Scintillation index of astigmatic annular beams in a turbulent atmosphere

The scintillation properties of astigmatic annular beams in a weak turbulent atmosphere are investigated. Expression for the on-axis scintillation index of an astigmatic annular beam is derived. It is found that the scintillation index of an astigmatic annular beam can be smaller than that of a Gaussian beam, an elliptical Gaussian beam and a stigmatic annular beam in a weak turbulent atmosphere under certain conditions. The scintillation properties of astigmatic annular beams are closely controlled by its beam parameters.     

Scintillation properties of dark hollow beams in a weak turbulent atmosphere

The on-axis scintillation index for a circular dark hollow beam (DHB) propagating in a weak turbulent atmosphere is formulated, and the scintillation properties of a DHB are investigated in detail. The scintillation index for a DHB reduces to the scintillation index for a Gaussian beam, an annular beam and a flat-topped beam under certain conditions. It is found that the scintillation index of a DHB is closely related to the beam parameters and can be lower than that of a Gaussian beam, an annular beam and a flat-topped beam in a weak turbulent atmosphere at smaller waist sizes and longer propagation lengths. PACS 42.25.Bs; 42.68.Ay     

Spectral shifts and spectral switches of elliptical Gaussian beam propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the spectrum of elliptical Gaussian beam (EGB) propagating through turbulent atmosphere can be derived analytically by tensor method. It can avoid time-consuming numerical integral that was commonly used in the previous study of spectral changes. Analytical results show that the on-axis normalized spectrum S(ω) of EGB propagating through turbulent atmosphere is different from the original spectrum S₀(ω) and there exist spectral shifts and spectral switches for EGB propagating through turbulent atmosphere. Besides, spectral shifts and spectral switches of EGB are closely related with the structure constant of the turbulent atmosphere, the beam parameters and the coordinate of observation point. Compared with the Gaussian beam, there are two spectral switches for EGB propagating through turbulent atmosphere.     

漂移对聚焦高斯光束闪烁影响的数值模拟

 采用非自适应坐标变换对聚焦高斯光束在湍流大气中的传输进行了数值模拟，结果显示轴闪烁指数并没有出现如Rytov理论所预言的随初始光束半径的增大而明显减小的现象，其原因在于Rytov近似理论未考虑大尺度湍涡产生的漂移效应对闪烁的贡献。对比数值模拟结果与漂移理论结果以及相关实验结果，三者相吻合,表明未考虑漂移效应的Rytov近似理论不能完全准确地描述聚焦光束的闪烁特征，在研究聚焦光束的闪烁时，应当考虑漂移的影响。     

Intensity fluctuations in J-Bessel–Gaussian beams of all orders propagating in turbulent atmosphere

The scintillation index of a J _n -Bessel–Gaussian beam of any order propagating in turbulent atmosphere is derived and numerically evaluated at transverse cross-sections with the aid of a specially designed triple integral routine. The graphical outputs indicate that, just like the previously investigated J ₀-Bessel–Gaussian beam, higher-order members of the family also offer favorable scintillation characteristics at large source sizes. This advantage is maintained against rising beam orders. Viewed along the propagation axis, beams with lower orders and smaller widths exhibit smaller values of the scintillation index at shorter propagation distances and large values at longer propagation distances. Further, it is shown that the scintillation index of the J _n -Bessel–Gaussian beams (n>0) is larger than that of the fundamental Gaussian and the J ₀-Bessel–Gaussian beams only near the on-axis points, while remaining smaller towards the edges of the beam.     

Average intensity and spreading of an elliptical gaussian beam propagating in a turbulent atmosphere

An analytical formula for the average intensity of an elliptical Gaussian beam (EGB) propagating in a turbulent atmosphere is derived. The spreading properties of an EGB in a turbulent atmosphere are studied. It is found that an EGB will eventually become a circular Gaussian beam in a turbulent atmosphere. This interesting phenomenon is quite different from the propagation of an EGB in free space. The evolution properties are closely related to the parameters of the beam and the turbulent atmosphere.     

Effect of spatial coherence on the scintillation properties of a dark hollow beam in turbulent atmosphere

With the help of a tensor method, we derive an explicit expression for the on-axis scintillation index of a circular partially coherent dark hollow (DH) beam in weakly turbulent atmosphere. The derived formula can be applied to study the scintillation properties of a partially coherent Gaussian beam and a partially coherent flat-topped (FT) beam. The effect of spatial coherence on the scintillation properties of DH beam, FT beam and Gaussian beam is studied numerically and comparatively. Our results show that the advantage of a DH beam over a FT beam and a Gaussian beam for reducing turbulence-induced scintillation increases particularly at long propagation distances with the decrease of spatial coherence or the increase of the atmospheric turbulence, which will be useful for long-distance free-space optical communications.     

Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere

The scintillation index of a Gaussian Schell-model beam with twist phase (i.e., twisted GSM beam) in weak turbulent atmosphere is formulated with the help of a tensor method. Variations of the scintillation index of a twisted GSM beam on propagation in turbulent atmosphere are studied in detail. It is interesting to find that the scintillation index of a twisted GSM beam can be smaller than that without twist phase in weak turbulent atmosphere. Thus, modulation of the twist phase of a partially coherent beam provides a new way to reduce turbulence-induced scintillation.     

Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere

The propagation of an elliptical Gaussian beam (EGB) through an astigmatic ABCD optical system in a turbulent atmosphere is investigated. An analytical formula for the average intensity of an EGB and a generalized tensor ABCD law for the generalized complex curvature tensor are derived. As an application example, we derived an analytical formula for the average intensity of an elliptical flat-topped beam propagating through an astigmatic ABCD optical system in a turbulent atmosphere. As a numerical example, the focusing properties of an EGB focused by a thin lens in a turbulent atmosphere are studied. It is found that the focused beam at the focal plane becomes a circular Gaussian beam when the atmospheric turbulence is strong enough, and the beam width of the circular Gaussian beam is determined by atmospheric turbulence strength, focal length of the thin lens, and wavelength of the initial beam but is independent of the initial beam widths (i.e., initial intensity distribution).     

Annular beam scintillations in non-Kolmogorov weak turbulence

In a weakly turbulent atmosphere governed by the non-Kolmogorov spectrum, the on-axis scintillation index is formulated and evaluated when the incidence is an annular Gaussian type. When the power law of the non-Kolmogorov spectrum is varied, the scintillation index first increases, and reaches a peak value, then starts to decrease, and eventually approaches zero. The general trend is that when turbulence has a non-Kolmogorov spectrum with power law larger than the Kolmogorov power law, the scintillation index values become smaller. For all power laws, collimated annular Gaussian beams exhibit smaller scintillations when compared to pure Gaussian beams of the same size. Intensity fluctuations at a fixed propagation distance diminish for the non-Kolmogorov spectrum with a very large power law, irrespective of the focal length and the thickness of optical annular Gaussian sources.     

啁啾脉冲高斯光束在大气湍流中的传输特性北大核心CSCD

基于广义惠更斯-菲涅耳原理,推导出啁啾脉冲高斯光束在湍流大气中传输的光谱解析表达式,并对解析表达式进行了数值仿真。结果表明:啁啾参数越大,光源谱宽越宽;当光源相对谱宽大于0.336时,轴上点光谱产生蓝移;湍流使得轴上点光谱的相对频移量减小,相对频移量随源光谱宽的增大而非线性增大;增大光束束腰半径可减小湍流对光谱频移、光束展宽的影响。     

Scintillation index of a stochastic electromagnetic beam propagating in random media

We study the behavior of the scintillation index (the normalized variance of fluctuating intensity) of a wide-sense statistically stationary, quasi-monochromatic, electromagnetic beam propagating in a homogeneous isotropic medium. In particular, we show that in the case when the beam is treated electromagnetically apart from the correlation properties of the medium in which the beam travels not only its degree of coherence but also its degree of polarization in the source plane can affect the values of the scintillation index along the propagation path. We find that, generally, beams generated by unpolarized sources have reduced level of scintillation, compared with beams generated by fully polarized sources, provided they have the same intensity distribution and the same state of coherence in the source plane. An example illustrating the theory is considered which examines how the scintillation index of an electromagnetic Gaussian Schell-model beam propagates in the turbulent atmosphere. These results may find applications in optical communications through random media and in remote sensing.     

The on-axis average intensity for Gaussian beam excitation limited by an annular aperture in turbulent atmosphere

Starting with a Gaussian beam excitation limited by an annular aperture, the on-axis average intensity is presented in turbulent atmosphere. The on-axis average intensity profile is evaluated by altering the outer and inner radius of an annular aperture, the propagation distance and wavelength. The results show that the outer radius of an annular aperture within a certain size impacts the on-axis intensity distributions. When the propagation distance or the outer radius of an annular aperture is large enough, the on-axis average intensity distributions is not affected by the size of the annular aperture. By calculation and analyses, the variation of the inner radius of the annular aperture and the wavelength of the Gaussian beam that impact on the axial average intensity distributions is also discussed.     

椭圆涡旋光束在海洋湍流中的传输特性

本文采用分步相位屏方法来仿真椭圆涡旋光束在海洋中的实际传输情况,并对椭圆涡旋光束在海洋湍流中的传输光强和闪烁因子进行了仿真。研究发现,椭圆涡旋光束在海洋传输过程中,光斑会发生明显的旋转,同时光斑会产生暗核且暗核个数与光束的拓扑荷数相等。一个拓扑荷数为m的相位奇点会分裂成m个拓扑荷数为1的相位奇点,并且海洋湍流越强,光斑受到的干扰越严重。研究还发现,在较弱的海洋湍流中,随着传输距离的增加,椭圆涡旋光束的闪烁因子会低于高斯光束和涡旋光束的闪烁因子,而且在远距离处拓扑荷数越大闪烁因子降低越明显,同时也发现,传播一段距离后涡旋光束的闪烁因子会低于高斯光束的闪烁因子。在较强湍流中,椭圆涡旋光束的闪烁因子会交叠在一起。对于不同强度的海洋湍流,随着均方温度耗散率的增大,椭圆涡旋光束的轴上点闪烁因子也增大。在同一传输距离处,束腰宽度越小的椭圆涡旋光束闪烁因子越小。     

Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence

Atmospheric turbulence causes strong irradiance fluctuations of propagating optical wave under the severe weather conditions in long-distance free space optical communication. In this paper, the scintillation index for a Gaussian beam wave propagation through non-Kolmogorov turbulent atmosphere is derived in strong fluctuation regime, using non-Kolmogorov spectrum with a generalized power law exponent and the extended Rytov theory with a modified spatial filter function. The analytic expressions are obtained and then used to analyze the effect of power law, refractive-index structure parameter, propagation distance, phase radius of curvature, beam width and wavelength on scintillation index of Gaussian beam under the strong atmospheric turbulence. It shows that, with the increasing of structure parameter or propagation distance, scintillation index increases sharply up to the peak point and then decreases gradually toward unity at rates depending on power law. And there exist optimal value of radius of curvature and beam width for minimizing the value of scintillation index and long wavelength for mitigating the effect of non-Kolmogorov strong turbulence on link performance.     

Effect of spherical aberration on scintillations of Gaussian beams in atmospheric turbulence

The effect of spherical aberration on scintillations of Gaussian beams in weak, moderate and strong turbulence is studied using numerical simulation method. It is found that the effect of the negative spherical aberration on the on-axis scintillation index is quite different from that of the positive spherical aberration. In weak turbulence, the positive spherical aberration results in a decrease of the on-axis scintillation index on propagation, but the negative spherical aberration results in an increase of the on-axis scintillation index when the propagation distance is not large. In particular, in weak turbulence the negative spherical aberration may cause peaks of the on-axis scintillation index, and the peaks disappear in moderate and strong turbulence, which is explained in physics. The strong turbulence leads to less discrepancy among scintillations of Gaussian beams with and without spherical aberration.     

Optimized multiemitter beams for free-space optical communications through turbulent atmosphere

Using laser beams with less than perfect spatial coherence is an effective way of reducing scintillations in free-space optical communication links. We report a proof-of-principle experiment that quantifies this concept for a particular type of a partially coherent beam. In our scaled model of a free-space optical communication link, the beam is composed of several partially overlapping fundamental Gaussian beams that are mutually incoherent. The turbulent atmosphere is simulated by a random phase screen imprinted with Kolmogorov turbulence. Our experiments show that for both weak-to-intermediate and strong turbulence an optimum separation between the constituent beams exists such that the scintillation index of the optical signal at the detector is minimized. At the minimum, the scintillation reduction factor compared with the case of a single Gaussian beam is substantial, and it is found to grow with the number of constituent beams. For weak-to-intermediate turbulence, our experimental results are in reasonable agreement with calculations based on the Rytov approximation.     

INNER AND OUTER SCALE EFFECTS ON SCINTILLATION INDEX FOR AN INFRARED LASER PROPAGATING ON EARTH-SPACE PATHS

The effects of the inner-and outer-scale of turbulent atmosphere on the scintillation index for an infrared laser beam propagating through atmospheric turbulence are discussed under the assumption that small-scale irradiance fluctuation is modulated by large-scale irradiance fluctuation on Earth-space paths. A model about the scintillation index with the inner-and outer-scale is developed. A numerical analysis is done by using this model. It is shown that the effect of the inner scale on scintillation index is larger than the outer scale effect for the lesser wavelength wave at visible and infrared band. From moderate to saturation regime, the inner scale effect becomes gradually small; however, the outer scale effect becomes gradually obvious. Under moderate to strong regime, therefore, the effects of the inner-and outer-scale on scintillation index must be considered for theoretical prediction scintillation of an infrared laser beam propagating through turbulent atmosphere on Earth-space paths.     

Scintillation behavior of cos, cosh and annular Gaussian beams in non-Kolmogorov turbulence

For a non-Kolmogorov spectrum, scintillation aspects of cos, cosh and annular Gaussian beams are investigated. The appropriate mathematical formulation is developed, the derived scintillation index is evaluated and its variation is plotted in graphs. We find that, when the values of the power coefficient of the spectrum are just above 3, low scintillation is encountered, then as the power coefficient is increased, rises will occur with a peak being reached around 3.21. From there onwards, scintillation will drop, as the power coefficient approaches a value of 5. For extreme off-axis positions, there will be slight increases in scintillation at high power coefficient values. At points near on-axis and when the beams have small width sizes, cosh Gaussian beam having a bigger displacement parameter will offer the lowest scintillation. At large width sizes, this advantage will switch to the side of the cos Gaussian beam. In this study, the variation of scintillation with other sources and propagation parameters is examined as well.     

Scintillation behavior of Laguerre Gaussian beams in strong turbulence

In strong atmospheric turbulence, the asymptotic on-axis scintillation behaviors of Laguerre Gaussian (LG) beams are examined. To arrive at the strong-turbulence solution, we utilize the existing filtering approach for weak-turbulence solutions and our recently reported weak-turbulence scintillation index formula for LG beams. In the limiting case, our solution correctly predicts the asymptotic strong-turbulence behavior of Gaussian beam wave scintillation. Investigation of the scintillations versus the propagation distance, source size, wavelength and refractive index structure parameter lead to the conclusion that the LG beams with higher order radial modes can provide less scintillation. The results are applicable to long-haul atmospheric optical communication links.