双曲余弦高斯列阵光束在湍流大气中的光束传输因子

本文推导出了双曲余弦高斯(ChG)列阵光束在湍流大气中的光束传输因子( M ^{2因子)的解析公式,并采用相对 M 2因子研究了湍流对 M 2因子的影响.研究表明,在湍流大气中 M 2因子不再是一个传输不变量,湍流使得 M 2因子增大.非相干合成情况下, M 2因子随着传输距离、光束参数、相对子光束间距和子光束数目的增大而增大.相干合成情况下, M 2因子随光束参数和相对子光束间距的增大呈现振荡上升.相干合成情况下的 M 2因子比 关键词： M2因子)')" href="#">光束传输因子(M2因子) 光束质量 双曲余弦高斯列阵光束 大气湍流}     

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     

部分相干双曲正弦高斯光束的M~2因子与湍流距离

基于广义惠更斯-菲涅耳原理和维格纳分布函数方法,推导出了部分相干双曲正弦高斯(ShG)光束在湍流大气中M2因子的解析表达式。在此基础上研究了部分相干ShG光束的湍流距离,即湍流引起的光束扩展可忽略的范围。采用Von Karman谱分别对M2因子和湍流距离进行了数值计算,并分析了内外尺度的影响。研究表明:M2因子随束腰宽度和离心参数的增加存在极小值;湍流距离随束腰宽度的增加存在极大值,随离心参数的增加而增加,大气湍流对离心参数较大的光束影响较小。另外,M2因子和湍流距离与折射率结构参数、内尺度、外尺度、波长和相干参数等密切相关。     

厄米-高斯光束的M2因子矩阵

提出了厄米-高斯光场的M²因子矩阵.引入束半宽平方的交叉项、M²因子的交叉项,理论推导出了在同一坐标系下光场旋转一定角度后的M²因子矩阵,数值模拟了与M²因子矩阵有关的各参数随光场旋转角度变化的规律,给出了光场的M²因子矢量点随光场旋转角度变化的轨迹曲线.计算结果与理论推导结果相符,证实了利用M²因子矩阵可以将旋转前后的二维厄米-高斯光场用旋转矩阵统一起来.该方法可推广到对一般的二维高阶高斯光束的光束质量的理论分析上,具有普适性,对光束质量的实际测量有重要的理论指导意义. 关键词： M²因子矩阵')" href="#">M²因子矩阵 厄米-高斯光束 非对称激光束 矩阵光学     

部分相干离轴涡旋光束在大气湍流中的光强分布

根据广义惠更斯-菲涅耳原理以及交叉谱密度函数,利用Kolmogorov湍流谱推导得到部分相干离轴涡旋光束在大气湍流中传输时光束的光强分布表达式,讨论了离轴距离、拓扑荷数、束腰宽度、相干长度、传输距离、湍流强度参数对光强分布的影响。仿真结果表明,拓扑荷数的大小不会改变暗核的位置;离轴距离的正负号决定了暗核移动的方向和光强集中区域的方向;暗核向上移动的距离随相干长度、束腰宽度的增大而减小,随传输距离、湍流强度的增大而增大;光斑展宽随相干长度、束腰宽度、传输距离、湍流强度的增大而增大。     

湍流对部分相干双曲余弦高斯光束的瑞利区间的影响

推导出了部分相干双曲余弦高斯光束在自由空间和湍流大气中传输瑞利区间的解析公式,并研究了湍流对光束瑞利区间的影响.研究表明,部分相干双曲余弦高斯光束的瑞利区间由湍流强度和光束参数等因数共同确定.湍流使得光束的瑞利区间缩短,并且湍流越强瑞利区间越短.在自由空间中,瑞利区间随光束相干参数 α 、光束参数 β 和高斯束宽 w ₀的增大以及波长 λ 的减小而增大.但是, α,β 和 w ₀越小以及 λ 越大,瑞利区间受湍流的影响越小.并且,当 关键词： 瑞利区间 部分相干双曲余弦高斯光束 大气湍流 自由空间     

湍流大气中激光相干探测回波光强与空间相干特性研究

本文利用广义惠更斯-菲涅尔原理结合Goodman目标散射理论,推导出了激光探测中目标反射光的交叉谱密度函数解析式,并进一步得到了目标反射光的光强分布和空间相干长度表达式。利用得到的表达式在湍流大气条件下,分析了不同光源参数和目标反射光参数对目标反射光光强分布和相干长度的影响。研究结果表明:光源相干长度对归一化反射光强影响较小;光源束腰半径和反射光斑半径值越大接收光的相干长度值越小;随着传输距离的增加,相干长度增加越来越缓慢;在弱湍流大气传输过程中,光源参数对接收光的影响占主导作用,光源束腰半径越大接收光的光强和相干长度值越小;在强湍流大气传输过程中,大气湍流对反射光的影响起主导作用。     

复宗量厄米-高斯光束在大气湍流中的传输特性

采用广义惠更斯-菲涅耳衍射积分方法和Wigner分布函数的二阶矩定义,推导出在直角坐标系下激光光束经大气湍流传输的远场发散角、束宽以及M2因子的解析表达式,并以复宗量厄米-高斯(EHG)光束为例,定量分析了EHG光束在大气湍流中的传输特性。研究表明,光束在大气湍流中传输后的M2因子与入射面上的M2因子、入射面的二阶矩、传输距离、波数以及湍流的影响因子有关;随着在大气湍流中传输距离的增加,EHG光束的远场发散角、束宽和M2因子均会逐渐增大;大气湍流对高阶EHG光束的远场发散角、束宽和M2因子的影响更小;EHG光束在大气湍流中的M2因子与传输距离、湍流的折射率结构参数、光束波长、光束阶数以及基模高斯光束的束腰宽度密切相关。     

部分相干双曲余弦高斯光束通过湍流大气的光束扩展

基于广义惠更斯-菲涅尔原理，并采用将部分相干双曲余弦高斯光束用厄米-高斯光束的非相干叠加表示的方法，研究了部分相干双曲余弦高斯光束通过湍流大气的光束扩展问题，推导出了部分相干双曲余弦高斯光束通过湍流大气均方根束宽的解析表达式.研究表明，部分相干双曲余弦高斯光束的扩展随着湍流大气的折射率结构常数C²_n和光束离心参数δ的增大而加剧.但是，随着δ的增大，部分相干双曲余弦高斯光束受到湍流的影响减小. 关键词： 部分相干双曲余弦高斯光束 湍流大气 光束扩展     

双曲余弦高斯列阵光束通过湍流大气传输的角扩展及方向性

 采用积分变换,推导出了双曲余弦高斯（ChG）列阵光束通过湍流大气传输的二阶矩束宽和角扩展的解析公式,给出了ChG列阵光束与一束高斯光束具有相同角扩展的条件。研究表明:相干合成的ChG列阵光束的角扩展比非相干合成的小,但是,非相干合成的ChG列阵光束的角扩展受湍流影响比相干合成ChG光束小;相干合成情况下,ChG列阵光束的角扩展随离心参数、束腰宽度和相对子光束间距的变化均出现振荡,但在湍流中的振荡减弱,非相干合成情况下,ChG列阵光束的角扩展与相对子光束间距和光束数无关。     

Spreading of partially coherent polychromatic Hermite-Gaussian beams propagating through non-Kolmogorov turbulence

The spreading of partially coherent polychromatic Hermite-Gaussian (PCPHG) beams propagating through non-Kolmogorov turbulence is studied, where the effect of non-Kolmogorov turbulence and beam bandwidth on the beam width spreading and angular spread is stressed. It is shown that the variation of the relative beam width of PCPHG beams with the generalized exponent parameter of non-Kolmogorov turbulence is non-monotonic. The larger bandwidth of PCPHG beams is, the smaller the relative beam width and the smaller the relative angular spread. Therefore, PCPHG beams with larger bandwidth are less affected by non-Kolmogorov turbulence than those with smaller bandwidth. PCPHG beams are less sensitive to the effect of non-Kolmogorov turbulence than fully coherent polychromatic Hermite-Gaussian (FCPHG) beams and polychromatic Gaussian Schell-model (PGSM) beams. The results are illustrated by numerical examples and interpreted.     

Effect of Non-Kolmogorov Turbulence on the Spreading of Polychromatic Partially Coherent Hermite–Gaussian Array Beams

Based on the extended Huygens–Fresnel principle, we derive an analytical expression for the beam width of polychromatic partially coherent Hermite-Gaussian array (PPCHGA) beams propagating through non-Kolmogorov turbulence and study in detail the effect of bandwidth, array parameters, and non-Kolmogorov turbulence on the beam-width spreading. We show that the beam width of PPCHGA beams increases with increase in the bandwidth, beam number, and relative distance of beam separation. The spreading of polychromatic array beams with increasing generalized exponent parameter is smaller than that of monochromatic array beams under the same conditions. The results are illustrated by numerical examples.     

Beam propagation factor of partially coherent elegant Hermite-cosh-Gaussian beam through non-Kolmogorov turbulence

Based on the extended Huygens–Fresnel principle and the second moments of the Wigner distribution function, an analytical expression for the propagation factors of partially coherent elegant Hermite-cosh-Gaussian beams (EHChGB) in non-Kolmogorov is derived. The M² factor of partially coherent EHChGB through non-Kolmogorov turbulence is studied analytically and numerically. The results show that partially coherent EHCHGB with higher beam order and longer wavelengths is less affected by non-Kolmogorov turbulence.     

Parametric characterization of truncated Hermite-cosh-Gaussian beams

Starting from the generalized second-order moments definition, a closed-form expression of M_G²-factor of hard-edge diffracted Hermite-cosh-Gaussian beams is investigated theoretically and some numerical calculations examples are illustrated. Our results constitute a more generalized study of M_G²-factor of some laser beams.     

Propagation of partially coherent controllable dark hollow beams with various symmetries in turbulent atmosphere

Normalized intensity distribution, the complex degree of coherence and power in the bucket for partially coherent controllable dark hollow beams (DHBs) with various symmetries propagating in atmospheric turbulence are derived using tensor method and investigated in detail. Analytical results show that, after sufficient propagation distance, partially coherent DHBs with various symmetries eventually become circular Gaussian beam (without dark hollow) in turbulent atmosphere, which is different from its propagation properties in free space. The partially coherent DHBs return to a circular Gaussian beam rapidly for stronger turbulence, higher coherence, lower beam order, smaller p or smaller beam waist width. Another interesting observation is that the profile of the complex degree of coherence attains a similar profile to that of the average intensity of the related beam propagating in a turbulent atmosphere. Besides the laser power focusablity of DHBs are better than that of Gaussian beam propagating in turbulent atmosphere.     

Spreading of apertured partially coherent beams in turbulent media

The closed-form expression for the mean-squared width of apertured partially coherent beams propagating through turbulent media is derived by using the integral transform technique. The influence of turbulence on the spreading of apertured partially coherent beams is studied quantitatively by examining the relative mean-squared width, which is defined as the ratio of the mean-squared width of an apertured partially coherent beam in turbulence to the mean-squared width of the same beam in free space. On the other hand, the range of turbulence-independent propagation, also a reasonable measure of the resistance of a beam to turbulence, is obtained by examining the mean-squared width. It is shown that the spreading of apertured partially coherent beams is less affected by turbulence with smaller truncation parameter δ and coherence parameter α than with larger δ and α. In addition, the influence of turbulence on the spreading of apertured partially coherent beams increases first and then decreases due to increasing waist width w₀. The results obtained are explained physically.     

Paraxial propagation of partially coherent flat-topped beam

The propagation of flat-topped beam passing through a paraxial optical ABCD system is extended to partially coherent case and has been studied in detail. Based on Wigner distribution function (WDF), the irradiance distribution of partially coherent flat-topped beam is derived. Furthermore, two propagation parameters, such as M²-factor and Power in Bucket (PIB) are illustrated analytically and numerically.     

Partially coherent elegant Hermite–Gaussian beam in turbulent atmosphere

Based on the extended Huygens–Fresnel integral, analytical formulas for the cross-spectral density, mean-squared beam width and angular spread of a partially coherent elegant Hermite–Gaussian (HG) beam in turbulent atmosphere are derived. The evolution properties of the average intensity, spreading and directionality of a partially coherent elegant HG beam in turbulent atmosphere are studied numerically. It is found that the partially coherent elegant HG beam with smaller initial coherence width, larger beam order and longer wavelength is less affected by the atmospheric turbulence. Compared to the partially coherent standard HG beam, the partially coherent elegant HG beam is less affected by turbulence under the same condition. Furthermore, it is found that there exist equivalent partially coherent standard and elegant HG beams, equivalent fully coherent standard and elegant HG beams, and an equivalent Gaussian–Schell-model beam may have the same directionality as a fully coherent Gaussian beam whether in free space or in turbulent atmosphere. Our results can be utilized in short and long atmospheric optical communication systems.     

非Kolmogorov大气湍流对部分相干厄米高斯光束传输因子的影响

基于非Kolmogorov谱模型,利用广义惠更斯-菲涅耳原理和维格纳分布函数的二阶矩定义,推导出部分相干厄米高斯(H-G)光束在非Kolmogonov大气湍流中传输因子的解析表达式,并用以研究了非Kolmogorov大气湍流对部分相干H-G光束传输因子的影响。结果表明,部分相干H-G光束在非Kolmogorov大气湍流中传输时,传输距离、湍流外尺度、广义结构常量和空间相关长度越小,湍流内尺度和光束阶数越大,光束传输受非Kolmogorov大气湍流影响越小,光束质量越好。当广义指数取3.11时,部分相干H-G光束在传输过程中表现的光束质量最差。     

Propagation factor of electromagnetic concentric rings Schell-model beams in non-Kolmogorov turbulence

We derive an analytical expression for the propagation factor(known as M2-factor) of electromagnetic concentric rings Schell-model(EM CRSM) beams in non-Kolmogorov turbulence by utilizing the extended Huygens–Fresnel diffraction integral formula and the second-order moments of the Wigner distribution function(WDF). Our results show that the EM CRSM beam has advantage over the scalar CRSM beam for reducing the turbulence-induced degradation under suitable conditions. The EM CRSM beam with multi-rings far-fields in free space is less affected by the turbulence than the one with dark-hollow far-fields or the electromagnetic Gaussian Schell-model(EGSM) beam. The dependence of the M2-factor on the beam parameters and the turbulence are investigated in detail.