The Wigner distribution functions of coherent and partially coherent Bessel-Gaussian beams

Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function (WDF) for a coherent or partially coherent Bessel-Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.     

部分相干光光束的振荡自陷特性

用互相干函数法研究了圆形横截面的部分相干光光束在光折变晶体中的自陷行为.光束的初态及材料的非线性决定了光束自陷的变化形式,导出空间周期表达式,获得了光束相干半径的解析表达式,发现部分相干光光束的相干特性会随传播距离发生周期性的演化,并将圆形光束的讨论结果扩展到椭圆形光束中. 关键词： 空间孤子 部分相干光光束 相干半径     

部分相干Airy光束及其传输的研究

利用高斯-谢尔模型的交叉谱密度公式和惠更斯衍射积分, 得到了部分相干Airy光束的表达式. 对不同相干度的部分相干Airy光束的无衍射和横向加速偏移的性质进行了理论分析并予以实验验证, 结果一致表明部分相干Airy光束也具有无衍射和横向加速度的特性, 而且相干度越低, 部分相干Airy光束的无衍射距离越短, 横向加速度越小. 关键词： 傅里叶光学 全息 部分相干 艾里光束     

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.     

Propagation factor of a truncated partially coherent flat-topped beam in turbulent atmosphere

Analytical expression for the propagation factor of a truncated partially coherent flat-topped (FT) beam in turbulent atmosphere is derived based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. Numerical results show that the radius of the aperture (i.e., truncation parameter) has strong influence on the evolution properties of the propagation factor of a truncated partially coherent FT beam, and the advantage of a truncated partially coherent FT beam over a truncated Gaussian Schell-model (GSM) beam or a truncated coherent FT beam for overcoming the turbulence-induced degradation disappears gradually with the decrease of the radius of the aperture.     

Circular partially coherent flattened Gaussian beam

An alternative theoretical model called circular partially coherent flattened Gaussian beam (FGB) is developed to describe a circular partially coherent beam with a flat-topped spatial profile. Explicit expression for the propagation factor of a circular partially coherent FGB is derived. We drive the analytical formulae for the cross-spectral density and mean-squared beam width of a circular partially coherent FGB propagating through a paraxial ABCD optical system based on the generalized Collins formula. The intensity, spreading and directionality properties of a circular partially coherent FGB propagating in free space are studied as numerical examples. The propagation properties of a circular partially coherent FGB agree well with those of a partially coherent flat-topped beam reported in the literature. Thus, our model provides an alternative but reliable model for describing a circular partially coherent beam with flat-topped profile.     

Partially coherent vortex beams propagation in a turbulent atmosphere

Based on the Rytov approximation and the cross-spectral density approximation for the mutual coherence function of the partially coherent field, the propagation properties of the partially coherent beams with optical vortices in turbulent atmosphere are discussed. The average intensity and the mutual coherence function of the partially coherent vortex beams propagation in weak turbulent atmosphere are obtained.It is shown that the vortex structure of the average cross-spectral density of partially coherent beams has the same helicoidally shape as that of the phase of the fully coherent Laguerre-Gauss beams in free space and the relative intensity of the beam is degraded by optical vortex.     

聚焦部分相干涡旋光束的焦移

基于部分相干光的传输理论获得了部分相干涡旋光束被光阑透镜聚焦后的传输方程。基于这些方程研究了部分相干涡旋光束的焦移现象。研究结果表明,部分相干涡旋光束的焦移不仅依赖于菲涅耳数,而且依赖于光束的相干长度和涡旋光束的拓扑荷数。菲涅耳数越小,焦移量越大;部分相干涡旋光束的相干长度越小,焦移量越大;涡旋光束的拓扑荷数越大,焦移量越大。     

部分相干光与相干光在湍流中的传输特性实验研究

相干光经湍流传输引起光强闪烁效应,理论研究表明利用部分相干光可降低该影响,而相关的实验验证鲜有报道。利用水介质的对流湍流池模拟产生了Rytov方差为0.04~0.16的湍流,进行了弱起伏区湍流中部分相干光及相干光的传输实验,由接收光强计算出其光强闪烁指数随湍流Rytov方差的变化关系。实验结果表明:随着湍流强度的增加,部分相干光与相干光的闪烁效应均增强,但部分相干光的闪烁指数小于相干光。将实验数据与Andrews等人建立的闪烁指数理论模型进行比较,得出了较为一致的结论。     

Propagation of a partially coherent beam through Selfoc fibers

Propagation of a partially coherent beam through a Selfoc fiber is considered. The inhomogeneous Helmholtz equations satisfied by the mutual coherence function are solved using the modal expansion. The result is applied to the cases when the incident beam is either incoherent or coherent. An expression for the intensity distribution is also obtained.     

Experimental investigation on partially coherent higher-order non-diffractive beams

We experimentally study the generation of a partially coherent non-diffractive beam by focusing a partially coherent vortex beam with an axicon. The investigation results show that when the partially coherent vortex beam is focused by the axicon, the beam is transferred into a partially coherent higher-order non-diffractive beam. In the non-diffractive zone, the transverse intensity distribution of the partially coherent higher-order non-diffractive beam is invariant during propagation. In addition, the range of the non-diffractive zone is related to the coherence of the partially coherent vortex beam. The poorer the coherence of the partially coherent vortex beam, the shorter the range of the non-diffractive zone.     

M 2-factors of a non-circular partially coherent flat-topped beam

Based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function, analytical formulae for the propagation factors (known as M ²-factors) of a non-circular (i.e., rectangular or elliptical) partially coherent flat-topped beam in turbulent atmosphere are derived. The properties of the M ²-factors of a non-circular partially coherent flat-topped beam in turbulent atmosphere and in free space are studied numerically and comparatively. It is found that the evolution properties of the M ²-factors are mainly determined by the parameters of the beam and the turbulent atmosphere. The relative M ²-factors of a non-circular partially coherent flat-topped beam can be smaller than a circular partially coherent flat-topped beam and a Gaussian Schell-model beam, particularly at long propagation ranges in turbulent atmosphere. Our results will be useful in long-distance free-space optical communications.     

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。     

部分相干双曲余弦厄米高斯光束在非Kolmogorov大气湍流中的传输特性

基于广义Huygens-Fresnel原理和非Kolmogorov大气湍流折射率起伏谱密度函数, 采用Wigner分布函数的二阶矩方法, 推导出了在大气湍流中传输的部分相干双曲余弦厄米高斯光束束宽和M²因子的解析表达式. 研究表明: 相对束宽和归一化M²因子随传输距离的增大而增大; 光束阶数越大、相干长度越小、双曲余弦参数越小, 相对束宽和归一化M²因子受大气湍流影响越小; 相对束宽随束腰宽度的增大存在极大值, 在一定的相干长度范围内, 归一化M²因子随束腰宽度的增大存在极小值; 相对束宽和归一化M²因子随广义指数的变化均存在极大值, 随内尺度的增大而逐渐减小, 随外尺度的增大几乎没有变化.     

Propagation of partially coherent beams: turbulence-induced degradation

We show that, when a partially coherent beam propagates through an inhomogeneous medium such as atmospheric turbulence, the phase randomization that is induced is less effective in degrading the spatial coherence properties. By evaluating the final beam widths we report what is to our knowledge the first experimental demonstration that, on propagation through thermlly induced turbulence, a partially coherent beam is less affected than a spatially coherent beam.     

激光场相干叠加光束合成技术

光束拼接激光相干合成中,拼接占空比不高导致合成光束能量集中度不够理想,为了解决这个问题,提出了激光场相干叠加光束合成技术路线,设计了基于半反半透合束镜的多级激光场相干叠加光束合成方案。研究了子光束之间的光强差和波面误差对相干合成的影响,结果表明,激光场相干叠加光束合成中,对参与合成子光束的光强差、相位差的容差均不难满足:仅考虑单一因素时,子束光强相差三倍时合成效率仍可达90%,相位误差小于π/5时,合成效率可达到90.5%。搭建了基于半透半反合束镜的两束激光场相干叠加光束合成实验装置,实验验证了激光场相干叠加光束合成技术的可行性,在闭环情况下得到了稳定的合成光束输出,合成效率可达95%以上。     

部分相干光对周期性局域空心光束的影响

用旋转毛玻璃和光阑把激光变成部分相干光, 再经过双轴棱锥系统把一束平行光变成两束同频率但不同径向波矢分量的无衍射贝塞尔光, 相干叠加产生了部分相干的周期性局域空心光束. 通过干涉理论与实验结果相互佐证, 得出局域空心光束的周期为2.5 mm. 进一步探究入射光场相干度对产生局域空心光束的影响, 发现随着相干度的降低局域空心光束中心暗斑与周围光强的衬比度会降低, 但不影响局域空心光束的周期以及中心暗斑尺寸.     

部分相干椭球光笼

 从理论上研究部分相干光束经透镜聚焦的三维光强分布。研究结果表明，在几何焦点附近的光强分布不仅依赖于入射部分相干光束的光强分布，而且还依赖于入射光束的空间相干度。基于这一点，提出了一种控制部分相干光束的空间相干度，在几何焦点附近获得了类似椭球光笼形状的光强分布的新方法。通过控制入射部分相干光的空间相干度，来改变聚焦在几何焦点附近的三维光强分布，从而获得希望得到的光强分布。     

一维激光阵列相干合束远场特性的研究

利用傅里叶光学方法,获得了相干合束远场光强的解析表达式,数值模拟和实验研究了一维锁相二极管激光阵列的相干合束远场特性。研究表明:随着参与合束的发光单元数目的增加,尖峰变锐;同相模的光能集中在更小的立体角内,使得相干合束的亮度增加;异相模的光束能量较为分散,其峰值光强有所降低。系统抖动引起远场峰值光强的降低,破坏了远场的对称性和光束质量。相干合束发光单元数目越多,系统抖动对远场的影响便可以忽略。     

Experimental determination of the azimuthal and radial mode orders of a partially coherent LG_(pl) beam(Invited Paper)

It is known that one can determine the mode orders(i.e.,the azimuthal order and radial order)of a partially coherent LG_(pl) beam(i.e.,a partially coherent vortex beam)based on the measurement of the cross-correlation function(CCF)and the double correlation function(DCF)together.The technique for measuring the CCF is known.In this Letter,we propose a method for measuring the DCF.Based on the proposed method,the determination of the mode orders of a partially coherent LG_(pl) beam is demonstrated experimentally.