Transformation of optical-vortex beams by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by the “fork” holograms from incident circular Laguerre-Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the Kummer beam or of the hypergeometric-Gaussian beam. Physically, in most cases its structure is formed under the influence of the divergent spherical wave originating from the discontinuity caused by the hologram’s groove bifurcation. Presence of this wave is manifested by the ripple structure in the near-field beam pattern and by the power-law amplitude decay at the beam periphery. Conditions when the divergent wave is not excited are discussed.The diffracted beam carries a screw wavefront dislocation (optical vortex) whose order equals to algebraic sum of the incident beam azimuthal index and the topological charge of the singularity imparted by the hologram. The input beam singularity can be healed when the above sum is zero. In such cases the diffracted beam can provide better energy concentration in the central intensity peak than the Gaussian beam whose initial distribution coincides with the Gaussian envelope of the incident beam. Applications are possible for generation of optical-vortex beams with prescribed properties and for analyzing the optical-vortex beams in problems of information processing.     

Optical vortex generation with a “fork” hologram under conditions of high-angle diffraction

Spatial characteristics of the optical-vortex (OV) beams created during the Gaussian beam diffraction by a grating with groove bifurcation are analyzed theoretically and numerically. In contrast to previous works, condition of small-angle diffraction is no longer required and the diffracted beam can be strongly deformed. This causes the intensity profile rotation and the high-order OV decomposition into a set of secondary single-charged OVs. These effects are studied quantitatively and confronted with similar properties of a Laguerre-Gaussian beam that undergoes astigmatic telescopic transformation. In contrast to the latter case, the secondary OVs do not lie on a single straight line within the beam cross section, and morphology parameters of the individual secondary OVs carried by the same beam are, in general, different. Conditions for maximum relative separation of the secondary OVs with respect to the beam transverse size are specified. The results can be used for practical generation of OV beams and OV arrays with prescribed properties.     

Generation of optical vortex light beams by volume holograms with embedded phase singularity

Special features of the optical-vortex (OV) beams generated by thick holographic elements (HE) with embedded phase singularity are considered theoretically. The volume HE structure is based on the 3D pattern of interference between an OV beam and a standard reference wave with regular wavefront. The incident beam diffraction is described within the framework of a linear single-scattering model in which the volume HE is represented by a set of parallel thin layers with the “fork” holographic structure. An explicit integral expression is derived for the complex amplitude distribution of the diffracted paraxial beam with OV. The numerical analysis demonstrates that the HE thickness may essentially influence not only selectivity and efficiency of the OV beam generation but also the amplitude and phase profile of the diffracted beam as well as regularities of its propagation. We have studied the generated OV morphology and laws of its evolution; in particular, the possibility of obtaining a circularly symmetric OV beam regardless of the diffraction angle is revealed.     

Evaluation of a phase shifting method for vortex localization in optical vortex interferometry

The optical vortex interferometer uses a regular lattice of the optical vortices. In the previous papers we showed that changes in vortex lattice geometry can be related to physical quantities of the object being measured. The accuracy of such a measurement depends strongly on the precision of vortex point localization (vortex points are points where wavefront phase is undetermined). In this paper we compared the measurements of object wave tilt calculated from different localization methods applied to real interferograms and evaluate various localization methods.     

Full-vectorial analysis of optical vortex propagation in anisotropic cubic-quintic non-linear optical medium

This paper presents for the first time a full-vectorial analysis of optical vortex propagation in anisotropic cubic-quintic (CQ) non-linear medium. The purpose is to investigate the energy transfer mechanism and stability between orthogonal field components and how they are affected by the presence of material anisotropy in CQ materials. The numerical simulations were carried out via a three-dimensional finite difference based beam propagation method (3D-FD-BPM) which is capable of handling variations in any of the permittivity tensor components. Therefore, in this work we allowed all tensor components to vary independently and simulate vortex propagation for distances several times longer than the diffraction length. We expect that this work can provide new and important information regarding the behavior of these objects that may become valuable for the design of new photonic devices.     

The new method of topological charge determination of optical vortices in the interference field of the optical vortex interferometer

In this paper, the new method of determination of the topological charge of vortex points in the interference field obtained by three plane waves interference is presented. Such optical fields are used in the optical vortex interferometer (OVI) and the determination of vortex points’ topological charge allows of unique determination of the relative phase between interfering waves (phase unwrapping problem). The new method uses additional plane wave, which produce a characteristic fork-like fringe structure in the neighbourhood of vortex points. By analysing the orientation of these fork-like patterns one can read the sign of the topological charge of the given vortex point. The method is simple and can be used for OVI calibration performed before the measurements.     

Focus evolution of linearly polarized Lorentz beam with sine-azimuthal variation wavefront induced by one on-axis optical vortex

Focus evolution of linearly polarized Lorentz beam with sine-azimuthal variation wavefront induced by one on-axis optical vortex was investigated theoretically in this article. Calculation results show that the focal pattern can be altered considerably by the charge number of on-axis optical vortex under condition of certain beam parameters and phase parameter that indicates the sine phase change frequency on increasing azimuthal angle. And the focal evolution principle differs remarkably for different beam parameters and the phase parameter. In focus evolution process, some novel focal patterns appear, including annular focal pattern, two-peak focal pattern, intensity lines, hexagon containing two peaks, swallowtail shape, multipede shape, and complex focal pattern. Introduction of optical vortex adds one controllable parameter to alter focal pattern, which may extend application of Lorentz beam in some focusing systems.     

Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity

Properties of vortex light beams produced by a diffraction grating with groove bifurcation (“fork” structure) are studied in the case of small diffraction angles. Analytical expressions are derived for the amplitude distribution of a diffracted beam generated from an incident Gaussian beam with arbitrary radius and wavefront curvature, transversely shifted and inclined with respect to the nominal axis (normal to the grating crossing it at the bifurcation point). In such situations, the output beam becomes asymmetric; the optical vortex core and the intensity maximum displace orthogonally to the incident beam shift direction. The nearest vicinity of the vortex core preserves its circular symmetry and the optical vortex remains locally isotropic. The effects of misalignment depend on the incident beam characteristics, the diffraction order and the propagation distance behind the grating. Experimental measurements support the results of calculations.     

Propagation of a four-petal Gaussian vortex beam through a paraxial ABCD optical system

Based on the Collins diffraction integral formula, an analytical expression of a general four-petal Gaussian vortex beam passing through a paraxial ABCD optical system is derived by means of the mathematical technique. As a numerical example, the normalized intensity distribution of a four-petal Gaussian vortex beam propagating in free space is graphically demonstrated. The influences of beam order and topological charge on the normalized intensity distribution are discussed in detail. This research is useful to the optical trapping, optical communications, and beam splitting techniques, etc.     

大气湍流中高斯空心涡旋光束的焦面光强分布

运用广义惠更斯-菲涅耳原理和相位结构函数的平方近似,研究了聚焦高斯空心涡旋光束通过湍流大气传输后在焦平面内的光强分布的理论模型,同时分析了不同大气折射率结构常数C2n、聚焦距离、光束拓扑荷和湍流外尺度对焦面光强分布特性的影响.结果表明:随着聚焦距离的增加,焦面光强分布由中央凹陷状向高斯分布转变.弱湍流对焦面光强分布的影响可以忽略;高拓扑荷光束在湍流大气中传输时光波奇异性的保持较低拓扑荷奇异光束要强;随着湍流外尺度增加,焦面光强分布的中央凹陷状变浅,光强分布变平滑.     

Real-time optical reconstruction of the diffused 3D object using phase information calculated by Continuous Wavelet Transform

We propose the real time optical reconstruction of a three-dimensional (3D) object from a digitally recorded hologram. Phase distribution of the recorded hologram is numerically calculated by 1-dimensional Continuous Wavelet Transform (1D-CWT) for digital reconstruction with phase only information. Also, the phase distribution of 1D-CWT transferred to the spatial light modulator (SLM) is used to obtain optically reconstructed image. It is observed that an efficient real-time analysis can be achieved, if phase of 1D-CWT is used. In the same time, optically reconstructed 3D objects obtained by only phase information are about three times brighter than bleached hologram intensity's. So the minimum power loss can be obtained. Numerical and experimental results are presented.     

大气湍流中部分相干聚焦涡旋光束的传输特性

基于广义惠更斯-菲涅耳原理和相位结构函数的平方近似,研究了部分相干高斯-谢尔模型涡旋光束被聚焦后在大气湍流中的传输特性,得到了焦平面上光强解析表达式.利用该表达式,详细研究了该类光束在大气湍流中传输焦平面上的光强分布特性.结果表明：在大气湍流中,随着传输距离的增加,涡旋光束的奇异性逐渐降低.对于拓扑荷大的以及空间相干长度较长的涡旋光束,光束奇异性的保持相对要好.在一定的焦距长度和湍流大气条件下,我们可以通过调整光源的拓扑荷和相干长度控制焦面光强分布和焦斑大小.另外,有一定拓扑荷的涡旋光束可以在一定程度上降低大气湍流对传输光束焦面光强分布的影响.     

Optical transfer function of an optical system with a vortex phase mask in the presence of primary aberrations

The impact of primary aberrations on the optical transfer function of an optical system with a vortex phase mask has been investigated in detail. The optical transfer function of such a system becomes negative in a certain frequency range even in the absence of aberrations, a feature different from the case of an optical system in which center of the point spread function is bright.     

Splitting and rotating of optical vortices due to non-circular symmetry in amplitude and phase distributions of host beams

Discussed is the dynamics of optical vortices carrying multi-topological charges, which are nested in optical envelopes with non-circular symmetric amplitudes and phases. As a result of the non-circular symmetry either in amplitudes or in phases, the vortices can split in pairs from the centers of the host beams. During the splitting process of every constituent vortex, its carried integer charges evolve into fractional ones. Furthermore, the overall rotations of the host optical envelopes are found to happen in the splitting process. The theoretical results may find potential applications in beam shaping and engineering.     

FDTD simulation of time varying optical vortex phenomena in SOI photonic crystal structures

In this paper we analyze the time varying optical vortex phenomena in the gain photonic crystals built on the silicon-on-insulator (SOI) wafer by using the finite difference time domain (FDTD) method. With launching the optical waves in 1.55 μm wavelength to the SOI rib waveguide, optical vortices are generated and the spinning details are observed at various time steps. The analysis results are helpful to understand the progress of optical vortices which may be utilized for the development of future nonlinear optical switches.     

用四台阶相位板产生涡旋光束

涡旋光束的产生与应用是当前光学领域的研究热点. 利用傅里叶级数展开法分析了四台阶相位板的相位结构, 发现四台阶相位板可看作是由一系列不同拓扑荷数的螺旋相位板所组成, 用线偏振光直接照射相位板时, 将产生多级衍射光波, 各级衍射光均为不同拓扑荷数的涡旋光波, 由于多级衍射光波间的干涉导致光强分布偏离轴对称分布, 因而与涡旋光波有一定差距. 在此基础上, 提出了用四台阶相位板产生涡旋光束的新方案, 借助于Mach-Zehnder 干涉仪光路, 两块四台阶相位板产生的衍射光干涉叠加, 通过调节干涉仪光路的相位差, 使一部分衍射级干涉相消, 另一部分衍射级干涉相长, 相互加强, 从而把线偏振光转换为涡旋光束. 数值模拟计算了几种周期数不同的四台阶相位板衍射光强和角动量分布, 并与螺旋相位板进行比较, 证明用简单的四台阶相位板不仅能够获得与用螺旋相位板相同的涡旋光束, 而且可以用周期数较小的四台阶相位板产生具有大拓扑荷数的涡旋光束, 降低了制作相位板的难度.     

Simplified system configuration for real-time Fourier transformation of optical pulses in amplitude and phase

Real-time Fourier transformation (RTFT) of optical waveforms in amplitude and phase (i.e. transform-limited RTFT) is a fundamental operation that enables the realization of many interesting ultrafast signal processing applications, including wavelength-tunable optical pulse filtering, all-optical temporal correlations and convolutions and temporal imaging, among others. In this paper, we demonstrate that under certain conditions, a single time lens (quadratic-phase temporal modulator) followed by a suitable dispersive delay line can be used to implement transform-limited RTFT of optical pulses. The design specifications and constraints of the proposed transform-limited RTFT systems are derived and discussed. As compared with the conventional methods, the proposed design does not require the use of an input dispersive device preceding the time lens or a second time lens after dispersion, thus resulting in a simpler and more practical alternative for implementing TL-RTFT of optical signals. The feasibility of our proposal to operate on picosecond optical waveforms using electro-optic time lenses has been confirmed by numerical simulations.     

利用非传统螺旋相位调控高阶涡旋光束的拓扑结构

本文提出一种利用非传统螺旋相位调控高阶涡旋光束拓扑结构的方法.数值模拟并实验研究了具有不均匀旋转梯度的非传统螺旋相位对高阶涡旋光束的调控行为.结果表明, 携带有非传统螺旋相位的高阶涡旋光束在传输过程中, 将退化为沿一条直线排列的多个一阶相位奇点, 并且, 这种非传统螺旋相位对高阶涡旋光束的调控特性, 可抑制相位噪声等扰动所引起的拓扑结构随机退化现象.本文的结论为涡旋光束拓扑结构的调控提供了一种可行的新途径, 在基于涡旋光束的光学通信、光学操控等方面具有潜在应用.     

部分相干涡旋光束在湍流大气中的传输特性

根据广义的惠更斯-菲涅耳原理,推导了部分相干涡旋光束在湍流介质中传输时光强分布情况的理论公式,详细研究了部分相干涡旋光束在湍流介质中的传输变化规律。研究结果表明,湍流介质的强弱,光源的相干性以及光束所带拓扑电荷数大小均会影响光束传输特性。