Average Orbital Angular Momentum Research Articles

Optical communication in a turbulent atmosphere via the orbital angular momentum of a laser beam. II. Symbol error rate in a data line

A numerical simulation is applied to study the symbol error rate (SER) in an optical communication system with data modulation by the orbital angular momentum (OAM) of an optical beam propagating through a turbulent atmosphere. In this case, the OAM is calculated from pre-recorded powers of azimuthal modes, while the complex modes are the coefficients of expansion of the wave field of the beam into spiral harmonics. The SER is calculated as a function of turbulence conditions for the LG1 and LG4 beams and data line lengths, as well as the number of receiving channels (number of recorded powers of azimuthal modes) and size of the input aperture of the receiving telescope. It is shown that the range of angular harmonics can be optimized to diminish the SER. It is found that knowing the probability density of OAM fluctuations, with a pre-determined average OAM and its variance, we can estimate the SER without conducting special numerical tests.

Generation of discrete higher-order optical vortex lattice at focus.

Higher-order vortices (HOVs) extend the dimensions of optical vortex regulation, which is of great significance in optical communication and optical tweezers. Herein, we demonstrate an alternative scheme to produce a HOV in the focus plane using multiple Laguerre-Gaussian (LG) beam interference, termed a discrete higher-order optical vortex lattice (DHOVL). The modulation depth of the DHOVL exceeds 2π. In this case, the topological charge (TC) of the DHOVL is determined by the difference of the phase period between the innermost and the outermost interference beams. Compared with a conventional HOV (CHOV), the vortex exists in a form of multiple unit singularities sharing a dark core. In addition, the average orbital angular momentum per photon of the DHOVL increases with increasing TC, surpassing that of the CHOV. This work provides a novel, to the best of our knowledge, scheme to produce a HOV, which will facilitate several advanced applications, including optical micromanipulation, optical sensing and imaging, and optical fabrication.

Gauge-invariant measure of the magnon orbital angular momentum

Unlike the Berry phase, the orbital angular momentum (OAM) of magnons with two-dimensional wave vector $\mathbf{k}$ in band $n$ is not gauge invariant for arbitrary phase ${\ensuremath{\lambda}}_{n}(\mathbf{k})$ and so is not physically observable. However, by integrating the OAM over the orientation $\ensuremath{\phi}$ of wave vector $\mathbf{k}$, we construct a gauge-invariant function ${F}_{n}(k)$. Like ${F}_{n}(k)$, the average OAM for magnon band $n$ in a circle of radius $k$ is also gauge invariant and can be directly observed. We demonstrate these results for a ferromagnet on a honeycomb lattice with Dzyalloshinskii-Moriya interactions between next-nearest neighbor spins. With wave vectors $\mathbf{k}$ restricted to the first Brillouin zone, the angular averaged OAM ${F}_{n}(k)$ then has opposite signs for lower and upper bands $n=1$ and 2 for all $k$.

Generation, Topological Charge, and Orbital Angular Momentum of Off-Axis Double Vortex Beams

Compared with the on-axis vortex beam and the off-axis single vortex beam, the off-axis double vortex beam has more control degrees of freedom and brings rich physical properties. In this work, we investigate theoretically and experimentally the generation, topological charge (TC), and orbital angular momentum (OAM) of off-axis double vortex beams. It is demonstrated that the tilted lens method can detect not only the magnitudes and signs of two TCs of the off-axis double vortex beam but also the spatial distribution of the TCs. Moreover, the average OAM value of the off-axis double vortex beam decreases nonlinearly as the off-axis distance increases, although its TC is independent of the off-axis distance of phase singularities. The results indicate that the average OAM of the off-axis double vortex beam can be easily controlled by changing the relative position of two-phase singularities, thereby realizing the applications of multi-degrees of freedom particle manipulation, optical communication, and material processing.

Control of orbital angular momentum of optical vortex beams with complex wandering perturbations.

This work investigates how independent perturbations and cross-correlation perturbations affect optical vortex beams. Theoretical and experimental results show that both perturbations cause the intensity, average orbital angular momentum (OAM), and the OAM spectrum of the vortex beam to vary periodically with the perturbation direction, but with different periods. When the beam is subjected to independent perturbations, the average OAM changes periodically with θ in every π/2; when the beam is subjected to cross-correlation perturbations, the average OAM varies with θ in every π. The results of this work provide a method to control the OAM and regulate low-coherence vortex beams in turbulent environments.

Mitigating Vortex Splitting by Controlling the Wavefront Isophase Line Curvature of Vector Autofocusing Airy Vortex Beams in Free Space

The match between the orbital angular momentum (OAM) transmission and receipt is a prerequisite for vortex beams as a carrier of the wireless optical communication system in free space. However, the vortex splitting induced by atmospheric turbulence results in an offset in the average OAM measured after propagating over the free space optical communication link. Therefore, how to reduce the vortex splitting effect to improve the stability of orbital angular momentum propagation is studied in this paper. First, a new parameter (m) is introduced to modulate the radial distribution of the polarization state of the autofocusing Airy vortex beams (AAVBs). Second, to control the optical field distribution in focal plane, the wavefront isophase line curvature of the AAVBs is reconstructed by using the Pancharatnam-Berry phase generated in the polarization conversion process. Finally, by comparing the vortex splitting rates of the AAVBs with different wavefrontisophase line curvatures under different turbulence environments, it can be found that the vortex splitting in free space can be effectively mitigated by choosing an appropriate wavefront isophase line curvature. In addition, the mitigation effect is more obvious in the atmosphere with stronger turbulence. This study provides a new feasible method to control the phase structure of vortex beams and promises potential applications in the OAM-based free space optical communication system.

Shack-Hartmann Wavefront Sensing of Ultrashort Optical Vortices.

Light beams carrying Orbital Angular Momentum (OAM), also known as optical vortices (OV), have led to fascinating new developments in fields ranging from quantum communication to novel light–matter interaction aspects. Even though several techniques have emerged to synthesize these structured-beams, their detection, in particular, single-shot amplitude, wavefront, and modal content characterization, remains a challenging task. Here, we report the single-shot amplitude, wavefront, and modal content characterization of ultrashort OV using a Shack-Hartmann wavefront sensor. These vortex beams are obtained using spiral phase plates (SPPs) that are frequently used for high-intensity applications. The reconstructed wavefronts display a helical structure compatible with the topological charge induced by the SPPs. We affirm the accuracy of the optical field reconstruction by the wavefront sensor through an excellent agreement between the numerically backpropagated and experimentally obtained intensity distribution at the waist. Consequently, through Laguerre–Gauss (LG) decomposition of the reconstructed fields, we reveal the radial and azimuthal mode composition of vortex beams under different conditions. The potential of our method is further illustrated by characterizing asymmetric Gaussian vortices carrying fractional average OAM, and a realtime topological charge measurement at a 10Hz repetition rate. These results can promote Shack-Hartmann wavefront sensing as a single-shot OV characterization tool.

Spontaneous symmetry breaking in persistent currents of spinor polaritons

We predict the spontaneous symmetry breaking in a spinor Bose–Einstein condensate of exciton-polaritons (polaritons) caused by the coupling of its spin and orbital degrees of freedom. We study a polariton condensate trapped in a ring-shaped effective potential with a broken rotational symmetry. We propose a realistic scheme of generating controllable spinor azimuthal persistent currents of polaritons in the trap under the continuous wave optical pump. We propose a new type of half-quantum circulating states in a spinor system characterized by azimuthal currents in both circular polarizations and a vortex in only one of the polarizations. The spontaneous symmetry breaking in the spinor polariton condensate that consists in the switching from co-winding to opposite-winding currents in opposite spin states is revealed. It is characterized by the change of the average orbital angular momentum of the condensate from zero to non-zero values. The radial displacement of the pump spot and the polarization of the pump act as the control parameters. The considered system exhibits a fundamental similarity to a superconducting flux qubit, which makes it highly promising for applications in quantum computing.

Generation of relativistic positrons carrying intrinsic orbital angular momentum

High energy positrons can be efficiently created through high-energy photons splitting into electron-positron pairs under the influence of the Coulomb field. Here we show that a new degree of freedom-the intrinsic orbital angular momentum (OAM) can be introduced into relativistic positrons when the incident photons are twisted. We developed the full-twisted scattering theory to describe the transfer of angular momentum before and after the interaction. It is found that the total angular momentum (TAM) of the photon is equally distributed among the positron and electron. For each photon TAM value, the generated leptons gain higher average OAM number when the photon spin is anti-parallel to its TAM. The impact of photon polarization on the OAM spectrum profile and the scattering probability is more significant at small photon TAM numbers, owing to the various interaction channels influenced by flipping the photon spin. Our work provides the theoretical basis to study OAM physics in particle scattering and to obtain copious relativistic vortex positrons through the Beth-Heitler process.

Fluctuations of the orbital angular momentum of a laser beam registered by a finite-size receiver aperture after propagation through a turbulent atmosphere

The fluctuation characteristics of the orbital angular momentum (OAM) are studied numerically in the computer experiment simulating the propagation of an OAM-carrying laser beam through a turbulent atmosphere and OAM registering by a finite-size receiver aperture. The wave-optics numerical simulation employs the conventional split-operator method (with phase screens) and the Monte Carlo averaging technique. OAM statistical characteristics in the turbulent medium are compared for two employed definitions of the specific (normalized) orbital angular momentum. For the non-vortex Gaussian beam, the correlation between OAM fluctuations and intercepted power is found to be negligibly small at arbitrary size of the receiver aperture. For the vortex Laguerre—Gaussian beam, the correlation between OAM fluctuations and intercepted power is significant (the correlation coefficient can achieve 0.7). In this case, the values of OAM variance for these definitions differ almost twice. It is shown that the OAM value averaged over realizations of the turbulent medium for the aperture size intercepting almost the entire beam power becomes equal to that in the homogeneous medium. As the aperture size decreases, the average OAM value decreases, and when the aperture size tends to zero, it tends to zero as well. The results obtained in the paper can be used in development and improvement of methods for optical transmission of information by optical beams with OAM, as well as in development of optical means for manipulating micron-sized particles.

Isolated intense half-cycle attosecond pulse generation with orbital angular momentum

A relativistic linearly polarized Laguerre–Gaussian (LG) laser pulse interacting with a combination of gas plasma and an oblique foil target is proposed to generate an intense attosecond pulse carrying large orbital angular momentum (OAM). The LG laser pulse firstly produces an ultra-thin relativistic electron sheet (RES) in underdense plasma and transfers the OAM to the latter at the same time. When the RES passes through the oblique foil, it radiates an intense half-cycle attosecond pulse carrying large OAM. Three-dimensional particle-in-cell simulation confirms that an isolated ultra-intense half-cycle attosecond pulse with a duration of 542 as and a peak electric field of 5 × 1012 V m−1 is produced. The average OAM per photon of the attosecond pulse is about −1ћ. Such an intense, isolated attosecond pulse with the large OAM would provide new possibilities in attosecond scientific research.

The evolution of spectral intensity and orbital angular momentum of twisted Hermite Gaussian Schell model beams in turbulence.

We introduce a new class of twisted partially coherent beams with a non-uniform correlation structure. These beams, called twisted Hermite Gaussian Schell model (THGSM) beams, have a correlation structure related to Hermite functions and a twist factor in their degree of coherence. The spectral density and total average orbital angular momentum per photon of these beams strongly depend on the distortions applied to their degree of coherence. On propagation through free space, they exhibit both self-splitting and rotation of their spectral density profile, combining the interesting effects of twisted beams and non-uniformly correlated beams. We demonstrate that we can adjust both the beam order and the twist factor of THGSM beams to improve their resistance to turbulence.

OAM content and propagation dynamics of integer-order Gamma vortices

We clarify, both theoretically and experimentally, the conceptual difference between a general vortex beam and an orbital angular momentum (OAM) beam regardless of carrying the same integer topological charge. We use a phase-only spatial light modulator to generate various non-canonical vortices, i.e., Gamma vortices, whose phase structures are described mathematically by the Gamma function. To further explore the OAM content of Gamma vortices, we perform a mode decomposition in the basis of OAM eigenstates. The measured OAM spectra indicate that each Gamma vortex is a coherent superposition of high-dimensional OAM states, but its average OAM value remains the same as the topological charge. In addition, resulting from the different Gouy phases among the OAM states, we find that the Gamma vortex carrying a high-order topological charge will generally decay into several unit-charge vortices and these vortices deviate unsymmetrically from the center of the light beam. Our work may find potential applications where the structured phase engineering is desired.

2.7 μm optical vortex beam directly generated from an Er:Y2O3 ceramic laser.

We demonstrate, to the best of our knowledge, the first direct vortex beam generation in the 3μm spectral region by employing an Er:Y2O3 ceramic laser. Controllable handedness with high purity is achieved by introducing asymmetric cavity loss and reducing the number of longitudinal modes. The average orbital angular momentum of the produced scalar vortex beam is quantitatively evaluated to be 0.95ħ for the LG0,+1 mode and -0.94ħ for the LG0,-1 mode. The corresponding optical spectrum is centered at 2710.8 and 2710.5nm, respectively.

Power-scalable and high-speed orbital angular momentum modulator

A device that can modulate the average orbital angular momentum (OAM) per photon of a laser beam continuously from −mħ to +mħ is presented. The OAM state is addressed by the controlled polarization state using a spiral phase plate, an electro-optic modulator and a modified Mach–Zehnder interferometer, which allows one to adjust the average OAM value by overlapping two beams carrying opposite angular momenta with varying intensity ratio. The maximum achievable modulation frequency is much higher than what spatial light modulators or digital micro-mirror devices can achieve. The demonstration is performed with nanosecond Q-switched pulses in a master oscillator power amplifier with a double-pass configuration that produces a gain of more than 500. Other variants as well as applications of this device are discussed.

Propagation and orbital angular momentum of vortex beams generated from a spiral phase plate-fiber

We report on the generation of vortex beams employing a spiral phase plate (SPP)-fiber, which is fabricated by directly imprinting an SPP on the tip of a single-mode optical fiber. The generated high-order Laguerre-Gaussian (LGp,l) modes with a radial number of p > 0 diverge quickly, thereby leaving the main LG0,−1 mode in the far field. Employing 1D Fourier transform, the average orbital angular momentum is determined to be −0.989ħ per photon, close to the theoretically calculated value of ~ −ħ. Such an SPP-fiber, offering a simple way to produce vortex beams, could be a promising candidate for applications in multi-dimensional optical trapping and material microstructure processing.

Diffraction of relativistic vortex harmonics with fractional average orbital angular momentum

Vortex harmonics with fractional average orbital angular momentum are generated when a relativistic fractional vortex beam is incident on and reflected from an over-dense plane plasma target. A two-step model is presented to explain the far-field patterns of the harmonics. In the first step, a fundamental spot-shaped hole is produced during the hole-boring stage, and harmonics are generated simultaneously. In the second step, different order harmonics are diffracted by the hole and propagate to the far field. This process can be accurately described by the Fraunhofer diffraction theory. This work facilitates a basic recognition of fractional vortex beams.

Generating high-power asymmetrical Laguerre-Gaussian modes and exploring topological charges distribution.

We employ an off-axis pumped Nd:YVO4 laser and control the reflectance of output coupler to directly generate asymmetrical Hermite-Gaussian (HG) modes with various transverse orders. By using an astigmatic mode converter, the generated asymmetrical HG modes are straightforwardly transformed into asymmetrical Laguerre-Gaussian (LG) modes with a crescent-like shape. The average output power of all the crescent-shaped LG modes can exceed 1W at the pump power of 4W. Furthermore, experimental results are theoretically verified by resonant modes derived from the inhomogeneous Helmholtz equation with the localized source distribution. Theoretical resonant modes are also used to explore the dependence of the phase structures of LG modes on the system loss. As the loss increases, it is found that the singularities at the origin will be rearranged and new singularities are formed in the outside region with average orbital angular momentum remaining unchanged.

Conservation of orbital angular momentum for high harmonic generation of fractional vortex beams.

This work demonstrates conservation of average orbital angular momentum for high harmonic generation of fractional vortex beams. High harmonics are generated in reflected light beams in a three-dimensional particle-in-cell simulation. The average orbital angular momentum of the beam is calculated when a relativistic linearly polarized fractional vortex beam impinges on a solid foil. The harmonic generation progress can be well explained by using the vortex oscillating mirror model. Both simulation and theoretical analysis show that the average orbital momentum of the nth harmonic is n times that of the fundamental frequency beam. This provides evidence that the average orbital angular momentum obeys momentum conservation during the harmonic generation of fractional vortex beams.

Orbital angular momentum of channeling radiation from relativistic electrons in thin Si crystal

We propose to use channeling radiation (CR) from relativistic electrons as a source of high energy twisted photons in the MeV range. We calculate numerically the orbital angular momentum (OAM) of radiation produced by electrons with the energies 155÷2500 MeV for the axial and planar channeling in the thin Si crystal. We obtain that the average OAM of CR in this case is approximately 1÷6ħ per photon with the photon energies about 1÷2 MeV.