through the turbulent atmosphere

Considering free-space optical communication systems, we analyze the performance of the intensity scintillation of the optical-wave propagation in the slant path under different atmospheric turbulences. Under the zero scale, we derive the log-intensity spatial covariance function of the optical-wave propagation in the slant path through the turbulent atmosphere based on the modified Rytov method. We demonstrate the relationship between the reception performance of the distributed antenna array and the aperture-averaging factor. Furthermore, we also obtain the optimum aperture diameter, number of sub-antennas, and the sub-antenna interval of the array receiver in intermediate turbulence. This study can benefit the design of the receiving system for the optical-wave propagation in the slant path through the turbulent atmosphere in free-space optical communication systems.     

Pulsed single-photon Bessel beams propagation in non-Kolmogorov turbulent atmosphere

The analytic expressions are derived for the turbulent broadening, the long-term temporal broadening, the acquisition probability of single-pulse and the transmittance probability density of a pulsed space-time Bessel photon-beam propagating along a slant path in weak non-Kolmogorov atmospheric turbulence, based on the assumption of a pulsed Bessel beam with the initial Gaussian temporal shape of pulse and diffraction-free spatial distribution. It is shown that the turbulent broadening and the long-term temporal broadening are the nolinear-increase functions of the index of non-Kolmogorov turbulence and the effect of non-Kolmogorov index on the acquisition probability of single-pulse can be approximatively described by a Gaussian function with a peak value at non-Kolmogorov index close to 3.7 for the case of the input half-pulse width greater than picosecond (ps). The transmittance of probability density is decreasing as the increasing of the structure constant of the index of refraction, the zenith angle of communication channel, the propagation path and the pulse broadening. There is turbulent diffraction for Bessel beam propagation in turbulent atmosphere, but its free-space diffraction-free characteristic is reservation.     

湍流大气中斜程传输光场的相位特性

运用功率谱反演法对斜程传输大气湍流扰动相位屏进行了数值模拟。通过建立激光束初始畸变相位模型,从波前峰谷值和波前功率谱密度函数两个方面,对激光束通过大气湍流后的相位特性进行了研究,重点分析了湍流传输距离和天顶角对激光束波前相位分布的影响。研究结果表明:激光束在湍流大气斜程传输后,其波前相位会发生明显畸变,且空间高频相位较低频相位所占比例明显增加;通过湍流后的波前相位与传输距离及天顶角密切相关,传输距离越长,天顶角越大,相位畸变程度越大,高频相位所占比例越多。     

The relay propagation of partially coherent cosh–Gaussian–Schell beams in turbulent atmosphere

We have studied the relay propagation of a partially coherent cosh–Gaussian–Schell beam in turbulent atmosphere. Analytical expressions for both the cross-spectral density at the relay system and average intensity at the target are derived. By using the analytical expressions some special cases are studied and some numerical simulation comparisons are made, especially the effects of the coherence of the beam, turbulence strength, aperture and its size on the relay propagation. Our study shows that the effects of diffraction and coherence of initial beam on the intensity profiles at the relay system are so small that they can be neglected when the effects due to turbulence are large enough. Even though the correction to the receiving beam at relay system is important, it is not necessary to improve the receiving beam when the effect of turbulence over the travel path is strong. A high peak intensity at target can be obtained by optimizing these factors, such as propagation distance, aperture and spatial correlation length.     

Relay propagation of partially coherent flattened Gaussian beam in turbulent atmosphere

Relay propagation of partially coherent flattened Gaussian–Schell beam in turbulent atmosphere has been studied. The analytical expresses of average intensity distribution at target are derived. The effects of spatial correlation length of initial and relay beam on the average intensity are analyzed in details. Study shows that the effects of the variation of spatial correlation length of relay beam are much larger than that of initial beam. The effects of spatial correlation length on relay propagation become smaller and smaller with the increase of structure constant. When the spatial correlation length is large and turbulence is strong, the effects of the variation of spatial correlation length on relay propagation are so small that can be neglected.     

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.     

大气湍流像差散焦和像散与高斯涡旋光束焦面光强

分别研究了构成大气湍流波像差中的散焦和像散两个低阶像差对高斯涡旋激光束传输和成像的影响.采用菲涅耳-基尔霍夫衍射积分理论和大气湍流波相位结构函数的平方近似研究了聚焦高斯涡旋光束在大气湍流中散焦和像散影响下焦面光强的分布特性.导出了斜程传输条件下接收面上平均光强分布的积分表达式,并采用数值模拟方法研究湍流强度、传输距离和拓扑电荷对焦面光强的调制规律.结果表明:在弱湍流起伏区域,散焦和像散两类像差对高斯涡旋光束的光强分布影响都很小,可以忽略;在中等湍流区域,随着光束传输距离和湍流强度的增加,两类像差都导致高斯涡旋光束的光强峰值降低、束径扩展、中心暗斑扩大.当单拓扑电荷高斯涡旋光束传输时,在同等传输条件下,像散导致的光强峰值降低比散焦更严重,主亮斑区域外的次级亮环强度更大,光斑和中心暗斑扩展更明显.与单拓扑电荷光束相比较,散焦和像散导致双拓扑电荷光束的扩展更加明显,中心光斑更大,亮环区域外的次级亮环更明显;但是,由于光的相干性的降低和光束的偏折效应,像散导致光束中心的暗斑变为次级亮斑.     

Degree of polarization for single-photon beam in a turbulent atmosphere

The polarization fluctuations of single-photon beam propagation through the slant path turbulent atmosphere are studied. The Stokes operators and the degree of polarization of single-photon beam in a turbulent atmosphere are obtained. It is shown by analytical calculations, that the quantum degree of polarization of linearly polarization light is a decrease function of the atmospheric turbulence strength and the propagation distance for lower detection photon number.     

Propagation of supercontinuum laser sources in a slant path through the atmosphere

Taking the atmospheric refraction, extinction and turbulence into account, the propagation characteristic of supercontinuum laser sources in a slant path through the turbulent atmosphere is investigated. The effect of spectral width, initial spot size and zenith angle in a slant path on the beam width and propagation efficiency are studied in details. Numerical examples reveal that the beam width and propagation efficiency are different values while the spectral width varies. With the zenith angle in a slant atmospheric path increasing, the beam width of supercontinuum laser sources will increase and propagation efficiency will decrease. The initial spot size has an optimal value when spectral width and zenith angle are fixed.