Orbital angular momentum density and spiral spectra of Lorentz–Gauss vortex beams passing through a single slit

Based on the Hermite–Gaussian expansion of the Lorentz distribution and the complex Gaussian expansion of the aperture function, an analytical expression of the Lorentz–Gauss vortex beam with one topological charge passing through a single slit is derived. By using the obtained analytical expressions, the properties of the Lorentz–Gauss vortex beam passing through a single slit are numerically demonstrated. According to the intensity distribution or the phase distribution of the Lorentz–Gauss vortex beam, one can judge whether the topological charge is positive or negative. The effects of the topological charge and three beam parameters on the orbital angular momentum density as well as the spiral spectra are systematically investigated respectively. The optimal choice for measuring the topological charge of the diffracted Lorentz–Gauss vortex beam is to make the single slit width wider than the waist of the Gaussian part.     

Dynamic generation of plasmonic Moiré fringes using phase-engineered optical vortex beam

Dynamic generation of plasmonic Moiré fringes using a phase engineered optical vortex (OV) beam is experimentally demonstrated. Owing to the unique helical phase carried by an OV beam, the initial phase of surface plasmon polaritons (SPPs) emanating from a metallic grating can be adjusted dynamically by changing the phase hologram displayed on a spatial light modulator. Plasmonic Moiré fringes are readily achieved by overlapping two SPP standing waves with certain angular misalignment, excited by the positive and negative topological charge components, respectively, of a cogwheel-like OV beam. The near-field scanning optical microscopy measurement result of SPP distributions has shown a good agreement with the numerical predictions.     

Measuring the orbital angular momentum of elliptical vortex beams by using a slit hexagon aperture

The far-field diffraction pattern of an elliptical vortex beam by a slit hexagon aperture is investigated theoretically and experimentally. It is found that the number of the dark spots or stripes in the Fraunhofer diffraction intensity distribution is just equal to the topological charge value of the measured optical vortex, and that the centre of each dark spot or stripe is just a phase singularity point. Based on this property, it provides us a simple way to detect the orbital angular momentum (OAM) of an optical vortex beam.     

Microscale vortex laser with controlled topological charge

A microscale vortex laser is a new type of coherent light source with small footprint that can directly generate vector vortex beams. However, a microscale laser with controlled topological charge, which is crucial for virtually any of its application, is still unrevealed. Here we present a microscale vortex laser with controlled topological charge. The vortex laser eigenmode was synthesized in a metamaterial engineered non-Hermitian micro-ring cavity system at exceptional point. We also show that the vortex laser cavity can operate at exceptional point stably to lase under optical pumping.The microscale vortex laser with controlled topological charge can serve as a unique and general building block for nextgeneration photonic integrated circuits and coherent vortex beam sources. The method we used here can be employed to generate lasing eigenmode with other complex functionalities.     

阿基米德螺旋微纳结构中的表面等离激元聚焦

研究光在微纳结构中的分布与传播, 实现在纳米范围内操纵光子, 对于微型光学芯片的设计有着重要意义. 本文利用聚焦离子束刻蚀方法, 在基底为石英玻璃的150 nm厚金膜上刻制了不同参数的阿基米德螺旋微纳狭缝结构, 通过改变入射光波长、手性、及螺旋结构手性和螺距等方式, 在理论和实验上系统地研究了阿基米德螺旋微纳结构中的表面等离激元聚焦性质. 我们发现, 除了入射激光偏振态、螺旋结构手性之外, 结构螺距与表面等离激元波长的比值也可以用来控制结构表面电场分布, 进而在结构中心形成0阶、1阶乃至更高阶符合隐失贝塞尔函数的涡旋电场. 通过相位分析, 我们对涡旋电场的成因进行了解释. 并利用有限时域差分的模拟方法计算了不同螺距时, 结构中形成的电场及相应空间相位分布. 最后利用扫描近场光学显微镜, 观测结构中不同的光场分布, 在结构中心得到了亚波长的聚焦光斑及符合不同阶贝塞尔函数的涡旋形表面等离激元聚焦环.     

Pattern formation using optical vortices in a photorefractive single feedback system

We analyze numerically the dynamics of optical patterns in a photorefractive single feedback system where a vortex beam is used as the input beam. Depending on the topological charge of the vortex and on the nonlinear photorefractive coupling strength, we observe different pattern geometries with a rotating dynamics.     

基于塔姆激元-表面等离极化激元混合模式的单缝加凹槽纳米结构的增强透射

金属单缝纳米结构因为结构简单、易于集成,常用在基于表面等离极化激元(surface plasmon polaritons,SPPs)的纳米结构中构建光源.但是,金属亚波长单缝结构一直存在透射率低的问题,如何提高其透射率一直是研究的重点.为了更好地提高金属亚波长单缝的透射率,本文对之前文献提出的分布式布拉格反射镜(distributed bragg reflector,DBR)和金属银薄膜纳米缝结构进行改进,在金属银薄膜两侧设计凹槽.当TM偏振光由DBR侧入射至DBR-银纳米缝结构时,DBR-银膜界面上和银膜入射侧凹槽一起激发的塔姆激元(Tamm plasmon polaritons,TPPs)和SPPs,以及纳米缝和银膜出射侧凹槽对的SPPs同时激发,利用凹槽激发的SPPs和银膜表面处的TPPs-SPPs混合模式的干涉相长耦合作用,通过塔姆激元的局域场增强效应和两侧凹槽与单纳米缝的干涉相长耦合作用进一步提高了表面等离极化激元模式的激发效率,再加上纳米缝中的类法布里-珀罗腔共振效应,使纳米缝的透射率得到增强.本文采用有限元方法研究了DBR-银纳米缝结构上单纳米缝加凹槽的透射特性.经过一系列参数优化,使DBR-银纳米缝凹槽结构的最大透射率增加到0.22,相对于TiO_2-银纳米缝结构的透射率(0.01)提高了22倍,比文献[23]得到的最大透射率0.166有所提高.研究结果在纳米光源设计、光子集成电路和光学信号传输等相关领域具有一定的应用价值.     

Dynamic evolution of transverse energy flow in focused asymmetric optical vector-vortex beams

We present here controlled generation of asymmetric optical vector-vortex beams using a two-mode optical fiber and study the dynamic evolution of the transverse energy flow (TEF) when focused through a spherical lens. The dependence of the TEF on various factors such as the vortex charge, vortex anisotropy and polarization structure around the vortex core is explored. It is found that the TEF is directly proportional to the phase gradient and its direction is governed by the vortex charge. The presence of C-point polarization singularity in the beam and the polarization structure around it results in vibrational phase gradient which is the major factor deciding the TEF in vector-vortex beams.     

Gap surface plasmon polaritons enhanced by a plasmonic lens

We numerically investigate the optical field enhancement based on gap surface plasmon polaritons (GSPPs) that are enhanced by propagating surface waves launched by a circular slit at a metal-dielectric interface. The optical field enhancement originates not only from multiple scattering and coupling of GSPPs in the spacer region between two metal layers but also from propagating surface plasmon polaritons (SPPs) launched by a circular plasmonic lens. We find that the combination of the GSPPs and the propagating SPPs launched by the plasmonic lens can achieve extremely strong field confinement, and we find that the surface-enhanced Raman scattering (SERS) enhancement factor can be up to 10(15) at the tip of the equilateral triangular nanostructures. The structure proposed here is expected to find promising applications where strong field enhancement is desired, such as optical sensing with the SERS effect.     

4Pi focusing of spatially modulated radially polarized vortex beams

We propose a method for generating focal beams with special intensity distributions using radially polarized vortex beams in a 4Pi configuration. A spherical dark-hollow beam and hollow beam array can be obtained by vortex beams with topological charge of m=1. A dark channel can be generated using vortex beams with topological charge of m=2. The length of the well-defined hollow beam array and the dark channel is about 30λ. These interesting beams are useful in optical trapping and manipulation.     

Estimating topological charge of propagating vortex from single-shot non-imaged speckle

Encoding information using the topological charge of vortex beams has been proposed for optical communications. The conservation of the topological charge on propagation and the detection of the topological charge by a receiver are significant in these applications and have been well established in free-space. However, when vortex beams enter a diffuser,the wavefront is distorted, leading to a challenge in the conservation and detection of the topological charge. Here, we present a technique to measure the value of the topological charge of a vortex beam obscured in the randomly scattered light. The results of the numerical simulations and experiments are presented and are in good agreement. In particular, only a single-shot measurement is required to detect the topological charge of vortex beams, indicating that the method is applicable to a dynamic diffuser.     

Detecting the topological charge of vortex beams using an annular triangle aperture

The Fraunhofer diffraction pattern of a vortex beam by an annular triangle aperture is analyzed theoretically and experimentally. It is found that the pattern of the far-field diffraction intensity distribution exhibits a triangular lattice array, which becomes much clearer with the increase of the ratio of the inner to the outer side of the annular triangle aperture. The number of spot points of any external side of the triangular lattice array minus one is just equal to the topological charge value of the measured optical vortex. For the vortex beam with negative topological charge, the triangular diffraction pattern after the annular triangle aperture will be rotated by 180° in relation to the case of the positive topological charge. Based on the above properties, we propose a simple and feasible method to determine the magnitude and sign of the topological charge of an optical vortex beam.     

Measuring the topological charge of vortex beams by using an annular ellipse aperture

We theoretically and experimentally investigate the Fraunhofer diffraction pattern of a vortex beam passing through an annular ellipse aperture. It is found that the pattern of the far-field diffraction intensity distribution exhibits some dark spots, which become clearer with increasing the value of the ellipticity factor of the annular ellipse aperture. The diffraction phenomenon is more obvious with increasing the value of the ratio of the inner long axis (or short axis) to the outer side of the annular ellipse aperture. The number of the dark spots in the Fraunhofer diffraction intensity distribution is just equal to the topological charge value of the measured optical vortex, and the centre of each dark spot is just a phase-singularity point. Based on this property, we can measure the topological charge of an optical vortex beam.     

Tunable directional beaming assisted by asymmetrical SPP excitation in a subwavelength metallic double slit

We present a design for tunable directional beaming through a subwavelength metallic double slit surrounded by dielectric surface-relief gratings.On-axis and off-axis beaming can be switched by controlling the incident angle to asymmetrically excite surface plasmon polaritons(SPPs) that are subsequently coupled out to propagating beams by the two gratings on the left and the right sides of the double slit.Furthermore,the division of optical power into two off-axis beaming directions can be tuned smoothly by varying the incident angle while keeping the total power almost unchanged.The mechanism of this effect is analyzed theoretically and verified using rigorous numerical simulations.     

Adaptive correction of vortex laser beam in a closed-loop system with phase only liquid crystal spatial light modulator

We propose and demonstrate the wave front correction of a vortex laser beam by using dual phase only liquid crystal spatial light modulators (LC-SLMs) and a stochastic parallel gradient descent (SPGD) algorithm. One phase only LC-SLM is used to generate vortex laser beam by loading spiral phase screen onto the wave front of input quasi-Gaussian beam. The other phase only LC-SLM under SPGD controller based on the subzone control method adaptively compensates the wave front of vortex laser beam. Numerical simulation and experimental results show that after correction, vortex doughnut like beam is focused into a beam with airy disk pattern distribution in the far field. The adaptive corrections of vortex laser beam with different optical topological charges are studied. The results show that the optical topological charge has little influence on adaptive correction. The powers in the main lobe of far field intensity distributions of vortex laser beams with different optical topological charges are all greatly improved by adaptive correction. The technique proposed in this paper can be used in optical communication, relay mirror and atmospheric turbulence correction.     

高斯涡旋光束的光束传输因子和峭度参数

基于强度二阶矩定义, 导出了高斯涡旋光束光束传输因子即M² 因子的解析表达式, 高斯涡旋光束的M² 因子唯一取决于拓扑电荷数n. 数值计算表明, 高斯涡旋光束的M² 因子随着拓扑电荷数n的增大而增大. 基于强度高阶矩, 还导出了高斯涡旋光束经傍轴ABCD光学系统传输时峭度参数的解析表达式, 高斯涡旋光束的峭度参数取决于拓扑电荷数n、参数δ、矩阵元A和矩阵元D. 在自由空间传输时, 高斯涡旋光束的峭度参数仅取决于拓扑电荷数n和参数δ. 自由空间传输时, 高斯涡旋光束峭度参数的变化规律为: 峭度参数随参数δ的增大先减小而后趋向于一最小值, 随拓扑电荷数n的增大而减小. 这一研究有助于高斯涡旋光束的实际应用.     

Spatial coherence properties of surface plasmon investigated by Young's slit experiment

In this Letter, we present an original method to extract the optical properties of surface plasmon polaritons (SPPs) on silver surfaces. A two Young's slit experiment combined with a leakage radiation microscope has been built. By correlating both imagery and coherence measurements on the same area, we are able to address the evolution of the SPP spatial coherence along its propagation. The proposed method could also be useful to explore the properties of complex plasmonic systems.     

Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma

In this paper, diffraction pattern of a vortex carrying beam with a Gaussian background has been studied by using Fresnel-Kirchhoff diffraction integral, in the presence of third-order coma. Results of intensity distribution and encircled energy at the Gaussian plane have been presented for two values of the topological charge. Positional shift and splitting of the dark core have been investigated in detail. It is noticed that the diffraction pattern of a beam with double topological charge is affected more by comatic aberration in comparison to the beam with single topological charge. We have also verified our results by using the optical transfer function approach. Propagation of an apertured Gaussian background vortex beam through a π-phase shifter has also been studied for two values of the topological charge.     

Study of interference in a double-slit without walls by plasmon tomography techniques

We investigate the free propagation of two parallel surface plasmon polaritons (SPP) beams using plasmon tomography. In the Fourier-plane images, we observed interference features that are not in correspondence with the images of SPPs on the sample's surface. We clearly observed that the interference maxima and minima are distributed over an arc of a circle. We explain the characteristics of the observed interference patterns assuming that each SPP beam can be considered as a “slit without walls”. We discuss important implications of this work for SPP tomography and interferometric plasmonic sensors.     

Topological charge inversion in polynomial astigmatic Gaussian beams

The evolution of the global topological charge in a general polynomial astigmatic Gaussian beam is investigated. The leading order terms of the polynomial prefactor determines the global topological charge and can be expressed as a product of first order polynomials, each representing an optical vortex function. We show that the global topological charge is bounded by the order of the polynomial and change during propagation in steps of 2 every time one of the optical vortices undergo topological charge inversion. We investigate the locations of the flip planes where charge inversions occur and provide expressions for a number of special cases. Numerical results are provided for an example of such a polynomial astigmatic Gaussian beam.