线偏振拉盖尔-高斯光束的远场发散特性

利用稳相法和矢量结构理论, 导出了线偏振拉盖尔-高斯光束的矢量结构项TE项和TM项在远场的解析表达式. 进而利用TE项和TM项的远场能流分布, 给出了TE项和TM项的功率占总功率比例的度量式,同时还给出了线偏振拉盖尔-高斯光束、TE项和TM项三者远场发散角的解析式以及三者远场发散角间的关系式. 所得到的公式不仅适用于傍轴情形,而且还适用于非傍轴情形. 通过数值计算, 分析了TE项和TM项在远场的功率占总功率的比例与参数f和模数间的依赖关系;还分析了拉盖尔-高斯光束、TE项和TM项的远场发散角随参数f、模数和线偏振角的变化关系.这一研究从矢量结构本性揭示了线偏振拉盖尔-高斯光束的远场发散特性, 丰富了对其传输特性的认识.     

被光阑衍射部分偏振高斯-谢尔模型光束的远场特性

从部分相干光的传输理论出发,采用光束相干-偏振矩阵方法研究了被光阑衍射部分偏振高斯-谢尔模型光束的远场特性,对远场偏振和光强特性作了详细的数值计算和物理分析。研究结果表明,光阑衍射部分偏振高斯-谢尔模型光束的远场特性与光阑截断参量、光的空间相干性和衍射角有关。并与自由空间的传输特性和以前的工作作了比较分析。     

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。     

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。     

高斯光束经圆形光阑衍射的远场发散特性

线偏振高斯光束经圆形光阑衍射后,其远场可表示成互相正交的横电(TE)项和横磁(TM)项之和。利用TE项和TM项的远场能流分布,导出了高斯衍射光束的TE项和TM项远场功率的解析表达式,由此可度量TE项和TM项在远场占总功率的比例。基于能流二阶矩的定义,给出了高斯衍射光束、TE项和TM项远场发散角的解析式以及三者远场发散角间的关系通式,重点分析了f参数和截取参数对远场发散角的影响。结果表明:随着f参数的增大,远场发散角先增大后趋向于各自的饱和值。截取参数对远场发散角的影响与f参数相关,当f参数较大时,截取参数对远场发散角的影响不明显;当f参数适中时,随着截取参数的增大,远场发散角先减小后趋向于各自的最小值;但当f参数较小时,高斯衍射光束和TM项二者的远场发散角出现一定的波动性。     

高斯光束经圆形光阑衍射的远场发散特性

线偏振高斯光束经圆形光阑衍射后,其远场可表示成互相正交的横电(TE)项和横磁(TM)项之和。利用TE项和TM项的远场能流分布,导出了高斯衍射光束的TE项和TM项远场功率的解析表达式,由此可度量TE项和TM项在远场占总功率的比例。基于能流二阶矩的定义,给出了高斯衍射光束、TE项和TM项远场发散角的解析式以及三者远场发散角间的关系通式,重点分析了f参数和截取参数对远场发散角的影响。结果表明:随着f参数的增大,远场发散角先增大后趋向于各自的饱和值。截取参数对远场发散角的影响与f参数相关,当f参数较大时,截取参数对远场发散角的影响不明显;当f参数适中时,随着截取参数的增大,远场发散角先减小后趋向于各自的最小值;但当f参数较小时,高斯衍射光束和TM项二者的远场发散角出现一定的波动性。     

双向剪切干涉法测量高斯光束远场发散角

对双向剪切干涉理论和高斯光束传输特性进行了研究.提出了一种测量高斯光束远场发散角的方法：利用双向剪切干涉仪分别在激光传输路径上两个特定位置测出波前曲率半径,然后由曲率半径得出发散角.通过理论推导建立了相应的检测模型,并对模型进行了实验验证.实验测量和误差分析表明该方法的测量准确度能达到10″;发散角测量准确度的主要影响因素为干涉条纹宽度测量误差.     

高斯—谢尔模型光束的变换特性

在一般情况下推导出高斯－谢尔模型光束经ＡＢＣＤ光学系统变换后的相干模迭加表示式。     

衍射扭曲高斯-谢尔模型光束在远场的光谱移动和光谱开关

从部分相干光的传输理论出发,研究了被光阑衍射扭曲高斯-谢尔模型光束远场的光谱变化规律。结果表明,扭曲高斯-谢尔模型光束在远场也会出现光谱移动和光谱开关效应。与衍射高斯-谢尔模型光束情况相比,光谱移动和光谱开关效应不仅与光束空间相关性、截断参量和源光谱谱宽有关,光束的扭曲因子也会对衍射扭曲高斯-谢尔模型光束远场的光谱移动和光谱开关效应产生影响。通过数值计算结果详细讨论了光束扭曲因子影响衍射扭曲高斯-谢尔模型远场光谱的规律。     

多色矢量高斯-谢尔模型光束的焦移和焦开关

从交叉谱密度矩阵的传输公式出发,对多色矢量高斯-谢尔模型（GSM）光束的焦移和焦开关作了详细的研究.插入偏振片之前,多色矢量高斯-谢尔模型（GSM）光束通过硬边光阑透镜分离光学系统后,有焦移,但无焦开关;而插入偏振片之后,会出现焦开关.改变偏振片的旋转角度可以控制焦开关的特性.     

The directionality of partially coherent beams expressed in terms of the far-field divergence angle and of the far-field radiant intensity distribution

Taking the partially coherent cosh-Gaussian beam (ChG) as an illustrative example, the far-field divergence angle and directionality of partially coherent beams are studied. There are three competing physical mechanisms, i.e., the spatial coherence, diffraction and decentration, which affect the far-field divergence angle of partially coherent ChG beams. Two partially coherent ChG beams may generate the same far-field divergence angle, and partially coherent ChG beams may also have the same far-field divergence angle as a fully coherent ChG beam or as a fully coherent Gaussian laser beam if the three physical mechanisms are appropriately balanced. The consistency of the directionality of partially coherent beams expressed in terms of the far-field divergence angle and in terms of the far-field radiant intensity distribution is examined. Generally, two partially coherent beams with the same far-field divergence angle have not certainly the same far-field radiant intensity distribution. However, under certain conditions, it is possible to achieve the consistency of the directionality expressed in terms of the far-field divergence angle and of the normalized far-field radiant intensity distribution.     

Polarization properties of nonparaxial partially polarized Gaussian Schell-model beams

The polarization properties of nonparaxial partially polarized Gaussian Schell-model (PGSM) beams are studied. Based on the beam coherence-polarization matrix, the propagation formula of the degree of polarization for the nonparaxial PGSM beams is derived. The paraxial approximation is dealt with as special cases of our general results. Some conditions that limit the choice of the parameters are established. The sufficiency condition of polarization invariance in propagation for the nonparaxial PGSM beams is derived. By using the derived formulae, the propagation properties of the degree of polarization for the nonparaxial PGSM beam in free space are illustrated and analyzed with numerical examples. Some detailed comparisons of the obtained results with the paraxial results are made.     

Beam quality of radial Gaussian Schell-model array beams

Taking the Rayleigh range z_R and the M²-factor as the characteristic parameters of beam quality, the beam quality of radial Gaussian Schell-model (GSM) array beams is studied. The analytical expressions for the z_R and the M²-factor of radial GSM array beams are derived. It is shown that for the superposition of the cross-spectral density function z_R is longer and the M²-factor is lower than that for the superposition of the intensity. For the two types of superposition, z_R increases and the M²-factor decreases with increase in beam coherence parameter, and both z_R and the M²-factor increase with increase in inverse radial fill-factor. For the superposition of the cross-spectral density function, z_R increases and the M²-factor decreases with increase in beam number, while for the superposition of the intensity both the z_R and M²-factor are independent of the beam number.     

Matrix representation of Gaussian Schell-model beams in optical systems

The behaviour of a Gaussian Schell-model beam at a spherical boundary is investigated in detail, and transformation laws for its propagation parameters are obtained. These laws are used to extend the classic ABCD-matrix method into the context of partially coherent beams. The matrix formalism is useful in designing and analysing real optical systems, which consist of spherical boundaries and uniform media of finite thickness. Explicit relations are derived that couple the input and output beam parameters in general optical systems of that type. The closed-form imaging equations ensuing for a single thin lens are discussed as an illustrative example.     

Propagation of partially polarized Gaussian Schell-model beams in anomalously dispersive media

By use of a tensor method, analytical transform formulae for isotropic partially polarized GSM beams propagating in anomalously dispersive media are derived. Based on the derived formula, the propagation properties of isotropic partially polarized GSM beams in anomalously dispersive media are studied in detail. The results show that the polarization and the irradiance distribution and the coherence degree properties are influenced by the anomalously dispersive media and beam's initial coherence. In addition, the evolution of the spectrum shows that spectrum splitting and spectral shift occur during propagation in anomalously dispersive media.     

Range of turbulence-negligible propagation of Gaussian Schell-model array beams

For linear Gaussian Schell-model (GSM) array beams, the range of turbulence-negligible propagation, in which all of the spatial and angular spreading and the beam propagation factor increasing due to turbulence can be neglected, has been investigated in detail. It is shown that this range of GSM array beams increases with decreasing turbulent parameter and coherent parameter, and depends on the beam number, the waist width, and the relative beam separation distance. This range of a GSM array beam is larger than that of a coherent Gaussian array beam, and this range of a GSM array beam with a large relative beam separation distance is larger than that of a single GSM beam, implying that a GSM array beam may be more appropriate to be used in atmospheric optical communication links than a coherent Gaussian array beam or a GSM beam.     

Focusing of stochastic electromagnetic Gaussian Schell-model beams through a high numerical aperture objective

Based on vectorial Debye diffraction theory, the focusing properties of stochastic electromagnetic Gaussian Schell-model beams in the focal region of high numerical aperture objective are investigated. Expressions for the intensity distribution and the degree of polarization are derived near the focus. Numerical calculations are performed to analyze the influences of varying corresponding parameters on the changes in the intensity distribution and in the degree of polarization in the focal region.     

Influence of turbulence on the beam propagation factor of Gaussian Schell-model array beams

The analytical expression for the beam propagation factor (M²-factor) of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the M²-factor of GSM array beams depends on the beam number, the relative beam separation distance, the beam coherence parameter, the type of beam superposition, and the strength of turbulence. The turbulence results in an increase of the M²-factor. However, for the superposition of the intensity the M²-factor is less sensitive to turbulence than that for the superposition of the cross-spectral density function. The M²-factor of GSM array beams is larger than that of the corresponding Gaussian array beams. However, the M²-factor of GSM array beams is less affected by turbulence than that of the corresponding Gaussian array beams. For the superposition of the cross-spectral density function a minimum of the M²-factor of GSM array beams may appear in turbulence, which is even smaller than that of the corresponding single GSM beams.     

Changes in polarization of Gaussian Schell-model beams and partially polarized Gaussian Schell-model beams through a polarization grating

The polarization properties of Gaussian Schell-model (GSM) beams and partially polarized Gaussian Schell-model (PGSM) beams passing through a polarization grating (PG) are studied based on the beam coherence-polarization (BCP) matrix formulism, where the finite size of the PG is considered. Detailed numerical calculation results are given and compared with the previous work.