离轴平顶高斯涡旋光束形成的合成光涡旋及其在自由空间中的传输

对两束拓扑电荷m_1,2=±1的平行、离轴平顶高斯涡旋光束在束腰面叠加形成的合成光涡旋及其在自由空间的传输做了研究.详细的数值计算和分析表明,合光涡旋的位置、数目和净拓扑电荷与光束的控制参数,包括相对位相,振幅比,束腰宽度比,相对离轴参数,光束阶数,以及传输距离有关,但拓扑电荷不总是守恒. 关键词： 奇点光学 合成光涡旋 平顶高斯涡旋光束 拓扑电荷     

Composite optical vortices in two noncollinear cosh-Gaussian vortex beams and their propagation properties in free space

The composite optical vortices (OVs) formed by superimposing two parallel, noncollinear cosh-Gaussian (ChG) vortex beams at the waist plane and their propagation in free space are studied. The dependence of the number, position and net topological charge of composite OVs on the control parameter, such as the relative phase, amplitude ratio, waist-width ratio, relative off-axis distance and decentered parameter, and on the propagation distance is illustrated numerically. A comparison with the previous work is also made.     

Half-plane diffraction of Gaussian beams carrying two vortices of equal charges

This paper derives explicit expressions for the propagation of Gaussian beams carrying two vortices of equal charges m=±1 diffracted at a half-plane screen, which enables the study of the dynamic evolution of vortices in the diffraction field. It shows that there may be no vortices, a pair or several pairs of vortices of opposite charges m=+1, -1 in the diffraction field. Pair creation, annihilation and motion of vortices may appear upon propagation. The off-axis distance additionally affects the evolutionary behaviour. In the process the total topological charge is equal to zero, which is unequal to that of the vortex beam at the source plane. A comparison with the free-space propagation of two vortices of equal charges and a further extension are made.     

Dynamic evolution of Riemann–Silberstein vortices for Gaussian vortex beams

The dynamic evolution of Riemann–Silberstein (RS) vortices for Gaussian vortex beams with topological charges m = ± 1 in free space is studied. It is shown that for Gaussian on-axis vortex beams there exist both RS vortex with m = + 2 and circular edge dislocation. For Gaussian off-axis vortex beams the circular edge dislocation splits into two RS vortices with opposite topological charges m = ± 1 and the RS vortex with m = + 2 decays into two vortices with same topological charges m = + 1. The motion of RS vortices takes place by varying the propagation distance, waist width, off-axis parameter, or topological charge. RS vortices for Gaussian vortex-free beams can be treated as a special case. The results are illustrated analytically and numerically.     

部分相干双曲正弦-Gauss涡旋光束叠加形成的合成相干涡旋在非 Kolmogorov 大气湍流中的动态演化

一些实验表明, 实际大气会偏离理想Kolmogorov模型. 本文基于广义Huygens-Fresnel原理和Toselli等提出的非Kolmogorov湍流模型, 推导出部分相干双曲正弦-Gauss (HSG)涡旋光束通过非Kolmogorov大气湍流的解析传输公式, 并用以对两束部分相干HSG涡旋光束相干叠加和非相干叠加形成的合成相干涡旋在非Kolmogorov大气湍流中的动态演化进行了研究. 结果表明, 合成光束平均光强的演化过程与非Kolmogorov湍流的广义指数α, 源平面上叠加涡旋光束拓扑电荷的符号, 以及叠加方式有关. 合成相干涡旋在非Kolmogorov大气湍流中传输时会出现移动、产生和湮灭. 广义指数α, 拓扑电荷符号, 以及叠加方式都会影响其演化行为. 最后, 将本文所得结果与相关文献做了比较.     

Composite coherence vortices and their propagation in free space

Taking Gaussian Schell-model (GSM) background vortex beams as an example of partially coherent vortex beams, the composite coherence vortices resulting from the superposition of the cross-spectral density function of two parallel, noncollinear partially coherent vortex beams and their propagation in free space are studied, and the main attention is paid to the effect of relative off-axis distance, coherence parameter and propagation distance on the composite coherence vortices. The number and location of composite coherence vortices vary by changing the relative off-axis distance, coherence parameter or propagation distance. In the coherent limit, the composite coherence vortex becomes the composite optical vortex.     

The Effect of the Spin Angular Momentum on the Tight-Focusing Vortex Hollow Gaussian Beams

The propagation properties of a hollow Gaussian beam (HGB) carrying on-axis and off-axis vortices through a high numerical aperture lens are investigated. The intensity of the focused beam in the focal plane can be controlled by choosing the different topological charges, the beam order, and the semi-aperture angle. As intrinsic properties, vortex beams possess both spin and orbital angular momenta. The spin angular momenta (SAM) density can be treated as a vector in 3D since it exists in arbitrary orientation during the beam propagation. The vectors of SAM density orientation of the focused beam in 3D rotate around the central axis whose locations mainly rely on the vortices. The magnitude of the SAM density near the focus plane abruptly varies by altering the focal length of the lens. Under tightly focusing condition, two new pairs of vortices generate alternately on x and y axes in the vectorial electric fields, while the topological charges increase by one.     

Propagation dynamics of optical vortices in Laguerre–Gaussian beams

We have calculated the propagation dynamics of an initial off-axis vortex with topological charge 1 in Laguerre–Gaussian background beams , which are examples of background beams with non-generic dislocation surfaces, on which the real and imaginary parts of the light field are zero. When initially a vortex with broad core (e.g., r-vortex) is embedded in the background beam, the dislocation surfaces are destroyed during propagation and two vortices with opposite charge are created per dislocation surface in planes perpendicular to the propagation direction. For a vortex with narrow core (e.g., point vortex) diffraction is important and leads to the birth of more than two vortices per dislocation surface. These results are also valid for other background beams with dislocation surfaces, e.g., Hermite–Gaussian and Ince–Gaussian beams. We investigated experimentally the spatial evolution of the intensity distribution of an initial off-axis vortex with narrow core and topological charge 1 in background beams. The experimental results are in good agreement with the calculated intensity distributions.     

Polarization singularities in near-field of Gaussian vortex beam diffracted by a circular aperture

Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory.It is shown that there exist C-points and L-lines,which depend on off-axis displacement parameters along the x and y directions,waist width,wavelength,and topological charge of the diffracted Gaussian vortex beam,as well as on propagation distance.The results are illustrated by numerical calculations.     

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.     

部分相干涡旋光束叠加场中的合成相干涡旋及其动态传输

对由两束平行、离轴部分相干平顶涡旋光束叠加形成的合成相干涡旋做了详细研究.结果表明:合成相干涡旋的数目和位置与光束阶数、相对离轴距离、相干参数以及相对传输距离有关.在部分相干范畴内“隐藏”的合成相干涡旋对应于完全相干范畴中的合成光涡旋.并且证明在相干极限下合成相干涡旋就演化为合成光涡旋. 关键词： 相关奇点光学 合成相干涡旋 部分相干平顶光束 离轴合成     

Optical vortices and topological effects in coiled fibers with combined anisotropy

The propagation of optical vortices in coiled anisotropic elliptical fibers is studied. The structure of high-order modes and their propagation constants are determined. The possibility of the generation of TE and TM modes from optical vortices with a unit topological charge in weakly anisotropic coiled fibers is demonstrated. The topological effects that arise upon the propagation of radiation along strongly anisotropic elliptical coiled fibers are investigated. It is established that topological effects are suppressed by anisotropy in the case of the propagation of l = 1 modes; the effects are manifested in these fibers in the form of the rotation of the field intensity distribution by a solid angle spanned by the light trajectory only for certain combinations of l > 1 modes.     

Propagation of Gaussian background vortex beams diffracted at a half-plane screen

Taking the Gaussian background vortex beam with topological charge +2 as a typical example, a closed-form expression for vortex Gaussian beams passing through a half-plane screen is derived and used to study the propagation dynamics of on-axis and off-axis vortex diffracted beams, and to compare with the case of the free-space propagation. It is shown that there may exist many phase singularities or no phase singularity of vortex diffracted Gaussian beams in the diffraction field. Number and position of phase singularities are dependent on the vortex position at the source plane and propagation distance. The creation, motion and annihilation of phase singularities in the diffraction field may appear by varying the vortex position and propagation distance.     

Dynamics of topological multipoles: II. Creation, annihilation, and evolution of nonparaxial optical vortices

The behavior of nonparaxial combined beams transferring two or four optical vortices with opposite topological charges (topological dipole or quadrupole) is studied. The paraxial and nonparaxial approaches are compared. It is shown that the behavior of a topologically neutral wave system is well characterized by the position of a representative point on the parametric plane. It is found that there exists a large region on this plane for which spatial trajectories of the optical vortices, both for dipoles and quadrupoles, do not intersect the focal plane, i.e., the vortices cannot exist within the forbidden zone. At the edges of the forbidden zone, the vortices are either created or annihilated. In contrast, there exists a region on the parametric plane for which the optical vortices can exist only near the waist plane.     

Generation of optical vortices in multihelical optical fibers

It is theoretically demonstrated that multihelical fibers are capable to change the topological charge of the incoming field by l units in the transmitted and reflected light. The magnitude of the change in the topological charge coincides with the number of coaxial helicoids forming the fiber core. This can be used in designing generators of optical vortices (OVs) from Gaussian beams: broadband ones in transmitted light and narrowband ones in reflected light.     

Composite spectral Stokes singularities in coherent and incoherent superpositions of partially coherent nonparaxial vortex beams

Taking the partially coherent cosh-Gaussian (ChG) vortex beam as an illustrative example, the composite spectral Stokes singularities formed by coherent and incoherent superpositions of partially coherent vortex beams beyond the paraxial approximation are studied, where the effect of superposition scheme on composite spectral Stokes singularities is stressed. It is shown that there exist s₁₂ (C-points), s₂₃ and s₃₁ composite spectral Stokes singularities, which are variable by varying a control parameter, such as the spatial correlation length, waist width, off-axis distance, or decentered parameter, as well as the propagation distance. In particular, the number, position, degree of polarization of composite spectral Stokes singularities and the critical point at which the creation–annihilation process takes place depend on the superposition scheme. A comparison with the previous work is also made.     

Interactions of optical vortex solitons superimposed on different background beams

The interaction between two optical vortex solitons (OVS), formed on different background beams is analyzed numerically. Analogous to the one-dimensional case, vector OVS seem obtainable [12]. The relative topological charges of the interacting (off-axis) vortices are found to rule their propagation characteristics. Attraction is found in the case of equal charges, in contrast to the opposite case, where repulsion is present.     

Interaction of two edge dislocations in free-space propagation

This paper studies in detail the interaction of two edge dislocations nested in a Gaussian beam propagating in free space. It shows that in free-space propagation the edge dislocations are unstable and vanish, and two noncanonical vortices with opposite topological charge take place when off-axis distances c₁ and c₂ of two edge dislocations are non-zero, and the condition k²w₀⁸+32c₁c₂(w₀²-2c₁c₂)z²>0 is fulfilled (k-wave number, w₀-waist width). A noncanonical vortex appears when one off-axis distance is zero. However, one edge dislocation is stable when two edge dislocations are perpendicular and one off-axis distance is zero. Two perpendicular edge dislocations both with zero off-axis distance are also stable. The analytical results are illustrated by numerical examples.     

单环多段光强分布检测光学涡旋拓扑荷值

针对涡旋光束检测范围局限这一问题, 提出了一种新的光学涡旋拓扑荷值检测方法-单环多段光强分布检测法, 它以分段数和环半径为两大检测常数, 将检测涡旋光束拓扑荷值范围扩大到了128种, 与以往利用旁瓣调控光学涡旋检测拓扑荷值方法相比, 检测范围扩大了1个数量级. 单环多段光强分布是基于计算机全息图实现在远场衍射焦平面上环半径相等的两束携带不同拓扑荷数的涡旋光束叠加后形成的光强分布. 计算机模拟和光学实验验证了所提出方法的可行性, 该方法在自由空间光通信领域具有一定的研究价值和应用潜力.     

Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium

In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ${\omega }_0$ are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.