部分相干平顶高斯光束通过球差透镜的聚焦特性

基于部分相干光的传输理论,研究了部分相干平顶高斯光束通过球差透镜聚焦后轴上点的光强分布。数值计算表明:轴上最佳聚焦点随着球差从负到正的变化而向几何焦点方向移动;光束阶数越大,实现最佳聚焦点越过几何焦点所需的正球差值越小;正负球差对应的最佳聚焦点始终分居于无球差时最佳聚焦点的两侧;轴上最佳聚焦点的光强随着球差从负到正的变化而变小;当正负球差绝对值较大时,光强随球差的变化较为缓慢,而在球差值为0附近,光强随球差的变化比较剧烈。     

部分相干修正贝塞尔高斯光束通过球差透镜的聚焦特性

由部分相干光的传输理论出发,对部分相干修正贝塞尔高斯光束通过球差透镜聚焦后轴上光强分布进行了研究.数值计算表明:当光谱相干度较小时,正、负球差对应的最佳聚焦点位于无球差时对应的最佳聚焦点的两侧;当光谱相干度较大时,正、负球差对应的最佳聚焦点将位于无球差时对应的最佳聚焦点的左侧.研究进一步表明,最佳聚焦点随着透镜菲涅耳数的增大向几何焦点方向靠近,并趋于一个定值.当光束菲涅耳数为1时,无球差时对应的最佳聚焦点逐渐趋于0.908,该值与光谱相干度无关,当透镜具有球差时,该值与光谱相干度有关.     

高斯光束经过负球差透镜的聚焦

本文讨论高斯光束经过负球差透镜的聚焦，得到了聚焦光场轴上点的光强分布的表示式，并对其进行数值计算。数值计算结果表明，在负球差的情况下，得到光强的最大点位置（最佳聚焦点）相对于无球差情况，往透镜方向移动，并且，最佳聚焦点的光强较无球差时大，当Ｎｗ＝１，Ｎａ＝５，ｋＳ１＝－０．２时，得到的最佳聚焦点的光强是无球差时的１．３４倍。本文还讨论了透镜的菲涅尔数对聚焦光场分布的影响。结果表明，当透镜的菲涅尔数小于１时，球差对高斯光束的聚焦的影响可以忽略。     

利用球差透镜获得平顶激光光束

本文根据Huygens-Fresnel衍射积分计算高斯光束经过球差透镜的聚焦。数值计算结果表明,当透镜的球差系数为负时,在聚焦光场的两个位置,可得到平顶的激光光束。并且,透镜的负球差系数越大,得到的平顶激光光束越平坦。     

球差透镜聚焦部分相干光束获得局域空心光束

基于Collins公式,研究了空间相干度为零阶贝塞耳函数的部分相干光通过球差透镜后在几何焦平面附近的光强分布情况.研究表明,通过改变部分相干光的光谱相干度,球差系数可以得到平顶光束和局域空心光束.球差系数决定了最佳聚焦点的位置.当球差系数为正时,最佳聚焦点随着球差系数的增大向远离透镜的方向运动,甚至超过几何焦点;当球差系数为负时,最佳聚焦点随着球差系数绝对值的增大向靠近透镜方向移动.另外,在正负球差绝对值相等时,光强分布以几何焦点相对称.     

柱面球差透镜聚焦部分相干光束的焦移

通过定义聚焦光束的等效菲涅耳数,研究了部分相干光经柱面球差透镜聚焦后的轴上光强分布,得到了相对焦移的简单公式,即相对焦移反比于等效菲涅耳数的平方.结果表明,这种基于等效菲涅耳数的计算聚焦光学系统的焦移方法是计算部分相干光束经球差透镜聚焦相对焦移简单且有效方法.还讨论了一种特殊等效菲涅耳数为纯虚数情况.结果证明,在这种情况下,该相对焦移简单公式仍然有效.     

椭圆平顶高斯光束的聚焦特性

利用级数分解法把椭圆平顶高斯光束(EFGB)分解成多个椭圆厄密-高斯模的叠加形式,利用椭圆厄密-高斯模的传输公式导出了EFGB通过非轴对称光学系统的传输公式,该公式和直接用矢量积分得出的结果是等效的.利用导出的公式,我们计算分析了EFGB通过轴对称透镜和非轴对称透镜的聚焦特性.结果表明,EFGB聚焦后,近场光强分布变化很快,特别是焦点前后,光强分布会快速旋转.另外,EFGB的聚焦特性与阶次有关.     

大气湍流对部分相干平顶高斯光束的影响

采用相屏近似处理方法对激光通过湍流大气的传输进行了数值模拟。从数值模拟的结果拟合出两个公式:一是通过湍流前后部分相干平顶高斯光束的束宽平方比随阶数、传输距离和湍流强度的变化关系式;一是通过湍流后的相干长度随初始光束相干长度、湍流相干长度的变化关系式。研究发现:部分相干平顶高斯光束分解为相互独立的厄米-高斯光束的叠加;相干性越差的光束受到湍流的影响程度就越小;湍流对光束传输的影响与光束自身相干特性对其传输的影响之间是不相关的。     

大气湍流对部分相干平顶高斯光束的影响

采用相屏近似处理方法对激光通过湍流大气的传输进行了数值模拟。从数值模拟的结果拟合出两个公式：一是通过湍流前后部分相干平顶高斯光束的束宽平方比随阶数、传输距离和湍流强度的变化关系式;一是通过湍流后的相干长度随初始光束相干长度、湍流相干长度的变化关系式。研究发现：部分相干平顶高斯光束分解为相互独立的厄米-高斯光束的叠加;相干性越差的光束受到湍流的影响程度就越小;湍流对光束传输的影响与光束自身相干特性对其传输的影响之间是不相关的。     

高斯光束通过双焦透镜的聚焦特性

 从Collins公式出发,研究了高斯光束通过双焦透镜后的聚焦特性。在无光阑的情况下,给出了轴上光强和x, y方向两束腰及其位置的解析公式。详细的数值计算表明,轴上光强最大点位于其中一个束腰位置附近或者相重合,但始终不能超过透镜较大的焦点。并且,相对束腰的位移随光阑效应的增加而增加。     

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.     

Radiation forces of a focused partially coherent flattened vortex beam on a Rayleigh spherical particle

A focused partially coherent flattened vortex beam used to trap a Rayleigh dielectric spherical particle with relative refractive index p < 1 is studied. The dependence of radiation forces (RFs) on the beam order N, waist width w₀, correlation length σ₀, particle radius a and focal length f is analyzed and illustrated by numerical examples. By a suitable choice of N, w₀, σ₀ and f a stable trap of the Rayleigh particle is achievable. In particular, there exist critical values w0,c, σ_0,c for a partially coherent flattened vortex beam the particle can be trapped by the beam with w₀ less than w0,c and σ₀ larger than σ_0,c. A comparison with the previous work is made.     

Focusing of flattened Gaussian beams by an annular lens

Focusing properties of flattened Gaussian beams (FGBs) passing through an annular lens is studied based on the Collins formula. It is found that the on-axis irradiance distributions of focused FGBs are unsymmetrical with respect to the geometrical focal plane even for large values of Fresnel number F_w associated with the beam, so that there exist focal shifts in general. Detailed numerical results show the dependence of focal shifts on the beam and system parameters. Focal shifts of FGBs by a lens without central obscuration and focal shifts of Gaussian beams by an annular lens can be treated as special cases of the obscure ratio =0 and beam order N=0, respectively. Furthermore, focal shifts of plane waves by an annular lens can also be treated as a special case of N=0 and F_w→∞.     

Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere

Analytical formulae for phase-locked partially coherent flattened beam array propagating in a turbulent atmosphere are derived based on the extended Huygens–Fresnel principle. Beam propagation factor (BPF) is introduced to evaluate the beam quality at the receiving plane. The influence of beam order, transverse coherence width length and the intensity of turbulence is discussed in detail.     

Focusing of a vortex carrying beam with Gaussian background by a lens in the presence of spherical aberration and defocusing

Diffraction pattern formed by a lens for a vortex containing truncated beam with Gaussian background, and in the presence of spherical aberration and defocusing has been studied by Fresnel–Kirchhoff diffraction integral. For the study, two different values of topological charge are selected. Compensation of aberration in the presence of appropriate value of defocusing is investigated. Presence of spherical aberration results in an increase in the size of the dark core of the diffraction pattern. Results are also presented for the encircled energy. Some results are also presented for the influence of truncation parameter of the beam, on the point spread function at different observation planes.     

平顶高斯光束和超高斯光束传输特性的相似性

 在直角坐标系下对平顶高斯光束和超高斯光束的传输特性的相似性问题作了讨论。研究表明,当有相同的M²因子但束宽不同的平顶高斯光束和超高斯光束通过光阑效应可忽略ABCD光学系统传输时,在广义菲涅尔数F相等处有相似的光强分布。对于有光阑和用球差透镜聚焦的情况,若平顶高斯光束和超高斯光束具有相同的M²因子和束腰宽度,则在相同传输距离处仍可得到相似的光强分布。     

Tight focusing of partially coherent radially polarized beam with high NA lens axicon

Tight focusing of radially polarized partially coherent vortex beam over a high numerical aperture lens axicon system is introduced and its propagation properties are studied based on vectorial Debye theory. The effect of propagation parameters on the intensity distribution, the polarization property and the coherent property of the beam is illustrated analytically and numerically. It is shown that the correlation length and maximal NA angle has a significant influence on the intensity profile.