With increasing interest in using orbital angular momentum (OAM) modes in high-power laser systems, accurate mathematical descriptions of the high-intensity modes at focus are required for realistic modelling. In this work, we derive various high intensity orbital angular momentum focal spot intensity distributions generated by Gaussian, super-Gaussian, and ideal flat-top beams common to high-power laser systems. These intensity distributions are then approximated using fitted Laguerre-Gaussian basis functions as a practical way for describing high-power OAM beams in theoretical and numerical models.
The additional degree of freedom as introduced by the orbital angular momentum (OAM) of light has revolutionized the various technological applications. Optical pulses with OAM have applications in the generation of twisted attosecond pulses, ultrafast spectroscopy, telecommunication, high harmonic generation and in many other areas of physics as well. In this paper, we present a numerical investigation of the propagation dynamics of ultrashort Laguerre Gauss (LG) vortices using nonlinear envelope equation (NEE) in a dispersive and nonlinear medium. Asymmetric splitting of ultrashort LG vortic…
We propose a generalization of the Laguerre Gauss Transform to include elliptical kernels in vortices metrology. To that end, we broaden the original pseudo field obtained using Laguerre Gauss Transform (LGT) that usually includes circularly a symmetric Gaussian core to include two parameters, the widths of the Gaussian filter in two perpendicular directions, thus generating a family of slightly elliptical kernels. This permits the generation of a family of very close vortices that improves the identification of homologous ones and the precision and locality of the measurements. We show exampl…
The electromagnetic field of optical vortices is in most cases derived from vector and scalar potentials using either a procedure based on the Lorenz or the Coulomb gauge. The former procedure has been typically used to derive paraxial solutions with Laguerre-Gauss radial profiles, while the latter procedure has been used to derive full solutions of the wave equation with Bessel radial profiles. We investigate the differences in the derivation procedures applying each one to both Bessel and Laguerre-Gauss profiles. We show that the electromagnetic fields thus derived differ in the relative str…
We propose and experimentally verify a novel scheme for diagnosing the order of a perturbed optical vortex using its 2-D spatial autocorrelation function. The order of a vortex was found to be equal to the number of dark rings or zero points present in the correlation function. We have provided a compact analytical expression for the correlation function in the form of Laguerre polynomials. Further, we have utilized the divergence of the first zero point of Laguerre polynomials upon propagation to obtain information about higher-order spatial modes, and compared it with our experimental result…
Plasma is an attractive medium for generating strong microscopic magnetic structures and tunable electromagnetic radiation with predictable topologies due to its extraordinary ability to sustain and manipulate high currents and strong fields. Here, using theory and simulations, we show efficient generation of multi-megagauss magnetic and tunable optical vortices when a sharp relativistic ionization front (IF) passes through a relatively long-wavelength Laguerre-Gaussian (LG) laser pulse with orbital angular momentum (OAM). The optical vortex is frequency upshifted within a wide spectral range …
Neglecting the electric field component along the light's propagation direction is a common practice, known as paraxial approximation. However, experimental evidence and theory on the head-on excitation of atoms by Laguerre-Gaussian beams reveal that the full vector character of the light field has to be taken into account. Optical vortices are a large family of fields, being Laguerre-Gaussian only one particular case. Now we extend the study of the applicability of the paraxial approximation to a broader set of optical vortices by considering the interaction of atoms with generalized Laguerre…
In this work, we present a novel and practical method for generating optical vortices in high-power laser systems. Off-axis spiral phase mirrors are used at oblique angles of incidence in the beam path after amplification and compression allowing for the generation of high-power optical vortices in almost any laser system. An off-axis configuration is possible via modification of the azimuthal gradient of the spiral phase helix and is demonstrated with a simple model using a discrete spiral staircase. This work presents the design, fabrication, and implementation of off-axis spiral phase mirro…
Thus, the results of our studies lie in developing and implementing the basic principles of digital sorting the Laguerre-Gauss modes by radial numbers both for a non-degenerate and a degenerate state of a vortex beam subject to perturbations in the form of a hard-edged aperture of variable radius. The digital sorting of LG beams by the orthogonal basis involves the use of higher-order intensity moments, and subsequent scanning of the modulated beam images at the focal plane of a spherical lens. As a result, we obtain a system of linear equations for the squared mode amplitudes and the cross am…
Longitudinal electromagnetic fields generally become comparable with the usually dominant transverse components in strongly-focussed, non-paraxial beams. For optical vortex modes it is highlighted here how their angular momentum properties produce longitudinal fields that in general must be accounted for, even within the paraxial regime. First-order longitudinal components of quantized Laguerre-Gaussian modes are derived and numerically studied with respect to the paraxial parameter, highlighting light-matter and spin-orbit interactions that stem from longitudinal fields of weakly-focussed, pa…
The generation of optical beams with multiple, mutually-coherent orbital-angular-momentum (OAM) modes using phase gratings is analyzed from the perspective of energy distribution and radial mode composition. We show that phase gratings designed with equally-weighted Laguerre-Gauss (LG) modes will generate beams with uneven energy distribution among OAM components. This unwanted outcome cannot be corrected by adjusting the width of the illuminating beam. We propose a way to design phase gratings that will produce a uniform energy distribution among the constituent OAM states after illumination,…
Improving axial resolution is of paramount importance for three-dimensional optical imaging systems. Here, we investigate the ultimate precision in axial localization using vortex beams. For Laguerre-Gauss beams, this limit can be achieved with just an intensity scan. The same is not true for superpositions of Laguerre-Gauss beams, in particular for those with intensity profiles that rotate on defocusing. Microscopy methods based on rotating vortex beams may thus benefit from replacing traditional intensity sensors with advanced mode-sorting techniques.
The chirality and helicity of linearly polarised Laguerre-Gaussian (LG) beams are examined. Such a type of light possesses a substantial longitudinal field when its beam waist is sufficiently small and so gives rise to non-zero chirality and helicity. In the simplest case of a doughnut beam of winding number $\ell=1$ and another identical to it but has $\ell= -1$, we obtain different chirality and helicity distributions at the focal plane $z=0$. We also show that this chiral behaviour persists and the patterns evolve so that on planes at $z<0$ and $z>0$ the beam convergence contributes differe…
The recognition in the 1990s that vortex beams (VBs), paraxial light beams with optical vortices, carry orbital angular momentum (OAM), has benefited applications ranging from optical manipulation to high-dimensional classical and quantum information communications. The transverse profiles of common VBs, e.g., Laguerre-Gaussian beam and high-order Bessel beam, are hollow donuts whose radii grow up with OAM inevitably. The inherently unperfect character of the VBs that the radius is always positively correlated with OAM, restricts the application of the VBs in many scenarios like fiber optic da…
The transverse field profile of light is being recognized as a resource for classical and quantum communications for which reliable methods of sorting or demultiplexing spatial optical modes are required. Here, we demonstrate, experimentally, state-of-the-art mode demultiplexing of Laguerre-Gaussian beams according to both their orbital angular momentum and radial topological numbers using a flow of two concatenated deep neural networks. The first network serves as a transfer function from experimentally-generated to ideal numerically-generated data, while using a unique "Histogram Weighted Lo…
Shenzhen University（深圳大学）；East China Normal University（华东师范大学）；University of Shanghai for Science and Technology（上海理工大学）；Northwestern Polytechnical University（西北工业大学）
We introduce a novel and simple modulation technique to tailor optical beams with a customized amount of orbital angular momentum (OAM). The technique is based on the modulation of the angular spectrum of a seed beam, which allows us to specify in an independent manner the value of OAM and the shape of the resulting beam transverse intensity. We experimentally demonstrate our method by arbitrarily shaping the radial and angular intensity distributions of Bessel and Laguerre-Gauss beams, while their OAM value remains constant. Our experimental results agree with the numerical and theoretical pr…
The properties of electron round lenses produced by the ponderomotive potential are investigated in geometrical optics. The potential proportional to the intensity distribution of a focused first-order Bessel or Laguerre-Gaussian beam is exploited to produce an electron round lens and a third-order spherical aberration corrector. Several formulas for the focal length and spherical aberration coefficients in the thin-lens approximation are derived to set the lens properties and associated light beam parameters. When the mode field of the optical beam is small, the electron trajectory calculatio…
The implementation of optical quantum gates comes at the cost of incorporating a source of nonclassical light, which suffers from a low flux of photons, and thus, long acquisition times. Quantum-mimetic optical gates combine the benefits of quantum systems with the convenience of using intense light beams. Here, we are concerned with the classical implementation of a controlled-SWAP (c-SWAP) gate using the tools of structured light. A c-SWAP gate is a three-qubit gate, where one of the input qubits controls the exchange of information between the other two qubits. We use Laguerre-Gauss beams t…
Measuring the positions of optical vortices is an essential part in the researches of speckles and adaptive optics. The measurement accuracy is restricted by the performance of optical devices and the properties of optical vortices, such as density and size. In order to achieve high accuracy and wide range of application, the dual shearing-type Sagnac interferometers is proposed using two shearing plates to adjust the precision of optical vortices measurement. The shearing displacements are able to balance the measuring precision and the value of the intensity ratio point to provide optimum me…
Extreme Energy Concentration of Band-Limited Superoscillatory Vortices for Efficient Optical Micromanipulation
University of Science and Technology of China（中国科学技术大学）；State Key Laboratory of Opto-Electronic Information Acquisition and Protection Technology（光电信息获取与防护技术国家重点实验室）；Anhui Key Laboratory of Optoelectronic Science and Technologies（安徽省光电子科学与技术重点实验室）；Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局材料研究与工程研究所）；Chengdu University of Technology（成都理工大学）；Nanyang Technological University（南洋理工大学）；Chinese Academy of Sciences Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学院量子信息与量子物理前沿卓越创新中心，中国科学技术大学）；Hefei National Laboratory, University of Science and Technology of China（合肥国家实验室，中国科学技术大学）
In any form of wave propagation, strong spatiotemporal coupling appears when non-elementary, three-dimensional wave-packets are composed by superimposing pure plane waves, or spontaneously generated by light-matter interaction and nonlinear processes. Ultrashort pulses with orbital angular momentum (OAM), or ultrashort vortices, furnish a critical paradigm in which the analysis of the spatiotemporal coupling in the form of temporal-OAM coupling can be carried out accurately by analytical tools. By generalizing and unifying previously reported results, we show that universal and spatially heter…
It has been recently shown that the orbital angular momentum (OAM) and temporal degrees of freedom in ultrafast (few-cycle) vortices are coupled. This coupling manifests itself with different effects in different parts of the vortex, as has been shown for the ring surrounding the vortex where the pulse energy is maximum, and also in the immediate vicinity of the vortex center. In may applications, however, the ring of maximum energy is not of primary interest, but that where the pulse peak intensity is maximum, which is particularly true in nonlinear optics applications such as the experiments…
