高斯-谢尔模型列阵光束的远场发散角和远场辐射强度

推导出了高斯-谢尔模型（GSM）列阵光束通过自由空间传输其二阶矩束宽、远场发散角和远场辐射强度的解析表达式,并给出了GSM列阵光束与高斯光束具有相同远场发散角的条件.研究表明,具有相同远场发散角的GSM列阵光束与对应的高斯光束并不具有相同的远场辐射强度分布,这一特性与单束GSM光束的差异很大. 关键词： 高斯-谢尔模型列阵光束 远场发散角 远场辐射强度     

Consistency of the directionality of partially coherent beams inturbulence expressed in terms of the angular spread and the far-field average intensity

Under the quadratic approximation of the Rytov's phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbulence. It finds that under a certain condition different types of partially coherent beams may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence if the angular spread is chosen as the characteristic parameter of beam directionality. On the other hand, it shows that generally, the directionality of partially coherent beams expressed in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, but the consistency can be achieved due to turbulence.     

Spatial coherence properties and directionality of partially coherent cosh-Gaussian beams

Based on the theory of optical coherence, the spatial coherence properties and directionality of partially coherent cosh-Gaussian (ChG) beams are studied. It is shown that unlike Gaussian Schell-model (GSM) beams, in the strict sense there do not exist partially coherent ChG beams which may produce the same far-field radiant intensity distribution as a fully coherent laser beam. However, under certain conditions it is possible to find partially coherent ChG beams with the same far-field radiant intensity distribution as a fully coherent laser beam.     

部分相干厄米-高斯光束杨氏实验中的光强分布

将杨氏干涉实验作为双缝衍射现象处理,以部分相干厄米-高斯(H-G)光束为例,研究分析了多模部分相干光的杨氏双缝干涉光强和干涉条纹可见度的空间分布。数值计算说明,多模部分相干光束的空间相干参数、模阶数和缝遮拦比对衍射场中光强的空间分布(干涉花样)都有影响。当多模部分相干光的阶数为奇数时,轴上光强与光束的相干性会出现相消干涉;当多模部分相干光的阶数为偶数时,轴上光强与光束的相干性会出现相长干涉等。     

光束相干合成中填充因子对远场光强分布的影响

理论推导了相干光束阵列远场光强分布的解析表达式.介绍了填充因子及五种相干合成效果评价参数的定义.分析了填充因子对远场光强分布的影响,发现填充因子通过影响空间调制因子来改变远场光强分布.求得了相干合成效果评价参数与填充因子的关系式,并绘制了关系曲线.计算结果表明,斯特列尔比与填充因子无关,恒为1;中央主瓣半径与填充因子成正比关系;中央主瓣能量密度受填充因子的影响较小;中央主瓣能量比与填充因子的平方成近似正比关系;桶中功率与填充因子的关系很复杂,但总体上随着填充因子的√减小而减小.分析显示,若要保证中央主瓣能量比和PIB值均大于最佳值的一半,则填充因子应大于2/2.     

Coherent and incoherent combinations of partially coherent beams beyond the paraxial approximation

The concept of coherent and incoherent combinations of partially coherent beams is described and interpreted physically. Taking the Gaussian Schell-model (GSM) beam as a typical example of a partially coherent beam, the analytical propagation expressions for the coherent and incoherent combinations of GSM beams beyond the paraxial approximation are derived and illustrated numerically. Some special cases of the general results are analyzed.     

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.     

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.     

部分相干双曲余弦-高斯光束的传输特性和空间整形

 通过加入高斯项的空间相干度，引入部分相干双曲余弦-高斯（ChG）光束，推导出部分相干ChG光束通过近轴ABCD光学系统传输的解析表达式，并用以研究其传输特性和空间整形。结果表明，部分相干ChG光束的光强分布不能保持传输不变性，其光强分布不仅与传输距离和离心参数有关，而且还与空间相干参数有关。在传输距离固定时，适当改变部分相干ChG 光束的离心参数和空间相干参数，可实现光束的空间整形。光束质量因子随空间相干性的增大和离心参数的减小而减小。高斯-谢尔模型光束和完全相干ChG光束可作为部分相干ChG光束的特例处理。     

Partially coherent non-paraxial vectorial Hermite-Gaussian beams and their far-field properities

The far-field theory of partially coherent vectorial non-paraxial beams is expanded and their analytical propagation expressions of the Wigner distribution function matrices and the cross-spectral-density matrices in free space are derived using the far-field approximation. Some interesting cases, in particular the vectorial non-paraxial partially coherent Hermite-Gaussian (HG) beams, are discussed and treated as special cases of our general expressions. It is shown that the f_σ and f parameters play an important role in determining vector and non-paraxiality of partially coherent HG beams. When two parameters are small enough, scalar and paraxial vectorial approximation is allowed; otherwise, non-paraxial vectorial approximation is applied. But the decided parameters additionally affect their far-field divergence angles.     

部分相干电磁光束的焦移

 基于有效菲涅耳数的概念,给出一种简单的表达式来评估部分相干电磁光束经圆形光阑透镜后所产生的相对焦移,对部分相干电磁光束经透镜聚焦的情况进行了研究。结果表明:当交叉谱密度函数的非对角元素为零时,有效菲涅耳数不仅依赖于真实的菲涅耳数大小,而且依赖于光束的偏振分布和入射部分相干电磁光束两个偏振分量的空间相干长度;相对焦移量仅由等效菲涅耳数决定。将此方法与数值积分法进行的比较表明,等效菲涅耳数可以简单、准确地评估焦移。     

部分相干厄米-双曲正弦-高斯光束通过湍流大气传输的平均光强分布演化和角扩展

推导出部分相干厄米-双曲正弦-高斯(H-ShG)光束通过湍流大气的平均光强和角扩展的解析表示式,并用以研究了部分相干H-ShG光束在湍流中的平均光强分布演化和角扩展. 结果表明,折射率结构常数C²_n的增加和空间相关长度σ₀的减小都会加速演化过程. 引入相对角扩展来定量描述光束抗拒湍流的能力. 空间相关长度σ₀,束腰宽度w₀和双曲 关键词： 平均光强分布演化 角扩展 湍流大气 部分相干厄米-双曲正弦-高斯(H-ShG)光束     

Axial intensity distribution and focal shifts of focused partially coherent conical Bessel–Gauss beams

Based on the generalized Huygens–Fresnel diffraction integral and the theory of partially coherent light, the axial intensity distribution and the focal shifts of focused partially coherent conical Bessel–Gauss beams are investigated. The dependence of the maximum on-axis intensity and the associated focal shift on the Fresnel number and the coherence parameter are examined and illustrated numerically. The results related to the J ₀-correlated beams and the fully coherent Bessel–Gauss beams are obtained as particular cases of this study.     

Transformation and spatial shaping of partially coherent cosh-Gaussian beams through an astigmatic lens

Based on the propagation law of partially coherent beams, the closed-form propagation expression for partially coherent cosh-Gaussian (ChG) beams through an astigmatic lens is derived. The transformation and spatial shaping of partially coherent ChG beams through the astigmatic lens are studied and illustrated by numerical examples. It is shown that a suitable choice of the spatial coherence parameter and/or astigmatic coefficient, different beam profiles, such as Gaussian-like, flat-topped and bottle beam profiles, and beam profile with a central dip, at the geometric focal plane and at a certain plane are realizable.     

Spectral switches of partially coherent nonparaxial beams diffracted at an aperture

Based on the generalized Rayleigh diffraction integral, the spectral shifts and spectral switches of nonparaxial partially coherent beams diffracted at an aperture are studied. Our main attention is paid to the effect of beam nonparaxiality on the spectral switches of partially coherent beams. It is shown that the spatial coherent parameter β, trunction parameter δ and waist width-to-central wavelength ratio w₀/λ₀ affect the behavior of spectral switches. Only when β, δ and w₀/λ₀ satisfy certain conditions, can the difference between the nonparaxial and paraxial results be negligible. The discrepancy arises physically from the change of the spectral modifier by using the paraxial approximation.     

Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere

The characteristics of partially coherent Bessel-Gaussian beams propagating in turbulent atmosphere are investigated. Based on the extended Huygens–Fresnel principle, the influence of topological charges and coherence of the source on the intensity and the degree of coherence in the received plane are considered. The influence of atmospheric turbulence on beam profile and coherence in the received plane is also analyzed. It is found that a Bessel-Gaussian shaped intensity distribution will eventually transform into a Gaussian distribution after propagating in turbulent atmosphere. Meanwhile, topological charges, coherence of the source and atmospheric turbulence will also influence the propagation characterizations of the beams.     

Directionality of partially coherent annular flat-topped beams propagating through atmospheric turbulence

The closed-form expression for the angular spread of partially coherent annular flat-topped beams propagating through atmospheric turbulence is derived by using the integral transform technique. In comparison with previous work, the results obtained in this paper are more general. It is shown that, except for equivalent Gaussian Schell-model (GSM) beams as pointed out in Ref. [T. Shirai, A. Dogariu, E. Wolf, Opt. Lett. 28 (2003) 610], there also exist equivalent annular and non-annular beams which may generate the same directionality as the corresponding fully coherent Gaussian beam both in free space and in turbulence. The theoretical results are illustrated by numerical examples and interpreted physically.     

Spectral intensity characteristics of partially coherent flattened multi-Gaussian beams with an axial shadow passing though paraxial ABCD optical systems

Based on the beam model for the flattened multi-Gaussian beams (FMGBs) with an axial shadow and partially coherent theory, the expression for cross-spectral density of partially coherent FMGBs with an axial shadow has been given, and the analytical expression for the spectral intensity of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems has been derived. The spectral shift of partially coherent FMGBs with an axial shadow focused by a thin lens has been analyzed quantitatively. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed in detail. Our results show that the spectral intensity and the spectral shift of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems depend on the source spectral density, the generalized Fresnel number of the system, the transverse coordinate, the spatially coherence parameter, as well as the beam orders.     

The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field

Based on the extended Huygens–Fresnel principle, the closed-form propagation equation of partially coherent Sinh-Gaussian (ShG) beams through the turbulent atmosphere has been derived by using the quadratic approximation of the Rytov's phase structure function. The influence of turbulence on propagation properties of partially coherent ShG beams and their beam quality in the far field are studied both analytically and numerical. The fully coherent ShG beam has been treated as a special case of the partially coherent ShG beam when the degree of spatial coherence α=∞. It is shown that in comparison with the free-space propagation the turbulence accelerates the evolution of three stages that partially coherent ShG beams undergo. The smaller α is, the less partially coherent ShG beams are affected by the turbulence. In particular, we find that the β parameter decreases as the decentered parameter δ increases, but the dependence of the Strehl ratio on δ is not monotonous. There exists an optimal δ_opt, the influence of turbulence on the maximum intensity of the corresponding partially coherent ShG beam with δ_opt is the smallest. Therefore, a suitable choice of δ may reduce the influence of turbulence on the beam quality in the far field in practice.     

Design and optimization of phase plates for shaping partially coherent beams by adaptive genetic algorithms

The adaptive genetic algorithms (AGAs) are applied to the design and optimization of phase plates for shaping partially coherent beams. The simulation procedure based on the AGAs is described. Numerical examples for shaping partially coherent Cosh-Gaussian (ChG) and Hermite-Gaussian (HG) beams demonstrate the advantage of the AGAs in applications to the partially coherent beam transformation and shaping.