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 particle manipulation.
Some interesting optical instruments such as the Eaton lens and the Invisible Sphere require singularities of the refractive index for their implementation. We show how to transmute those singularities into harmless topological defects in anisotropic media without the need for anomalous material properties.
We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting in graded profiles that are all-dielectric, do not require materials with unrealistic values, and that are impedance matched to the bounding medium. This is achieved by transmuting the singularities (or zeros) using the formalism of transformation optics, but with an additional boundary condition requiring the gradient of the co- ordinate transformation be …
In the field of transformation optics, metamaterials mimic the effect of coordinate transformations on electromagnetic waves, creating the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here we report the achievement of another "impossible task". We implement, for microwaves, a device that would normally require a dielectric…
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 …
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 …
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 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.
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 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.
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 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 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.
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…
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）
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 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 …
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…
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…
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）
Based on the Kirchhoff-Fresnel approximation, we numerically analyze spatial characteristics of the light field formed after a circular Laguerre-Gaussian beam with a single-charged optical vortex (OV) passes the transparent screen with a rectilinear phase step. The main attention is paid to the localization and interactions of the OVs, which form the singular skeleton of the transformed field. The phase-step influence depends on its value and position with respect to the beam axis. Upon "weak perturbation" (low phase step) the main effect is that the OV is shifted from the initial axial positi…
We theoretically study the generation of orbital angular momentum(OAM) based on four-wave mixing (FWM) process in a diamond-type inhomogeneously broadened $^{85}$Rb atomic system. We use density matrix formalism at weak probe limit to explain the origin of vortex translation between different optical fields and generated signal. We show how the singularities which are omnipresent in phase of the input optical vortex beams can be profoundly mapped to atomic coherence in the transverse plane that hold the origin of OAM translation. This translation process works well even for moderately intense …
Topological properties of materials, as manifested in the intriguing phenomena of quantum Hall effect and topological insulators, have attracted overwhelming transdisciplinary interest in recent years. Topological edge states, for instance, have been realized in versatile systems including electromagnetic-waves. Typically, topological properties are revealed in momentum space, using concepts such as Chern number and Berry phase. Here, we demonstrate a universal mapping of the topology of Dirac-like cones from momentum space to real space. We evince the mapping by exciting the cones in photonic…
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…
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…
