Tightly focused properties of a partially coherent radially polarized power-exponent-phase vortex beam

A partially coherent beam called a radially polarized multi-Gaussian Schell-model power-exponent-phase vortex beam is introduced. Both the analytical formula of the beam propagating through the high-numerical-aperture objective lens based on the vectorial diffraction theory, and the cross-spectral density matrix of the beam in the focal region are derived. Then,the tight focusing characteristics of the partially coherent radially polarized power-exponent-phase vortex beam are studied numerically, and the intensity distribution, degree of polarization and coherence of the beams in the focusing region with different topological charge, power order, beam index and coherence width are analyzed in detail. The results show that the contour of the spot becomes clearer and smoother with the increase in the beam index, and the focal fields of different structures that include the flattened beam can be obtained by changing the coherence width. In addition, by changing the topological charge and power order, the intensity can gather to a point along the ring. These unique properties will have potential applications in particle capture and manipulation, especially in the manipulation of irregular particles.

Propagation of the off-axis superposition of partially coherent beams through atmospheric turbulence

The propagation properties of the off-axis superposition of partially coherent beams through atmospheric turbulence and their beam quality in terms of the mean-squared beam width w（z） and the power in the bucket （PIB） are studied in detail, where the effects of partial coherence, off-axis beam superposition and atmospheric turbulence are considered. The analytical expressions for the intensity, the beam width and the PIB are derived, and illustrative examples are given numerically. It is shown that the maximum intensity/max and the PIB decrease and w（z） increases as the refraction index structure constant Cn^2 increases. Therefore, the turbulence results in a degradation of the beam quality. However, the resulting partially coherent beam with a smaller value of spatial correlation parameter γ and larger values of separate distance Xd and beam number M is less affected by the turbulence than that with a larger value of y and smaller values of Xd and M. The main results obtained in this paper are explained physically.

Coherence vortices of partially coherent beams in the far field

Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model correlator in the far field, where our main attention is paid to the evolution of far-field coherence vortices into intensity vortices of fully coherent beams. The results show that, although there are usually no zeros of intensity in partially coherent beams with Gaussian envelope and Schell-model correlator~ zeros of spectral degree of coherence exist. The coherence vortices of spectral degree of coherence depend on the relative coherence length, mode index and positions of pairs of points. If a point and mode index are kept fixed, the position of coherence vortices changes with the increase of the relative coherence length. For the low coherent case there is a circular phase dislocation. In the coherent limit coherence vortices become intensity vortices of fully coherent Laguerre-Gaussian beams.

Review on partially coherent vortex beams

Ever since vortex beams were proposed, they are known for owning phase singularity and carrying orbital angular momentum (OAM). In the past decades, coherent optics developed rapidly. Vortex beams have been extended from fully coherent light to partially coherent light, from scalar light to vector light, from integral topological charge (TC) to fractional TC. Partially coherent vortex beams have attracted tremendous interest due to their hidden correlation singularity and unique propagation properties (e.g., beam shaping, beam rotation and self-reconstruction). Based on the sufficient condition for devising a genuine correlation function of partially coherent beam, partially coherent vortex beams with nonconventional correlation functions (i.e., non-Gaussian correlated Schell-model functions) were introduced recently. This timely review summarizes basic concepts, theoretical models, generation and propagation of partially coherent vortex beams.

Characterization of tightly focused partially coherent radially polarized vortex beams

Tight focusing properties of partially coherent radially polarized vortex beams are studied based on vectorial Debye theory.We focus on the focal properties including the intensity and the partially coherent and polarized properties of such partially coherent vortex beams through a high numerical aperture objective. It is found that the source coherence length and the maximal numerical aperture angle have direct influence on the focal intensity,as well as coherence and polarization properties.This research is important in optical micromanipulation and beam shaping.

Generation and propagation of partially coherent vortex beams

The generation and propagation of partially coherent vortex beams have been investigated experimentally.It is found that a vortex beam with more uniform intensity distribution can be obtained by decreasing the coherence of the beam.We find that the beam shape of a completely coherent beam will keep hollow profile invariant during its propagation in free space.However,the center of the beam turns to be blurred for a partially coherent vortex beam on propagation.It is also found that the beam spreads more rapidly for the vortex beam with lower coherence,and this influence can be decreased by increasing the topological charge of the vortex beam.

部分相干多离轴涡旋矢量光束的传输特性

基于相干与偏振的统一理论,采用傅里叶变换和卷积定理的方法,研究了携带多个离轴涡旋相位的径向偏振矩形对称余弦-高斯关联结构光束的传输特性.结果表明,该光束因其独特的空间相干结构而具有自分裂特性,可以分裂成4束完全相同的子波瓣.更重要的是,多离轴涡旋相位的调制可以作用在每个子波瓣上.当相干度较大时,通过调制光束的离轴涡旋数量N_(0)和光束阶数可以在焦平面处产生具有三角形或正方形等多边形空心光强分布的光斑阵列,并且每个子波瓣上对应的偏振态呈现倒三角形或斜正方形的椭圆分布.当相干度较小时,部分相干光束的空间相干性调控占主导作用,多离轴涡旋相位的调制效果消失,每个子波瓣的光强退化成高斯形式分布,但其偏振态分布仍保持不变,与光束阶数和相干长度无关.此外,当利用障碍物遮挡住其中一个离轴涡旋相位时,光束仍具有一定的自修复能力.然而,若将其中一个离轴涡旋相位完全遮挡住,此时每个子波瓣的强度分布和偏振态分布都遭到破坏,会出现不同程度的“缺口”.

部分相干径向偏振环形艾里涡旋光束在大气湍流中的传输特性研究

为了探究部分相干径向偏振环形艾里涡旋光束在大气湍流中传输时的光强闪烁特性,利用分步相位屏法研究了其在各项异性湍流中的传输特性。结果显示:随着传输距离的增大,闪烁指数首先逐渐增大,当达到最大值后再逐渐减小。当传输距离一定时,闪烁指数随着相干长度的增大而增大。随着截断因子的减小,拓扑荷数的增大,闪烁指数减小。随着相干长度、拓扑荷数的增大,部分相干径向偏振环形艾里涡旋光束保持偏振特性的能力增强。

聚焦部分相干涡旋光束作用于不同折射率瑞利粒子上的辐射力

使用聚焦部分相干高斯谢尔涡旋光束,对不同折射率的瑞利粒子的辐射力做了分析,着重研究了相关长度和束腰宽度对辐射力和俘获稳定性的影响。结果表明:相关长度和束腰宽度分别存在临界值,相干长度小于等于其临界值或束腰宽度大于等于其临界值时,可利用其俘获相对折射率大于1的微粒;而在相关长度大于其临界值或束腰宽度小于其临界值时,可利用其俘获相对折射率小于1的微粒。对俘获稳定性的分析表明,需选择适当的相关长度和束腰宽度才能稳定俘获瑞利粒子。

衍射效应诱导涡旋光束的偏振度变化

基于惠更斯-菲涅耳衍射原理以及部分相干光的相干与偏振的统一理论,研究了衍射效应诱导部分相干涡旋光束的偏振度变化.通过理论分析与数值计算表明,部分相干涡旋光束经圆孔衍射后偏振度将发生变化,在衍射场中光束的偏振度分布情况与入射光束的相干度、入射光束的拓扑电荷数、衍射孔径的大小等因素有关.

部分相干圆偏振涡旋光束的深聚焦

基于德拜理论,研究部分相干圆偏振涡旋光束的深聚焦特性,比较左旋和右旋部分相干圆偏振涡旋光束的不同深聚焦特性,并给出相应的物理解释.分析入射光束相干性和聚焦透镜数值孔径大小对深聚焦特性的影响.研究表明,入射光束的相干度和聚焦透镜的数值孔径大小,都会影响深聚焦焦平面的光强和相干度.通过控制各相关参数的取值,可以在聚焦场中获得有广泛实际应用的平顶光束.

部分相干双涡旋光束在湍流介质中的传输

基于广义惠更斯—菲涅耳原理,推导了部分相干双涡旋光束在湍流介质中传输时光强分布变化规律的理论公式;并在实验上用螺旋相位板和随机相位板产生了此类光束,其内外双环可各自携带不同拓扑荷数;分析比较了此光束在传输中的光强分布,讨论了不同参数对其光斑大小的影响。结果表明部分相干双涡旋光束的双环在湍流大气中是相互独立传输的,其传输特性会受到光束的拓扑荷数、空间相干度、湍流扰动强弱和传输距离的影响。

部分相干涡旋光束在湍流大气中的相干性

根据广义的惠更斯-菲涅耳原理,得到了部分相干涡旋光束在湍流大气中传输时光谱相干性的理论表达式,然后详细研究了光束在湍流介质中传输时相干性的变化规律。研究表明,部分相干涡旋光束通过湍流介质后,光束的相干性主要受到湍流扰动强弱和光束所带的拓扑电荷数多少的影响,而与光源本身的相干性无关。光源所带的拓扑电荷数越多,光束的相干性越差;湍流扰动越强,光束的相干性越好。

部分相干涡旋光束的传输特性

研究了部分相干高斯-谢尔模型光束经过整数阶螺旋形位相板之后形成的部分相干涡旋光束,着重研究这种部分相干涡旋光束的传输特性。研究结果表明,这种光束在传输中呈现出环状结构的特点;整数阶螺旋形位相板的阶数越高,环状结构的半径越大;当入射的部分相干高斯-谢尔模型光束的空间相干度降低到一定程度时,环状结构消失了。此外,还研究了入射光束的空间相干度对衍射场中的光谱相干度的影响。

圆环衍射效应下涡旋光束的光强变化

为了分析拓扑电荷数以及相干性对部分相干涡旋光束的影响,利用部分相干光的统一理论和惠更斯-菲涅耳衍射原理,推导出随机电磁涡旋光束在自由空间中传播时,尤其是部分相干涡旋光束经圆环衍射后光强的计算公式,研究了部分相干涡旋光束通过圆环后的夫琅和费衍射特性。通过理论分析与数值计算表明,部分相干涡旋光束经圆环衍射后的光强分布情况与入射光的相干度、入射光束的拓扑电荷数、衍射孔径的大小等因素有关。当入射光束的拓扑电荷数越大,相干长度越长,衍射孔径越小时,衍射光束的光强分布会更加清晰,衍射效果也更加明显。

部分相干Airy涡旋光束在非Kolmogorov谱中的模态强度

为了探究部分相干Airy涡旋光束在非Kolmogorov谱中模态强度的演化规律,基于广义的Huygens-Fresnel原理和Rytov近似理论,推导了部分相干Airy涡旋光束的轨道角动量模态概率的解析式。结合MATLAB的数值模拟,研究了部分相干Airy涡旋光束在非Kolmogorov谱湍流大气中传输时湍流参量和波束参量与涡旋模态强度的关系,对部分相干Airy涡旋光束的相干宽度在传输过程中对模态强度的影响进行了理论分析。结果表明,选取拓扑荷数较小、主亮环半径较大、波长较长的部分相干Airy涡旋光束能有效减缓湍流效应的影响,减小强湍流中模态间的串扰;较大的湍流谱幂指数和较小的探测器孔径直径能提高部分相干Airy涡旋光束的模态强度;与完全相干涡旋光束相比,部分相干涡旋光束具有较强的湍流阻力,在大气湍流中能有更好的传输性能,相干性较差会导致螺旋谱分布弥散。这些结果对自由空间光通信的研究具有一定的参考价值。

部分相干径向偏振涡旋光焦场轨道角动量特性

将部分相干径向偏振涡旋光束的轨道角动量应用于焦场目标探测,根据部分相干及Richards-Wolf矢量衍射积分理论,推导了光束焦场目标平面处的光场分布,讨论了焦平面处的轨道角动量密度分布特性,分析了入射光束的相干长度和聚焦透镜的数值孔径对纵向分量轨道角动量密度分布和轨道角动量的影响。结果表明,随着相干长度的增大,轨道角动量和轨道角动量密度迅速变大,当增大至0.5 cm后,轨道角动量和轨道角动量密度的变化趋于平缓,此后,相干长度的变化不再影响轨道角动量和轨道角动量密度分布。随着数值孔径的增大,轨道角动量和轨道角动量密度始终表现出增长的变化趋势,并且,变化程度在数值孔径大于0.7后越来越大。

部分相干异常涡旋光束在大气湍流中的传输特性

研究了部分相干异常涡旋光束在湍流大气中传输时的光强特性和有效光斑尺寸。利用广义惠更斯-菲涅尔积分式推导了部分相干异常涡旋光束的互相干函数的表达式,并在此基础之上得到部分相干异常涡旋光束的光强和有效光斑尺寸的表达式。通过数值模拟分析了部分相干异常涡旋光束的归一化光强分布和有效光斑尺寸随空间相干长度和折射率常数的变化情况。研究结果表明:部分相干异常涡旋光束比完全相干异常涡旋光束受大气湍流的影响更小。而且随着空间相干长度的减小和大气折射率常数的增加,异常涡旋光束光强的中心点强度和有效光斑尺寸逐渐增加。

部分相干幂指数相位涡旋光束的传输特性研究

本文针对部分相干幂指数相位涡旋光束的传输特性开展研究,首先建立了部分相干幂指数相位涡旋光束的传输理论模型;然后,仿真研究了部分相干幂指数相位涡旋光束在自由空间和ABCD光学系统中的传输特性,研究结果表明部分相干幂指数相位涡旋光束在自由空间传输时,拓扑荷数、幂指数和相干长度都对光强的分布有着一定的影响,而随着传播距离的增大光斑的面积逐渐增大;当光束在聚焦系统中传输时,只有拓扑荷数和幂指数的变化会影响光强的分布,而相干长度对光束整体强度的分布没有太大的影响,只影响了光斑的质量.本文研究成果揭示了部分相干幂指数相位涡旋光束的传输特性,为其在光学捕获等领域的应用打下了理论基础,对促进新型光场调控理论及应用研究具有重要的意义.

部分相干圆偏振反常涡旋光束的紧聚焦及辐射力研究

根据矢量衍射理论和部分相干理论,推导了部分相干圆偏振反常涡旋光束经过高数值孔径聚焦透镜后的光强表达式。详细讨论了入射光束参数以及聚焦透镜的数值孔径大小对光束紧聚焦特性的影响。研究结果表明:自旋方向,拓扑荷数以及数值孔径大小对光强分布有影响,相干长度以及光束阶数仅改变光强值,光束经过紧聚焦后在轴向方向上自旋角动量可以转换为轨道角动量。此外,研究了紧聚焦后光束对金属瑞利粒子的辐射力。研究表明:低阶光学参数的部分相干左旋圆偏振反常涡旋光束形成的实心光强分布可对金属瑞利粒子捕获。研究结果对部分相干涡旋光束在光镊中的应用具有理论价值。