部分空间相干光束在非Kolmogorov湍流大气中的有效曲率半径

激光在湍流大气中的传输有重要的理论研究和实际应用意义.以高斯-谢尔模型(GSM)光束作为部分空间相干光的典型例,基于非Kolmogorov谱和广义惠更斯-菲涅耳原理, 推导出GSM光束在非Kolmogorov湍流中的有效曲率半径的解析表达式. 重点研究了湍流参数(包括广义指数α,内尺度l₀,和外尺度L₀) 和传输距离z分别对GSM光束有效曲率半径的影响.结果表明, 有效曲率半径R_x(z)随α和z增加先减小然后再增大, 随L₀的减小而增大(3.6<α< 4),随l₀的增加而增大.并对结果做了物理解释.     

一般光束等效曲率半径的传输方程

给出了一般光束等效曲率半径在湍流大气和自由空间中的传输方程,推导出等效曲率半径达到最小值时光束的传输距离公式,解析地讨论了等效曲率半径的特性,并用数值计算例加以说明。研究表明,在自由空间中,一般光束等效曲率半径的传输方程与理想高斯光束的相同,当传输距离足够远时一般光束的等效等相面可以看成球面。但是,在湍流大气中,当传输距离足够远时一般光束的等效曲率半径仍然与光束参数有关,等效曲率半径随湍流的增强而减小。     

厄米-高斯光束在非Kolmogorov大气湍流中的传输性质

基于广义惠更斯-菲涅尔原理和非Kolmogorov(非K)谱,推导出了厄米-高斯光束在非K大气湍流中传输的束宽、角扩展以及M²因子的解析表达式.数值计算表明,在传输距离比较远(如z≥3 km)时,厄米-高斯光束的束宽、角扩展和M²因子随广义指数参量α的增大而增加直到α=3.11时达到最大值后再随α的增大而减小;随湍流的内尺度l₀的减小而增大;随外尺度l₀的增加而增大(3.6<α<4).但是当广义指数参量α在3<α<3.6区间取值时,束宽和M²因子几乎不随外尺度的增加而变化.     

经光阑衍射的平顶涡旋光束位相奇点的演化特性

推导出了平顶涡旋光束通过有光阑ABCD光学系统的传输解析式,并以光阑透镜和矩形光阑系统为例,与平顶光束比较研究了截断参量、相对离轴距离和光束阶数对衍射场中位相奇点演化特性的影响.数值计算表明,平顶涡旋光束通过上述光学系统均存在位相奇点,即使源处涡旋被光阑阻拦时,衍射场中也会出现位相奇点;而平顶光束通过光阑透镜系统存在刃型位错,随着截断参量增大,会发生刃型位错的演化和湮灭现象,且平顶光束通过矩形光阑系统没有发现位相奇点.     

矩形分布高斯-谢尔模型列阵光束的等效曲率半径

 推导出矩形分布高斯-谢尔模型（GSM）列阵光束通过湍流大气传输的等效曲率半径的解析表达式。研究表明,等效曲率半径由湍流强度、GSM列阵光束参数及光束的叠加方式等因素共同确定。湍流使得等效曲率半径减小,但湍流对交叉谱密度函数叠加时等效曲率半径的影响要比光强叠加时大。在自由空间中,交叉谱密度函数叠加时GSM列阵光束的等效曲率半径要比光强叠加时的大。但是,随着湍流的增强,交叉谱密度函数叠加时GSM列阵光束的等效曲率半径可以大于、等于或小于光强叠加时的等效曲率半径。此外,若光束相干参数和子光束数目越大,则等效曲率半径受湍流的影响越大。GSM列阵光束的等效曲率半径受湍流的影响比高斯列阵光束要小。     

高斯涡旋光束的光束传输因子和峭度参数

基于强度二阶矩定义, 导出了高斯涡旋光束光束传输因子即M² 因子的解析表达式, 高斯涡旋光束的M² 因子唯一取决于拓扑电荷数n. 数值计算表明, 高斯涡旋光束的M² 因子随着拓扑电荷数n的增大而增大. 基于强度高阶矩, 还导出了高斯涡旋光束经傍轴ABCD光学系统传输时峭度参数的解析表达式, 高斯涡旋光束的峭度参数取决于拓扑电荷数n、参数δ、矩阵元A和矩阵元D. 在自由空间传输时, 高斯涡旋光束的峭度参数仅取决于拓扑电荷数n和参数δ. 自由空间传输时, 高斯涡旋光束峭度参数的变化规律为: 峭度参数随参数δ的增大先减小而后趋向于一最小值, 随拓扑电荷数n的增大而减小. 这一研究有助于高斯涡旋光束的实际应用.     

部分相干平顶光束通过湍流大气传输的等效曲率半径

推导出了部分相干平顶光束在湍流大气中传输的等效曲率半径的解析表达式,详细地研究了湍流对其等效曲率半径的影响.研究表明,湍流使得等效曲率半径R减小,但是只有当湍流足够强时等效曲率半径极小值出现的位置z_min才会改变.在弱湍流中,R随着光束相干长度β的增大而增大;但是在强湍流中,R随着β的增大而减小.R随着光束阶数M(N)的增大而缓慢减小.若β越大、 关键词： 等效曲率半径 湍流 部分相干平顶光束     

单口径相干合成系统激光光束的M2因子研究

单口径相干合成系统激光光束的光束质量是一个亟待解决的重要问题.基于二阶矩定义, 文中给出了单口径TEM₀₀, TEM₀₁及TEM₁₀两两相干光束M²因子的解析表达式, 并比较分析了束腰宽度、传输距离、振幅之比,以及源场位置矢量对相干光束M²因子的影响, 得到了诸如源场位置参量d₁<100λ时,各相干光束M²因子恒定,反之, 其随位置参量d₁的增大而增大等一些结论.最后,文章对两TEM₀₀模相干光束M²因子的 部分理论进行了实验验证.     

大气湍流对斜程传输准单色高斯-谢尔光束空间相干性的影响

由湍流大气中斜程传输时准单色高斯-谢尔(GSM)光束互相干函数的解析式导出了该光束的复相干度.然后，利用表征光束空间相干性的横向相干长度，研究了斜程传输时大气湍流对准单色GSM光束空间相干性的影响.研究结果表明：1)当传输路径偏离水平方向较大(即θ≤88°)时，准单色GSM光束横向相干长度随传输距离均为先迅速增加，后缓慢增加，最后基本保持不变.2)当传输路径接近水平方向(即θ≥89°)时，准单色GSM光束横向相干长度随传输距离均为先增大，达到一个最大值后开始下降并持续减小.3)     

双光子吸收的Franz-Keldysh效应

从实验上证实Hg_0.695Cd_0.305Te 光电二极管空间电荷区中存在双光子吸收的Franz-Keldysh效应.利用一个皮秒Nd:YAG激光器抽运的光学参量产生器和差频产生器作为激发光源，测量了入射波长为λ₀=7.92μm的脉冲激光所激发的光响应随入射光强的变化关系.脉冲光响应峰值强度随入射光强的增大呈现二次幂函数增强趋势.采用等效RC电路模型将脉冲光伏信号峰值与入射光强相关联，得到空间电荷区中强电场下单光束     

Propagation properties of apertured laser beams with amplitude modulations and phase fluctuations through atmospheric turbulence

The propagation properties of apertured laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) through atmospheric turbulence are studied in detail both analytically and numerically. The analytical expressions for the average intensity, power in the bucket (PIB) and Strehl ratio (S _R ) of apertured laser beams with AMs and PFs propagating through atmospheric turbulence are derived. It is found that the worse the phase fluctuation and the higher the amplitude modulation are, the less laser beams are affected by turbulence. Furthermore, apertured Gaussian beams are more sensitive to turbulence than apertured laser beams with AMs and PFs. The average intensity of apertured laser beams with AMs and PFs may be even larger than that of apertured Gaussian beams due to turbulence. In particular, the influence of turbulence on the average maximum intensity of apertured laser beams with PFs and AMs may become serious if an unsuitable truncated parameter is chosen, which should be avoided in practice.     

Beam quality of truncated laser beams with amplitude modulations and phase fluctuations in turbulence

The closed-form expressions for the Rayleigh range z_R and the M²-factor of truncated laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) in turbulence are derived, and the beam quality is studied by taking the z_R and the M²-factor as the characteristic parameters of beam quality. The M²-factor of truncated laser beams with AMs and PFs is always larger than that of truncated Gaussian beams both in free space and in turbulence. However, in turbulence the beam quality of truncated laser beams with AMs and PFs may be better than that of truncated Gaussian beams if the z_R is taken as the characteristic parameter of beam quality. For laser beams with AMs and PFs in turbulence, the beam quality expressed in terms of z_R is consistent with that in terms of the M²-factor versus the phase fluctuation parameter α, but not versus the intensity modulation parameter σ_A. The beam quality of truncated laser beams with AMs and PFs is less sensitive to turbulence than that of truncated Gaussian beams. The beam quality of laser beams with smaller α and larger σ_A is less affected by turbulence than those with larger α and smaller σ_A.     

M~2-factor of high-power laser beams through a multi-apertured ABCD optical system

Based on the generalized truncated second-order moments, an approximate analytical formula of the beam propagation factor M~2 of high-power laser beams passing through the optical system with multiple hard-edged apertures is deduced. Numerical examples of the beams passing through an aperture-spatial filter are enclosed, and the influences of amplitude modulations(AMs) and phase fluctuations(PFs) on the beam propagation quality of high-power laser beams passing through the multi-apertured ABCD optical system are considered and discussed. It is shown that PFs are able to degrade the beam propagation quality of laser beams more than AMs when the high-power laser beams passing through the aperture-spatial filter, furthermore, one or two aperture-lens optical systems configured appropriate aperture parameters are both able to upgrade the beam propagation quality of high-power laser beams. The M~2 factor of Gaussian beam passing through the multi-aperture optical system is a special case in this paper.     

Effective radius of curvature of Hermite–Gaussian array beams

Analytical expressions for the effective radius of curvature, R, of Hermite–Gaussian (H–G) array beams propagating in free space for both coherent and incoherent combinations are derived. It is shown that for the two types of beam combination a minimum of the effective radius of curvature, R_min, appears as the propagation distance z increases. For the coherent combination, R is larger than that for the incoherent combination. The position z_min where the effective radius of curvature reaches its minimum is further away from the source plane for the coherent combination than that for the incoherent combination. For the two types of beam combination, R and z_min increase with increasing beam number, increasing beam separation distance, increasing waist width, and decreasing beam order and wavelength. In particular, the R of single H–G beams is always smaller than that of H–G array beams; the R of Gaussian array beams is always larger than that of H–G array beams.     

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.     

Beam wander of J 0- and I 0-Bessel Gaussian beams propagating in turbulent atmosphere

Root mean square (rms) beam wander of J ₀-Bessel Gaussian and I ₀-Bessel Gaussian beams, normalized by the rms beam wander of the fundamental Gaussian beam, is evaluated in atmospheric turbulence. Our formulation is based on the first and the second statistical moments obtained from the Rytov series. It is found that after propagating in atmospheric turbulence, the collimated J ₀-Bessel Gaussian and the I ₀-Bessel Gaussian beams have smaller rms beam wander than that of the Gaussian beam, regardless of the choice of Bessel width parameter. However, the extent of such an advantage depends on the chosen width parameter, Gaussian source size, propagation distance and the wavelength. Focusing at finite distances of the considered beams causes the rms beam wander to decrease sharply at the propagation distances equal to the focusing parameter.     

An analysis on radius of curvature aspects of hyperbolic and sinusoidal Gaussian beams

The effective radius of curvature of hyperbolic and sinusoidal Gaussian beams in free space and turbulent atmosphere is studied analytically and numerically. It is shown that the radius of curvature rises with growing source size, and changes slowly with wavelength. In general, given the same source and propagation settings, the beams can be listed in descending order of radius of curvature magnitudes as sinh Gaussian, cosh Gaussian, sine Gaussian, pure Gaussian and cos Gaussian beams. However, the radius of curvature and the difference of the radius of curvature between the different beams reduce with growing strength of turbulence because the beam’s spatial phase distribution is destroyed by turbulence.     

大气湍流中光束束宽扩展和角扩展的比较研究

以厄米-双曲余弦-高斯（H-ChG）光束为例,对H-ChG光束通过大气湍流传输时的束宽扩展和角扩展做了详细研究.用相对束宽和相对角扩展代替束宽和角扩展来研究湍流对光束影响的灵敏程度.研究表明,折射率结构常数C²_n越小,光束束宽扩展和角扩展越小.有较大阶数m,n,较小参数Ω₀和束腰宽度w₀ H-ChG光束的角扩展受湍流影响较小.当传输距离足够远时,这一结论对H-ChG光束的束宽扩展也成立.当传输距离不长时,对H-ChG光束相对束宽随Ω₀和w₀的变化规律做了分析.用数值计算例做了说明,并对结果的正确性做了物理解释.厄米-高斯,双曲余弦高斯和高斯光束在大气湍流中的扩展可作为H-ChG光束的特例来处理. 关键词： 束宽扩展和角扩展 大气湍流 厄米-双曲余弦-高斯光束     

Changes in the spectrum of twist anisotropic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the spectrum of twist anisotropic Gaussian Schell-model (TAGSM) beams propagating through turbulent atmosphere is derived analytically by using the partially coherent complex curvature tensor. The relative spectral shift of TAGSM beams propagating through turbulent atmosphere is closely related with the strength of atmospheric turbulence, the beam’s parameter and the radial coordinate. The on-axis spectral shift of TAGSM beams propagating through turbulent atmosphere changes from blue shift to red shift with the increasing of the propagation distance z, and at a certain propagation distance z, there exists a rapid transition of the spectrum at the critical position r_c.