The creation-annihilation process of phase singularities of flat-topped beams in the focal plane

The creation-annihilation process of phase singularities of flat-topped beams in the focal plane is studied within the framework of the scalar paraxial approximation, where the new expression for flat-topped beams introduced by Li is taken as the beam model. It is shown that by suitably varying the truncation parameter, the phase singularities reorganize themselves, which leads to the annihilation of singularities in the focal plane, the creation of singularities outside the focal plane and subwavelength structures. Apart from the truncation parameter, the beam order of flat-topped beams additionally affects the spatial distribution of phase singularities.     

Influence of the comatic aberration of an apertured lens on the focused polychromatic Gaussian beams

The focusing of polychromatic Gaussian beams by an apertured lens with comatic aberration is investigated in this paper. We study the influence of the comatic aberration and truncation parameter on the intensity distribution at the focal plane, and singularities and spectral behavior near the focal plane in detail. The simulation results show that the maximum intensity at the focal plane will shift and split with the gradual increment of comatic aberration. We also find that the decrease of truncation parameter will counteract the influence of comatic aberration, which leads to the intensity variation. Furthermore, the singularity transformation and spectral anomalies are discussed. It is found that with the increment of comatic aberration, some singularities are split into several new singularities, and by combining some of these new singularities with other singularities near the focal plane, they vanish or form new singularities with the continuing increase of comatic aberration. The decreasing value of truncation parameter will cause similar phenomena.     

高阶贝塞尔-高斯脉冲光束相位奇点的演化

推导出被光阑衍射高阶贝塞尔-高斯脉冲光束的场和光强分布的解析公式,对其相位奇点的演化特性做了计算和分析。结果表明,高阶贝塞尔-高斯脉冲光束经光阑衍射后,中心光涡旋始终存在,拓扑电荷守恒。随脉冲频率和脉冲宽度增加,等相位线均沿逆时针方向旋转,涡旋核随脉冲频率增加而减小,而脉冲宽度对涡旋核大小几乎无影响。等相位线随截断参数和传输距离的增加分别沿逆时针和顺时针方向旋转,涡旋核大小随截断参数增加而变化,随传输距离和光束阶数的增加而增大。     

The effect of spherical aberration on the phase singularities of focused dark-hollow Gaussian beams

The phase singularities of focused dark-hollow Gaussian beams in the presence of spherical aberration are studied. It is shown that the evolution behavior of phase singularities of focused dark-hollow Gaussian beams in the focal region depends not only on the truncation parameter and beam order, but also on the spherical aberration. The spherical aberration leads to an asymmetric spatial distribution of singularities outside the focal plane and to a shift of singularities near the focal plane. The reorganization process of singularities and spatial distribution of singularities are additionally dependent on the sign of the spherical aberration. The results are illustrated by numerical examples.     

Phase singularities of nonparaxial cosh-Gaussian vortex beams diffracted by a rectangular aperture

Analytical expression for the propagation of nonparaxial cosh-Gaussian (ChG) beams diffracted by a rectangular aperture is derived based on the vector Rayleigh-Sommerfeld diffraction integrals and expansion of the aperture window function into a finite sum of complex Gaussian functions, and used to study the phase singularities of nonparaxial diffracted ChG vortex beams. The pair creation, annihilation, motion of phase singularities in the diffracted field and the dependence of position and number of phase singularities on the aperture and beam parameters, as well as on the beam nonparaxiality are illustrated by numerical examples.     

Influence of astigmatism and defocusing on the focusing of a singular beam

Using the Fresnel–Kirchhoff diffraction integral, the intensity distribution and encircled energy of a singular beam at the focal plane of a lens, has been numerically evaluated in the presence of astigmatism and defocusing. Study has been made for two values of topological charge. The aberration results in flattening of dark core and the effect is more pronounced for beam with double topological charge. Twofold symmetry in intensity distribution is observed for selected values of defocusing. The results have been verified by the optical transfer function (OTF) approach.     

Phase and polarization singularities of nonparaxial Gaussian vortex beams

The analytical expression for nonparaxial Gaussian vortex beams propagating in free space is derived, which enables us to study phase and polarization singularities in nonparaxial vector wavefields. Differing from the polarization singularities formed by two transverse electric-field components in the paraxial regime, the polarization singularities can be formed by the transverse and longitudinal electric-field components of nonparaxial beams, and there exist C-points and L-lines. The variation of the beam parameters and propagation distance will result in a shift of phase and polarization singularities, but their position relation remains unchanged and the topological relationship holds true.     

高阶贝塞尔-高斯脉冲光束相位奇点的演化

 推导出被光阑衍射高阶贝塞尔-高斯脉冲光束的场和光强分布的解析公式,对其相位奇点的演化特性做了计算和分析。结果表明,高阶贝塞尔-高斯脉冲光束经光阑衍射后,中心光涡旋始终存在,拓扑电荷守恒。随脉冲频率和脉冲宽度增加,等相位线均沿逆时针方向旋转,涡旋核随脉冲频率增加而减小,而脉冲宽度对涡旋核大小几乎无影响。等相位线随截断参数和传输距离的增加分别沿逆时针和顺时针方向旋转,涡旋核大小随截断参数增加而变化,随传输距离和光束阶数的增加而增大。     

离轴位相奇点的动态传输

推导出高斯背景的离轴位相奇点光束的半屏衍射解析公式,详细研究了离轴位相奇点的动态传输.结果表明,半屏衍射,偏移量和传输距离都会影响位相奇点的传输行为和衍射场位相奇点的分布.改变偏移量和传输距离,衍射场伴随有位相奇点的产生,移动和湮没. 关键词： 奇点光学 离轴位相奇点光束 半屏衍射 光涡漩     

The effect of tilt aberration and astigmatism of turbulent atmosphere on the intensity distribution of a vortex carrying Gaussian beam

The effect of tilt and astigmatism aberration of the turbulent atmosphere on the intensity distribution of a focused vortex carrying Gaussian beam was investigated based on the extended Fresnel-Kirchhoff diffraction integral and the quadratic approximation of phase structure function. Our results have shown that the intensity distribution on the focal plane in the effect of tilt aberration changes with the turbulent strength, the propagation distance and the topological charge of the initial beam. The propagation distance is larger, the focal spot size will be larger, and the central dip will be less deep. It is also noticed that the intensity distribution of a beam with single topological charge is affected more by tilt aberration in comparison to the beam with double topological charge. The effect of astigmatism on the intensity distribution is quite less than that of tilt aberration. For focused beam propagation in atmosphere, the effect of the tilt aberration on the intensity distribution of optical vortex beam is the main effect of total turbulent aberration.     

聚焦高斯涡旋光束焦区电场和磁场的偏振奇点

以高斯涡旋光束为例,研究了聚焦场中电场和磁场的偏振奇点变化规律.结果表明,高斯涡旋光束经透镜聚焦后,在焦区存在二维和三维电场和磁场的偏振奇点,其位置一般不重合.适当改变与焦面的距离以及光阑截断参数等出现圆偏振奇点的移动、产生和湮没.不同二维和三维电场和磁场圆偏振奇点湮没所对应的各参数临界值不同.在二维电场中,几何焦面上会有V点的产生.     

聚焦贝塞尔-高斯光束的焦开关效应

详细研究了贝塞尔-高斯光束被无光阑透镜聚焦后的焦开关效应。推导出了轴上最大光强位置满足的一元三次方程和相对跃迁量公式,并用数值计算对理论结果作了说明。研究表明,当光束参数大于2时,聚焦贝塞尔-高斯光束会有焦开关现象出现。相对跃迁量随着光束参数的增大而增大,轴上归一化光强最小值随着光束参数的增大而减小,并且当光束参数大于3.9时,轴上归一化光强最小值为零。     

On-axis spectral shifts and spectral switches of Gaussian Schell-model beams focused by an astigmatic aperture lens

Starting from the propagation law of partially coherent light, the on-axis spectral shifts and spectral switches of Gaussian Schell-model (GSM) beams focused by an astigmatic aperture lens are studied. It is shown that, as compared with an aberration-free case whose spectral shifts and spectral switches are induced by spatial correlation and aperture diffraction, the spectral shifts and spectral switches of GSM beams also depend upon the astigmatism of the lens for an astigmatism case. Detailed numerical calculations are made to illustrate the behavior of spectral shifts and spectral switches of GSM beams focused by an astigmatic aperture lens.     

Far-field properties of nonparaxial Gaussian beams with a pair of vortices

The analytical far-field expressions for the TE and TM terms and energy flux distributions of nonparaxial Gaussian beams with a pair of vortices are derived by using vector angular spectrum representation and stationary phase method. The far-field properties including phase singularities and energy flux distributions of the TE and TM terms and whole beam are studied in detail. It is shown that there exist a saddle point and phase singularities that depend on the off-axis distance, waist width, and propagation distance. By suitably varying the off-axis distance, the motion and variation of topological charge of phase singularities may take place. The results are interpreted and compared with the previous work.     

异常空心光束通过球差光阑透镜的聚焦和在焦区的位相奇异特性

研究了用德拜公式对异常空心这类新型光束经过光阑透镜后的聚焦特性.结果表明,异常空心光束的形状一般不能保持传输不变性,但选择合适的截断参数和球差异常空心光束在一定位置可保持其初始光强分布近似不变.在焦区位相奇点会出现移动、产生和湮灭,并与截断参数、球差和光阑透镜半角有关.当无球差时,出现鞍点,奇点对的湮灭过程与鞍点对湮灭相伴发生,导致亚波长结构.用计算例对结果做了说明,并与文献中已有工作做了比较. 关键词： 异常空心光束 球差光阑透镜 位相奇点     

Spectral anomalies of diffracted pulsed cosh-Gaussian beams in dispersive media

Starting from the Rayleigh–Sommerfeld diffraction integral, the closed-form expressions for the near- and far-field power spectra of diffracted pulsed cosh-Gaussian (ChG) beams propagating in dispersive media are derived, and the anomalous behavior of the far-field spectrum of diffracted pulsed ChG beams in dispersive media is studied. It is shown that near the phase singularities, the spectral switch may take place. The truncation parameter, decentered parameter and pulse duration of pulsed ChG beams and the dispersive property of the medium affect the behavior of the spectral switch of pulsed ChG beams.     

Effect of astigmatism on spectral switches of partially coherent beams

A detailed study of the spectrum of partially coherent beams diffracted at an astigmatic aperture lens is performed. Considerable attention is paid to the effect of astigmatism on spectral switches of polychromatic Gaussian Schell-model beams. It is shown that the spectral switch can also take place in the vicinity of intensity minimum in a geometrical focal plane for the astigmatic case, but the astigmatism of the lens and the spatial correlation of the beam affect the critical position u_c, spectral minimum S_{min}, and transition height Δ of spectral switches.     

The quadratic phase factor of tightly focused wavefronts

The phase structure is investigated at the focal plane of an aplanatic, high numerical aperture focusing optical system. The tightly focused field is numerically evaluated using combination of the Richards-Wolf approach and the Stratton-Chu diffraction integral. An investigation is performed for both 2D and 3D geometries for a number of different illumination structures, having piecewise quasi-constant phase at the entrance pupil and different polarization states. For the investigated illumination structures, the quadratic phase term of the focused field was found to depend on the structure of the incident illumination contrary to the paraxial case where it depends solely on the optical system parameters.     

部分相干刃型位错光束的谱Stokes奇点

利用交叉谱密度函数的传输公式,推导出部分相干刃型位错光束在自由空间中传输的解析表达式.结合谱Stokes参数,详细讨论了其Stokes场的奇点变化规律.结果表明,部分相干刃型位错光束在自由空间传输过程中存在谱s12,s23和s31奇点.改变刃型位错的离轴量、斜率、空间相关长度等光束参数以及随着传输距离的变化,会有谱Stokes奇点的移动、产生和湮没,也会有V点的产生和C点旋性的反转.     

The influence of high-frequency phase distortion on the phase correction effect in atmospheric turbulence

By using the method of the power-spectrum inversion, the turbulence phase screen has been built up, and the propagation characteristics of high-frequency phase of laser beam in atmospheric turbulence have been analyzed; in addition, the phase correction effect of laser beams by using the adaptive deformable mirror has been simulated, and its affecting factors in turbulence have also been analyzed quantitatively. The results show that the phase correction effect of laser beams in turbulence is mostly determined by the percent of high-frequency phase in distorted wavefront. With the increase of the intensity of atmospheric turbulence and the propagation distance in turbulence, the percent of high-frequency phase in distorted wavefront increases, resulting in the degradation of the phase correction effect.