Increasing demand for practical applications is forcing deeper research into optical vortices (OVs): from the generation and measurement to shaping and multiple singularities manipulation of OVs. Herein, we propose a new type of phase structure called the high-order cross phase (HOCP) can be employed to modulate OVs to implement both polygonal shaping and singularities manipulation. Theoretically, we investigate the propagation characteristics of OVs with the HOCP. In experiments, we achieve the shaping and singularities manipulation of OVs by utilizing the HOCP. On this basis, we discuss the interference patterns of superposed OVs after the modulation. This work provides an alternative method to achieve both polygonal shaping and multiple singularities manipulation, which will facilitate applications in optical micro-manipulation, optical communication, and high-dimensional quantum entanglement.
We apply the CP to CAVs for the first time experimentally. Firstly, we introduce the propagation properties of a CAV with the LOCP in the process of measuring TCs, and measure the TCs of CAVs in the self-focusing areas experimentally. Secondly, we shape the CAVs via the HOCP and discuss the manipulaiton of singularities.
In this article we propose a new type of optical vortex, the X-type vortex. This vortex inherits and develops the conventional noncanonical vortex, i.e., it no longer has a constant phase gradient around the center, while the intensity keeps invariant azimuthally. The strongly focusing properties of the X-type vortex and its effect on the beam shaping in three-dimensional (3D) fields are analyzed. The interesting phenomena, which cannot be seen in canonical vortices, are observed, for instance the 'switch effect' which shows that the intensity pattern can switch from one transverse axis to ano…
We investigate a method for the measurement and shaping of a perfect optical vortex (POV) by using the cross-phase for the first time. Experimentally, we propose a method to measure the topological charges +3 and +-5 of POVs with the low-order cross-phase (LOCP) at the Fourier plane; we realize shaping intensity distributions of POVs at the Fourier plane with the high-order cross-phase (HOCP) and show the asymmetric modulation ability of the HOCP for an optical field. Furthermore, we discuss the influence of parameters on the optical field in the shaping process. On this basis, we propose a se…
The focal field properties of radially/azimuthally polarized Zernike polynomials are studied. A method to design the pupil field in order to shape the focal field of radially or azimuthally polarized phase vortex is introduced. With this method, we are able to obtain a pupil field to achieve a longitudinally polarized hollow spot with a depth of focus up to $12λ$ and $0.14λ$ lateral resolution for a optical system with numerical aperture 0.99; A pupil field to generate 8 circularly polarized focal spots along the optical axis is also obtained with this method.
Dynamic generation of obitial angular momentum (OAM) of light has enabled complex manipulation of micro-particles, high-dimension quantum entanglement and optical communication. We report an analog vortex transmitter made of one bilaterally symmetric grating and an aperture, emitting optical vortices with the average OAM value continuously variant in the entire rational range. Benefiting from linearly-varying transverse dislocation along its axis of symmetry, this diffractive transmitter possesses extra degree of freedom in engineering broadband optical vortices meanwhile preserving a novel sp…
We experimentally demonstrate the generation of off-axis phase singularities in a vortex transmutation process induced by the breaking of rotational symmetry. The process takes place in free space by launching a highly-charged vortex, owning full rotational symmetry, into a linear thin diffractive element presenting discrete rotational symmetry. It is shown that off-axis phase singularities follow straight dark rays bifurcating from the symmetry axis. This phenomenon may provide new routes towards the spatial control of multiple phase singularities for applications in atom trapping and particl…
We have experimentally and theoretically shown that the circularly polarized beam bearing singly charged optical vortex propagating through a uniaxial crystal can be split after focusing into the radially and azimuthally polarized beams in vicinity of the focal area provided that the polarization handedness and the vortex topological charge have opposite signs. Quality of the polarization structure can reach unity.
We experimentally demonstrate the emergence of a purely azimuthally polarized vectorial vortex beam with a phase singularity upon Brewster reflection of focused circularly polarized light from a dielectric substrate. The effect originates from the polarizing properties of the Fresnel reflection coefficients described in Brewster's law. An astonishing consequence of this effect is that the reflected field's Cartesian components acquire local phase singularities at Brewster's angle. Our observations are crucial for polarization microscopy and open new avenues for the generation of exotic states …
Square-shaping of sturdy optical vortex droplets in quasi-phase-matched photonic crystals
Foshan University（佛山大学）；Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, Foshan University（佛山大学广东港澳智能微纳光电技术联合实验室）；Tel Aviv University（特拉维夫大学）；Instituto de Alta Investigación, Universidad de Tarapacá（塔拉帕卡大学高等研究所）
We address vortex solitons supported by optical lattices featuring modulation of both the linear and nonlinear refractive indices. We find that when the modulation is out-of-phase the competition between both effects results in remarkable shape transformations of the solitons which profoundly affect their properties and stability. Nonlinear refractive index modulation is found to impose restrictions on the maximal power of off-site solitons, which are shown to be stable only below a maximum nonlinearity modulation depth.
We find diffraction-free beams for graphene and MoS$_2$-type honeycomb optical lattices. The resulting composite solutions have the form of multi-vortices, with spinor topological charges ($n$, $n\pm1$). Exact solutions for the spinor components are obtained in the Dirac limit. The effects of the valley degree of freedom and the mass are analyzed. Passing through the van-Hove singularity the topological structure of the solutions is modified. Exactly at the singularity the diffraction-free beams take the form of strongly localized one-dimensional stripes.
We study, both theoretically and by experiment, migration of the amplitude zeros within a fixed cross section of the edge-diffracted optical-vortex beam, when the screen edge performs permanent translation in the transverse plane from the beam periphery towards the axis. Generally, the amplitude zeros (optical-vortex cores) describe spiral-like trajectories. When the screen edge advances uniformly, the motion of the amplitude zeros is not smooth and sometimes shows anomalously high rates, which make an impression of instantaneous "jumps" from one position to another. We analyze the nature, con…
Vortex solitons (dark solitons) are described in self-defocusing Kerr media whose phase line singularity is not parallel to the propagation direction, but is perpendicular or tilted almost arbitrary angles, depending on the medium linear dispersion. These solitons broaden the so-called spatiotemporal optical vortices recently observed in experiments to the nonlinear realm, opening new perspectives in practical applications of optical vortices.
We report the fabrication of large-area phase masks on thin fused-silica substrates that are suitable for shaping multi-terawatt femtosecond laser beams. We apply these phase masks for the generation of intense femtosecond optical vortices. We further quantify distortions of the vortex beam patterns that result from several common types of mask defects.
We show the existence of stable two- and three-dimensional vortex solitons carrying multiple, spatially separated, single-charge topological dislocations nested around a vortex-ring core. Such new nonlinear states are supported by elliptical gain landscapes in focusing nonlinear media with two-photon absorption. The separation between the phase dislocations is dictated mostly by the geometry of gain landscape and it only slightly changes upon variation of the gain or absorption strength.
Quantum vortices are the analogue of classical vortices in optics, Bose-Einstein condensates, superfluids and superconductors, where they provide the elementary mode of rotation and orbital angular momentum. While they mediate important pair interactions and phase transitions in nonlinear fluids, their linear dynamics is useful for the shaping of complex light, as well as for topological entities in multi-component systems, such as full Bloch beams. Here, setting a quantum vortex into directional motion in an open-dissipative fluid of microcavity polaritons, we observe the self-splitting of th…
When a circularly-symmetric light beam with optical vortex (OV) diffracts at an opaque screen with the sharp edge, the OV core is displaced from the beam axis and, in case of the m-charged incident OV, decomposed into |m| single-charged ones. By means of numerical simulations and based on examples of incident beams with topological charges |m| =1, 2, 3 we show that, while the screen edge monotonously advances towards the beam axis, the OVs in the diffracted beam cross section move away from the incident beam axis along spiral-like trajectories. The trajectories contain fine structure details t…
We report on a soft route towards optical vortex coronagraphy based on self-engineered electrically tunable vortex masks based on liquid crystal topological defects. These results suggest that a nature-assisted technological approach to the fabrication of complex phase masks could be useful in optical imaging whenever optical phase singularities are at play.
We investigate the dynamic behavior of optical vortices, or phase singularities, in random wavefields and demonstrate the direct experimental observation of the anomalous diffusion of optical vortices. The observed subdiffusion of optical vortices show excellent agreement with the fractional Brownian motion, a Gaussian process. Paradoxically, the vortex displacements are observed exhibiting a non-Gaussian heavy-tailed distribution. We also tune the extent of subdiffusion and non-Gaussianity of optical vortex by varying the viscoelasticity of light scattering media. This complex motion of optic…
Historically, infinity was long considered a vague concept - boundless, endless, larger than the largest - without any quantifiable mathematical foundation. This view changed in the 1800s through the pioneering work of Georg Cantor showing that infinite sets follow their own seemingly paradoxical mathematical rules. In 1924, David Hilbert highlighted the strangeness of infinity through a thought experiment now referred to as the Hilbert Hotel paradox, or simply Hilbert's Hotel. The paradox describes an "fully" occupied imaginary hotel having infinite number of single-occupancy rooms, the manag…
Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell's equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian be…
We show that ring-like localized gain landscapes imprinted in focusing cubic (Kerr) nonlinear media with strong two-photon absorption support new types of stable higher-order vortex solitons containing multiple phase singularities nested inside a single core. The phase singularities are found to rotate around the center of the gain landscape, with the rotation period being determined by the strength of the gain and the nonlinear absorption.
We present a set of paraxial light beams with cylindrical symmetry, smooth and localized transversal profile carrying finite power, that develop intensity singularities when they are focused in a linear medium, such as vacuum. They include beams with orbital angular momentum and with radial polarization, in which case they develop punctual phase and polarization singularities surrounded by infinitely bright rings, along with singular longitudinal fields. In practice, these effects are manifested in focal intensities and spot sizes, vortex bright ring intensities and radii, and strengths of the…
We consider the propagation of a tilted high order paraxial vortex-beam through a homogeneous anisotropic medium of a uniaxial crystal. We found that the initially circularly polarized beam bearing the l-order optical vortex splits into ordinary and extraordinary beams with a complex vortex structure. After a series of dislocation reactions the vortices gather together at the axis of the partial beam with the initial circular polarization shaping the l-order optical vortex. However, only l-1 vortices gather together on the axis of the partial beam with the orthogonal circular polarization. One…
Probing Internal Dynamics of Spatiotemporal Optical Vortex Strings: Spatiotemporal Attraction and Filament Stretching
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences（中国科学院上海光学精密机械研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Tianjin University（天津大学）；Chongqing University of Technology（重庆理工大学）
Optical vortex beam of fractional order is generated by the diffraction of a Gaussian beam using computer generated hologram embedded with mixed screw-edge dislocation. Unfolding of the generated fractional vortex beam into eigen-polarization components inside a birefringent crystal results in the conversion of scalar phase singularity to vector polarization singularities in the beam cross-section. The evolution of the singularities of the ellipse field namely C-points (points of undefined major axis) and L-lines (lines of undefined handedness) across the beam quantifies the transformation. Th…
Optical holography has undergone rapid development since its invention in 1948, but the accompanying speckles with randomly distributed intensity are still untamed now due to the fundamental difficulty of eliminating intrinsic fluctuations from irregular complex-field superposition. Despite spatial, temporal and spectral averages for speckle reduction, it is extremely challenging to reconstruct high-homogeneity, edge-sharp and shape-unlimited images via holography. Here we predict that holographic speckles can be removed by narrowing the probability density distribution of encoded phase to hom…
Vortex beams are stable solutions of Maxwell's equations that carry phase singularities and orbital angular momentum, unique properties that give rise to many applications in the basic sciences, optical communications, and quantum technologies. Scalable integration and fabrication of vortex beam emitters will allow these applications to flourish and enable new applications not possible with traditional optics. Here we present a general framework to generate integrated vortex beam emitters using photonic inverse design. We experimentally demonstrate generation of vortex beams with angular momen…
We investigate the generation of broadband terahertz (THz) pulses with phase singularity from air plasmas created by fundamental and second harmonic laser pulses. We show that when the second harmonic beam carries a vortex charge, the THz beam acquires a vortex structure as well. A generic feature of such THz vortex is that the intensity is modulated along the azimuthal angle, which can be attributed to the spatially varying relative phase difference between the two pump harmonics. Fully space and time resolved numerical simulations reveal that transverse instabilities of the pump further affe…
We propose a new kind of optical vortex called the Hermite-Gaussian-like optical vortex (HGOV) inspired by the crossphase (CP). Theoretically, we investigate how the CP is decoupled from the phase of a cylindrical lens. We also investigate the propagation characteristics of an HGOV, which has a Hermitian-Gaussian-like intensity distribution but still retains the orbital angular momentum. Furthermore, we derive the Fresnel diffraction integral of an HGOV and study the purity at infinity. Besides, we show a novel function of the self-measurement of the HGOV. Finally, we show that we can change t…
We consider the problem of singular beams in optics as a part of the general questions of interactions, shaping and transformations of vortex states with fractional topological charges in physics, in particular, in hydrodynamic and quantum mechanic. Starting from the representation of the fractional-order vortex states as a superposition of infinite number of integer-order vortices with distinctive energy distributions (the vortex spectra) we showed that the smooth wave front of the fractional vortex beam can either decay into an asymmetric array of integer-order vortices or, vice versa, the a…
We study coherent and incoherent interactions between discrete vortex and fundamental solitons in two-dimensional photonic lattices, presenting a new scheme for all-optical routings and topological transformations of vorticities. Due to the multi-lobe intensity and step-phase structure of the discrete vortex soliton, the coherent soliton-interactions allow both solitons to be steered into multiple different possible destination ports depending on the initial phase of the discrete fundamental soliton. We show that charge-flipping of phase singularities and orbital angular momentum transfer can …
Zhejiang Key Laboratory of 3D Micro/Nano Fabrication and Characterization, Department of Electronic Science and Engineering, School of Engineering, Westlake University（西湖大学工程学院电子科学与工程系三维微纳加工与表征浙江省重点实验室）；Westlake Center for Micro/Nano Fabrication, Westlake University（西湖大学微纳加工中心）；Eastern Institute of Technology（宁波东方理工大学）
Polygonal Spatiotemporal Optical Vortices Wavepackets with Prescribed Vortex Structure
University of Shanghai for Science and Technology（上海理工大学）；Westlake University（西湖大学）；Pusan National University（釜山国立大学）；Zhejiang Key Laboratory of 3D Micro/Nano Fabrication and Characterization, Department of Electronic and Information Engineering, School of Engineering, Westlake University（西湖大学工程学院电子信息工程系三维微纳加工与表征浙江省重点实验室）；Westlake Institute for Optoelectronics（西湖光电研究院）
Optical vortices host the orbital nature of photons, which offers an extra degree of freedom in photonic applications. Unlike vortices in other physical entities, optical vortices require structural singularities, which restrict their abilities in terms of dynamic and interactive characteristics. In this study, we present the spontaneous generation and external magnetic field-induced manipulation of an optical vortex and antivortex. A gradient-thickness optical cavity (GTOC) consisting of an Al/SiO2/Ni/SiO2 multilayer structure realised the distinct transition between the trivial and non-trivi…
We experimentally investigate the optical storage of perfect optical vortex (POV) and spatially multimode perfect optical vortex (MPOV) beams via electromagnetically induced transparency (EIT) in a hot vapor cell. In particular, we study the role that phase gradients and phase singularities play in reducing the blurring of the retrieved images due to atomic diffusion. Three kinds of manifestations are enumerated to demonstrate such effect. Firstly, the suppression of the ring width broadening is more prominent for POVs with larger orbital angular momentum (OAM). Secondly, the retrieved double-…
We present a novel procedure to solve the Schrödinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use the scattering modes, which are solutions of the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore permit to solve the problem. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role than La…
Nanophotonic platforms such as metasurfaces, achieving arbitrary phase profiles within ultrathin thickness, emerge as miniaturized, ultracompact and kaleidoscopic optical vortex generators. However, it is often required to segment or interleave independent subarray metasurfaces to multiplex optical vortices in a single nano device, which in turn affects the compactness and channel capacity of the device. Here, inspired by phyllotaxis patterns in pine cones and sunflowers, we theoretically prove and experimentally report that multiple optical vortices can be produced in a single compact phyllot…
All-optical programming of polarization singularities in a photonic-crystal laser
Ecole Centrale de Lyon, CNRS, INSA Lyon, Université Claude Bernard Lyon 1, CPE Lyon, Institut des Nanotechnologies de Lyon (INL)（里昂中央理工学院，法国国家科学研究中心，里昂国立应用科学学院，里昂第一大学，里昂高等化工学院，里昂纳米技术研究所）；Department of Physics, NISM Institute, University of Namur（纳慕尔大学物理系，NISM研究所）；Centre for OptoElectronics and Biophotonics (COEB), School of Electrical and Electronic Engineering, Nanyang Technological University（南洋理工大学电气与电子工程学院光电与生物光子学中心）；CNRS-International-NTU-Thales Research Alliance (CINTRA)（法国国家科学研究中心-国际南洋理工大学-泰雷兹研究联盟）
In TEM, a typical goal consists of making a small electron probe in the sample plane in order to obtain high spatial resolution in scanning transmission electron microscopy. In order to do so, the phase of the electron wave is corrected to resemble a spherical wave compensating for aberrations in the magnetic lenses. In this contribution we discuss the advantage of changing the phase of an electron wave in a specific way in order to obtain fundamentally different electron probes opening up new application in the (S)TEM. We focus on electron vortex states as a specific family of waves with an a…
Metasurfaces are engineered thin surfaces comprising two dimensional (2D) arrays of sub-wavelength spaced and sub-wavelength sized resonators. Metasurfaces can locally manipulate the amplitude, phase and polarization of light with high spatial resolution. In this study, we report numerical and experimental results of a vortex-beam-generating metasurface fabricated specifically for infrared (IR) and terahertz (THz) wavelengths. The designed metasurface consisted of a 2D array of dielectric cross-shaped resonators with spatially varying length, thereby providing desired spatially varying phase s…
The interaction of optical vortices (or phase singularities, screw dislocations) with ordinary matter is treated with simple approach. Using total internal reflection phenomenon and superposition of four plane waves incident on a material with refractive index lower than the original propagating medium, we are able to show birth and annihilation of optical vortices in the evanescent field with curved topological features. Until now, this phenomenon has been explored only in free space propagation. By a suitable tuning process, involving the incident angles and the amplitudes of the incident pl…
The City College of New York（纽约市立学院）；The Australian National University（澳大利亚国立大学）；University of Central Florida（中佛罗里达大学）；Air Force Research Laboratory（空军研究实验室）；City University of New York（纽约市立大学）
Efficient delivery of light into nanoscale volumes by converting free photons into localized charge-density oscillations (surface plasmons) enables technological innovation in various fields from biosensing to photovoltaics and quantum computing. Conventional plasmonic nanostructures are designed as nanoscale analogs of radioantennas and waveguides. Here, we discuss an alternative approach for plasmonic nanocircuit engineering that is based on molding the optical powerflow through 'vortex nanogears' around a landscape of local phase singularities 'pinned' to plasmonic nanostructures. We show t…
