We developed a method to characterize arbitrary superpositions of light orbital angular momentum (OAM) with high fidelity by using astigmatic tomography and machine learning processing. In order to define each superposition unequivocally, we combine two intensity measurements. The first one is the direct image of the input beam, which cannot distinguish between opposite OAM components. This ambiguity is removed by a second image obtained after astigmatic transformation of the input beam. Samples of these image pairs are used to train a convolution neural network and achieve high fidelity recognition of arbitrary OAM superpositions with dimension up to five.
We report the experimental preparation of optical superpositions of high orbital angular momenta(OAM). Our method is based on the use of spatial light modulator to modify the standard Laguerre-Gaussian beams to bear excessive phase helices. We demonstrate the surprising performance of a traditional Mach-Zehnder interferometer with one inserted Dove prism to identify these superposed twisted lights, where the high OAM numbers as well as their possible superpositions can be inferred directly from the interfered bright multiring lattices. The possibility of present scheme working at photon-count …
A general orbital angular momentum (OAM) mode selection principle is put forward involving the rotationally symmetric superposition of chiral states. This principle is not only capable of explaining the operation of spiral zone plate holograms and suggesting that naturally occurring rotationally symmetric patterns could be inadvertent sources of vortex beams, but more importantly, it enables the systematic and flexible generation of structured OAM waves in general. This is demonstrated both experimentally and theoretically in the context of electron vortex beams using rotationally symmetric bi…
Light beams carrying orbital-angular-momentum (OAM) play an important role in optical manipulation and communication owing to their unbounded state space. However, it is still challenging to efficiently discriminate OAM modes with large topological charges and thus only a small part of the OAM states have been usually used. Here we demonstrate that neural networks can be trained to sort OAM modes with large topological charges and unknown superpositions. Using intensity images of OAM modes generalized in simulations and experiments as the input data, we illustrate that our neural network has g…
Phase conjugation with stimulated Brillouin scattering can be used to correct wavefront aberrations in high-power laser systems. Here, we consider such process with cylindrical vector lasers beams. By using a vectorial approach and a modal decomposition, we obtain a differential matrix equation that enables the calculation of the structure of Stokes vector eigenmodes and their Brillouin gain. The emphasis is put on the mode with the largest gain, which contributes the most to the Stokes beam. We show that the phase conjugation of orbital angular momentum in cylindrical vector beams is prevente…
We present generalized expressions to calculate the orbital angular momentum for invariant beams using scalars potentials. The solutions can be separated into transversal electric TE, transversal magnetic TM and transversal electromagnetic TE/TM polarization modes. We show that the superposition of non-paraxial vectorial beams with axial symmetry can provide a well defined orbital angular momentum and that the modes superposition affects the angular momentum flux density. The results are illustrated and analyzed for Bessel beams.
Interaction of spin and intrinsic orbital angular momentum of light is observed, as evidenced by length-dependent rotations of both spatial patterns and optical polarization in a cylindrically-symmetric isotropic optical fiber. Such rotations occur in straight few-mode fiber when superpositions of two modes with parallel and anti-parallel orientation of spin and intrinsic orbital angular momentum (IOAM=$2\hslash$) are excited, resulting from a degeneracy splitting of the propagation constants of the modes.
Optical intrinsic angular momentum can be regarded as derivation from spatial superposition of optical vector fields embodied by spinning or and spiraling the electric field vector. We employ vectorial formulation derivation to comprehensively study all angular momentum contents of optical vector fields in arbitrary superposition states, including the longitudinal and transverse, spin and orbital (SAM and OAM) components. As for the orthogonal superposition fields, there inherently exists spin-orbit shift from longitudinal SAM to OAM, and the whole local spin flow manifests local multiple fold…
Spatial modes of light can potentially carry a vast amount of information, making them promising candidates for both classical and quantum communication. However, the distribution of such modes over large distances remains difficult. Intermodal coupling complicates their use with common fibers, while free-space transmission is thought to be strongly influenced by atmospheric turbulence. Here we show the transmission of orbital angular momentum modes of light over a distance of 143 kilometers between two Canary Islands, which is 50 times greater than the maximum distance achieved previously. As…
We experimentally demonstrate an interferometric protocol for multiplexing optical states of light, with potential to become a standard element in free-space communication schemes that utilize light endowed with orbital angular momentum (OAM). We demonstrate multiplexing for odd and even OAM superpositions generated using different sources. In addition, our technique permits one to prepare either coherent superpositions or statistical mixtures of OAM states. We employ state tomography to study the performance of this protocol, and we demonstrate fidelities greater than 0.98.
We present a tunable liquid crystal device that converts pure orbital angular momentum eigenmodes of a light beam into equal-weight superpositions of opposite-handed eigenmodes and vice versa. For specific input states, the device may thus simulate the behavior of a π/2 phase retarder in a given two-dimensional orbital angular momentum subspace, analogous to a quarter-wave plate for optical polarization. A variant of the same device generates the same final modes starting from a Gaussian input.
We report on the direct measurements of fluid flow vorticity using a spatially shaped beam with a superposition of Laguerre-Gaussian modes that reports on the rotational Doppler shift from microparticles intersecting the beam focus. Experiments are carried out on fluid flows with well-characterized vorticity and the experimental results are found to be in excellent agreement with the expected values even for 200 ms integration times. This method allows for localized real-time determination of vorticity in a fluid flow.
We report on an experiment that investigates the spatial mode conversion in the process of parametric down-conversion seeded by a light beam in a superposition of orbital angular momentum modes. This process is interpreted in terms of a geometric representation of first-order spatial modes in a Poincaré sphere, providing an intuitive image of the phase conjugation and the topological charge conservation. We also make a comparison with the analogous phenomenon for optical parametric oscillators.
We propose a reconstruction of vortex beams based on the implementation of quadratic transformations in the orbital angular momentum. The information is encoded in a superposition of Bessel-like nondiffracting beams. The measurement of the angular probability distribution at different positions allows for the reconstruction of the Wigner function.
We present an optical setup for generating a sequence of light pulses in which the orbital angular momentum (OAM) degree of freedom is correlated with the temporal one. The setup is based on a single $q$-plate within a ring optical resonator. By this approach, we demonstrate the generation of a train of pulses carrying increasing values of OAM, or, alternatively, of a controlled temporal sequence of pulses having prescribed OAM superposition states. Finally, we exhibit an "OAM-to-time conversion" apparatus dividing different input OAM states into different time-bins. The latter application pro…
A light beam with phase singularity (PS) characterized with azimuthally symmetric angular positions (APs) can be constructed by the rotationally symmetric superposition of n (n is N) fractional vortex light beams with identical charges. The profile of this light beam deforms after propagation owing to its orbital angular momentum (OAM) noneigenvalue, and the deformation degree can be evaluated by the degree of phase dislocation associated with the PS. The expectation value of the mean deviation of its OAM from its characteristic charge value and the variation of the degree of phase dislocation…
We report on an experiment in which orbital angular momentum of light is mapped at the single-photon level into and out of a cold atomic ensemble. Based on the dynamic electromagnetically-induced transparency protocol, the demonstrated optical memory enables the reversible mapping of Laguerre-gaussian modes with preserved handedness of the helical phase structure. The demonstrated capability opens the possibility to the storage of qubits encoded as superpositions of orbital angular momentum states and to multi-dimensional light-matter interfacing.
The transverse spatial modes of light offer a large state-space with interesting physical properties. For exploiting it in future long-distance experiments, spatial modes will have to be transmitted over turbulent free-space links. Numerous recent lab-scale experiments have found significant degradation in the mode quality after transmission through simulated turbulence and consecutive coherent detection. Here we experimentally analyze the transmission of one prominent class of spatial modes, the orbital-angular momentum (OAM) modes, through 3 km of strong turbulence over the city of Vienna. I…
Control of orbital angular momentum (OAM) in optical fields has seen tremendous growth of late, with a myriad of tools existing for their creation and detection. What has been lacking is the ability to arbitrarily modify the OAM spectrum of a superposition in amplitude and phase, especially if a priori knowledge of the initial OAM spectrum is absent. Motivated by a quasi-mapping that exists between the position and OAM of Laguerre-Gaussian modes, we propose an approach for single-step modulation of a field's OAM spectrum. We outline the concept and implement it through the use of binary ring a…
Perfect (optical) vortices (PVs) have the mooted ability to encode orbital angular momentum (OAM) onto the field within a well-defined annular ring. Although this makes the near-field radial profile independent of OAM, the far-field radial profile nevertheless scales with OAM, forming a Bessel structure. A consequence of this is that quantitative measurement of PVs by modal decomposition has been thought to be unviable. Here, we show that the OAM content of a PV can be measured quantitatively, including superpositions of OAM within one perfect vortex. We outline the theory and confirm it by ex…
The capacity of optical communication channels can be increased by space division multiplexing in structured optical fibers. Radial core optical fibers allows for the propagation of twisted light--eigenmodes of orbital angular momentum, which have attracted considerable attention for high-dimensional quantum information. Here we study the generation of entangled photons that are tailor-made for coupling into ring core optical fibers. We show that the coupling of photon pairs produced by parametric down-conversion can be increased by close to a factor of three by pumping the non-linear crystal …
Harnessing the Orbital Angular Momentum (OAM) of light is an appealing approach to developing photonic technologies for future applications in optical communications and high- dimensional Quantum Key Distributions (QKD). An outstanding challenge to the widespread uptake of the OAM resource is its efficient generation. We design a new device which can directly emit an OAM-carrying light beam. By fabricating micro-scale Spiral Phase Plates (SPPs) within the aperture of a Vertical-Cavity Surface-Emitting Laser (VCSELs), the linearly polarized Gaussian beam emitted by the VCSEL is converted into a…
We report on studying the dynamic evolution of orbital angular momentum (OAM) carrying light in sum frequency generation (SFG). Dynamic evolution of the SFG beam is studied in different cases, in which the two pump beams are either a single OAM mode or OAM superposition mode. For the cases when the two pumps are both in superposition mode, two kinds of spatial patterns and evolution behaviors are observed, one set of spatial pattern is non-diffractive and unchanged with propagating. In addition, SFG of two pump beams with opposite OAM will evolve into a kind of quasi-Gaussian mode. These obser…
In this paper, we present the design procedure of modulated metasurface leaky-wave antennas (MMLWAs) to generate coaxial superposition of vortex beams with several orbital angular momentum (OAM) states. Based on the Flat Optics (FO) technique and aperture field estimation (AFE) method, an analytical framework is proposed to facilitate the implementation of MMLWAs generating multiple topological charges in the OAM regimen. Furthermore, using the spectral analysis which has been derived from the proposed model, we have shown that the symmetry of aperture shape can affect the purity of the mode. …
Cat states are systems in a superposition of macroscopically distinguishable states; this superposition can be of either classically or quantum distinct state, regardless of the number of particles or modes involved. Here, we constructed an experimental model that simulates an optical cat state by engineering the classical orbital angular momentum of light, referred to here as an analogous cat state (a-CS). In our scheme, the behaviors of the a-CS in position space show many similarities to the quantum version of the optical cat state in phase space, for example, movement, rotation, and interf…
We present an experimental demonstration of a Laguerre-Gauss (LG) spectrum measurement technique using variable focus lenses that is able to measure the strengths of all modes present in an unknown, incoming light beam with the highest possible efficiency. The experiment modifies the classical projective, phase flattening technique by including a variable sized pinhole and a two electronic lens variable imaging system that is tuned for each mode to give the highest possible detection efficiency irrespective of the beam waist of LG mode chosen for the projection/decomposition. The modified expe…
Quantum complementarity states that particles, e.g. electrons, can exhibit wave-like properties such as diffraction and interference upon propagation. \textit{Electron waves} defined by a helical wavefront are referred to as twisted electrons~\cite{uchida:10,verbeeck:10,mcmorran:11}. These electrons are also characterised by a quantized and unbounded magnetic dipole moment parallel to their propagation direction, as they possess a net charge of $-|e|$~\cite{bliokh:07}. When interacting with magnetic materials, the wavefunctions of twisted electrons are inherently modified~\cite{lloyd:12b,schat…
We present a unified and extended perspective of Bessel beams, irrespective to their orbital angular momentum (OAM) -- zero, integer or noninteger -- and mode -- scalar or vectorial, and LSE/LSM or TE/TM in the latter case. The unification is based on the integral superposition of constituent waves along the angular-spectrum cone of the beam, and allows to describe, compute, relate, and implement all the Bessel beams, and even other types of beams, in a universal fashion. The paper first establishes the integral superposition theory. Then, it demonstrates the previously unreported existence of…
One of the most widely used techniques for measuring the orbital angular momentum components of a light beam is to flatten the spiral phase front of a mode, in order to couple it to a single-mode optical fiber. This method, however, suffers from an efficiency that depends on the orbital angular momentum of the initial mode and on the presence of higher order radial modes. The reason is that once the phase has been flattened, the field retains its ringed intensity pattern and is therefore a nontrivial superposition of purely radial modes, of which only the fundamental one couples to a single mo…
Here we show indirect precise angular control using a four-wave mixing (FWM) process. This was performed with a superposition of light with orbital angular momentum (OAM) in an M-Type configuration of a hot 85Rb atomic ensemble. A gear-shaped interference pattern is observed at FWM light with a donut-shaped input signal. The gear could be rotated and is controlled through the change of the polarization of the pump laser. Our experimental results that are based on nonlinear coherent interactions have applications in image processing and precise angular control.
The possibility of focusing light to an ever tighter spot has important implications for many applications and fields of optics research, such as nano-optics and plasmonics, laser-scanning microscopy, optical data storage and many more. The size of lateral features of the field at the focus depends on several parameters, including the numerical aperture of the focusing system, but also the wavelength and polarization, phase and intensity distribution of the input beam. Here, we study the smallest achievable focal feature sizes of coherent superpositions of two co-propagating beams carrying opp…
The composite optical beams being a result of superposition, are a promising way to study the orbital angular momentum and its effects. Their wide range of applications makes them attractive and easily available due to the growing interest in the Spatial Light Modulators (SLM). In this paper, we present a simple method for generating composite vortex patterns with high symmetry. Our method is simple, flexible and gives perfectly aligned beams, insensitive to mechanical vibrations. This method is based on the ability to split SLM cells between phase patterns that are to be superposed. This appr…
Instituto Nacional de Astrofísica, Óptica y Electrónica（墨西哥国家天体物理学、光学和电子学研究所）；Tecnologico de Monterrey（蒙特雷科技大学）；Universidad Politécnica Metropolitana de Hidalgo（伊达尔戈大都会理工大学）
A field superposition of singular beams incident on, and then reflected from a mirror has been investigated. It was demonstrated that the standing optical wave, which contains a vortex, possesses an orbital angle momentum where the energy flux circulates only in the azimuth direction of the beam. We show in this paper that the standing light wave containing the optical vortex transfers angular momentum to a substance located in the field of the vortex without moving the substance in the azimuth or radial directions. This property of the standing vortex present an opportunity to form the three-…
Light with helical phase structures, carrying quantized orbital angular momentum (OAM), has many applications in both classical and quantum optics, such as high-capacity optical communications and quantum information processing. Frequency conversion is a basic technique to expand the frequency range of fundamental light. The frequency conversion of OAM-carrying light gives rise to new physics and applications such as up-conversion detection of images and high dimensional OAM entanglements. Quasi-phase matching (QPM) nonlinear crystals are good candidates for frequency conversion, particularly …
While photons travel in a straight line at constant velocity in free-space, the intensity profile of structured light may be tailored for acceleration in any degree of freedom. Here we propose a simple approach to control the angular acceleration of light. Using Laguerre-Gaussian modes as our twisted beams carrying orbital angular momentum, we show that superpositions of opposite handedness result in a radially dependent angular acceleration as they pass through a focus (waist plane). Due to conservation of orbital angular momentum we find that propagation dynamics are complex despite the free…
Because of the unlimited range of state space, orbital angular momentum (OAM) as a new degree of freedom of light has attracted great attention in optical communication field. Recently there are a number of researches applying deep learning on recognition of OAM modes through atmospheric turbulence. However, there are several limitations in previous deep learning recognition methods. They all require a constant distance between the laser and receiver, which makes them clumsy and not practical. As far as we know, previous deep learning methods cannot sort vortex beams with positive and negative…
