Number Of Orbital Angular Momentum Modes Research Articles

Fundamental probing limit on the high-order orbital angular momentum of light.

The orbital angular momentum (OAM) of light, possessing an infinite-dimensional degree of freedom, holds significant potential to enhance the capacity of optical communication and information processing in both classical and quantum regimes. Despite various methods developed to accurately measure OAM modes, the probing limit of the highest-order OAM remains an open question. Here, we report an accurate recognition of superhigh-order OAM using a convolutional neural network approach with an improved ResNeXt architecture, based on conjugated interference patterns. A type of hybrid beam carrying double OAM modes is utilized to provide more controllable degrees of freedom for greater recognition of the OAM modes. Our contribution advances the OAM recognition limit from manual counting to machine learning. Results demonstrate that, within our optical system, the maximum recognizable OAM modes exceed l = ±690 with an accuracy surpassing 99.93%, the highest achieved by spatial light modulator to date. Enlarging the active area of the CCD sensor extends the number of recognizable OAM modes to 1300, constrained only by the CCD resolution limit. Additionally, we explore the identification of fractional high-order OAM modes with a resolution of 0.1 from l = ±600.0 to l = ±600.9, achieving a high accuracy of 97.86%.

Redefining uniform circular array’s limit by using square patch elements for higher order orbital angular momentum mode generation

This article proposes a technique to design the Uniform Circular Array (UCA) antenna for the generation of higher order of orbital angular momentum (OAM) modes using lesser number of antenna elements. Earlier, the highest possible OAM mode number (lmax) generated using conventional N-element UCA is limited by number of antenna elements N ≥ 2|lmax|. In the proposed design, a square patch element is placed between two antenna elements of conventional 4-element UCA to generate higher order OAM modes (0, ±1, ±2, and ±3 OAM modes) with lesser number of antenna elements. The proposed UCA is compact in size and requires less complex power dividing phase networks in comparison to conventional 8-element UCA to generate similar lmax. The proposed UCA with square patch is designed at 5.2 GHz and lmax of a N-element UCA with square patch is now limited by number of antenna elements as N ≥ |lmax|. The simulated and measured phase patterns for various OAM modes are in good agreement and supported by mathematical analysis. A comparison of the new structure with the conventional Uniform Circular Arrays available in the literature is also tabulated.

Analysis of Scattering characteristics of PEMC sphere by vortex Bessel beams

Generalized Lorenz-Mie theory (GLMT) is well known to analyze the scattering characteristics of spherical surfaces and metamaterials such as perfect electromagnetic conductor (PEMC) sphere. Also, metamaterials are explored very well when illuminated by electromagnetic waves/beams and their characteristics depend upon propagation and scattering response. So, in this manuscript, vortex Bessel beam (VBB) interaction from PEMC sphere has been investigated. The VBB interaction with material particles is of quite interesting due to association of orbital angular momentum (OAM) with them. By employing the Integral localized approximation (ILA) method, the beam‐shape coefficients (BSCs) regarding VBB are obtained. Computations for the scattering efficiency QSca and extinction efficiency QExt for PEMC sphere by considering the co‐polarized and cross‐polarized scattering components are presented and analyzed. Moreover, the influences of OAM mode number, electromagnetic admittance parameter, and diffraction angle are discussed. Numerical results have applications regarding transfer of OAM of VBB to PEMC sphere and associated applications in light manipulation and scattering, optical tweezers, metamaterial fields, and remote sensing.

Design of a multi-core photonic crystal fiber supporting 518 OAM modes

A multi-ring core photonic crystal fiber (PCF) with seven high-index ring regions is designed for the transmission of multiple orbital angular momentum (OAM) modes. The new structure which has an optimized air hole arrangement shows improved transmission quantity and number of OAM modes. Numerical analysis reveals that the PCF can transmit 518 OAM modes in the range of 1.4–1.75 µm stably while avoiding cross talk from the adjacent ring core resulting in a low cross talk of merely −208.5dB, confinement loss less than 10−9dB/m, as well as mode quality greater than 0.925. The results disclose a new method to increase the communication capacity and suggest that the PCF has great application potential.

Scattering of Laguerre–Gaussian Beam by a Topological Insulator Cylinder Coated with Metamaterials

A theoretical investigation is presented to study the orbital angular momentum (OAM) beam scattering from a topological insulator (TI) cylinder coated with metamaterials. To calculate the electromagnetic (EM) response of the scattered field, the field equations are modified using Laguerre–Gaussian (LG) potential and plane wave scattering. The response of the metamaterial coated geometry has been reported for Double positive (DPS), Double negative (DNG), Epsilon negative (ENG), and Mu negative (MNG) coating layers, respectively. The normalized bistatic echo widths for the TI cylinder also change by changing the topological charge ( $$l$$ ), the radius of the metamaterial coated layer $$(b)$$ , source frequency $$(f)$$ , and beam waist radius $$({w}_{0})$$ . Our result for $${LG}_{00}$$ beam exactly tones with plane wave scattering as a reference. Numerical results in the form of bistatic echo widths have been calculated. Besides, the prementioned parameters, the influence of OAM mode index on the bistatic echo width is also analyzed. It can be seen that OAM mode number plays major role in controlling the scattering amplitude and intensity.

Orbital Angular Momentum Radio-Wave-Based 2-D Target Angle Estimation With Mutual Coupling

Vortex electromagnetic waves are conveniently produced by a uniform circular array (UCA). The mutual coupling matrix (MCM) of UCAs presents rotational symmetry, which can be employed to cut down the parameters in the circuit model. The impedance matrix also does not rely on a specific port. This work uses rotational symmetry to expand the MCM into the orbital angular momentum (OAM) mode domain. The OAM-domain phase sequence is derived by the discrete Fourier transform (DFT) of the first row of the MCM. The connection between the number of OAM modes and the excitation of elements is described. Furthermore, an improved propagator method (PM) for OAM-based decoupled 2-D angle estimation is proposed. This method employs the original steering vector of OAM waves to process the receiving signal, which avoids errors caused by the Bessel function approximation. The estimation error is also reduced by redefining the propagator matrix. In terms of computational complexity, the proposed method avoids spectral search-and-element level eigenvalue decomposition (EVD). The results demonstrate that the coupling is compensated effectively by the OAM-mode domain MCM. The error of the proposed method is less than 1° under the condition of SNR = 20 dB and 1000 snapshots. The computational complexity is reduced by 1–2 orders of magnitude compared to the origin PM. The method is also suitable for 1-D estimation scenarios.

Terahertz fiber with multi-concentric ring cores for OAM modes propagation

A novel fiber incorporating central hollow, porous isolated layers, and concentric ring cores is proposed for the simultaneous propagation of multi-terahertz (THz) orbital angular momentum (OAM) modes with low-level inter-core and inter-mode crosstalk. The designed fiber can efficiently support 132 OAM modes in 0.6 ∼ 1.5 THz, 178 OAM modes in 0.7 ∼ 1.5 THz, etc, the high-order radial modes are suppressed within the whole frequency range meanwhile, and the number of OAM modes can be further boosted by further increasing the number of ring cores. In addition, the fiber has low confinement loss, flat dispersion, and high purity over a wide operating range. Hence it can be applied in mode-division multiplexing (MDM) based on OAM combined with core-division multiplexing (CDM) in THz range, and is also compatible with wavelength-division multiplexing (WDM) and multi-level modulation formats. The realized fiber is expected to dramatically extend the transmission capacity and spectral efficiency.

VO<sub>2 </sub>based terahertz anisotropic coding metasurface

Terahertz (THz) wave has the advantages of high resolution, large information capacity, easy beam focusing, etc, and can be used in the fields of communication, radar, detection and others. Firstly, as a two-dimensional artificial electromagnetic metamaterial, the coding metasurface is proposed in the microwave band. It uses the digital coding of the electromagnetic wave phase to adjust electromagnetic waves. Subsequently, as an important way to regulate THz, the metasurface extends to terahertz frequency band and becomes a research hotspot. In this paper, we design a coding metasurface based on vanadium dioxide (VO<sub>2</sub>) with anisotropic characteristics. It is composed of three layers, with a metal cross structure embedded in VO<sub>2</sub> at the top, polyimide in the middle, and pure metal at the bottom. The design of the cross shaped structure makes the coding metasurface unit anisotropic, which can provide complete and independent control of the orthogonally linearly polarized incident waves. The pure metal structure at the bottom can provide higher reflection amplitude for the incident wave. And VO<sub>2</sub> is introduced into the coding metasurface. As a phase change material, VO<sub>2</sub> can switch its properties between the insulating state and the metallic state, which further increases the flexibility of coding metasurface to regulate THz wave. Eight different coding metasurface units are designed in this work. They can be arranged according to a reasonable coding sequence to form a coding metasurface, which consisits of 20×20 metasurface units with an overall size of 2.4 mm × 2.4 mm. Its coding sequence will be changed with the phase of VO<sub>2</sub>, thus forming a corresponding 1 bit or 2 bit coding metasurface, and the generated beam form changes accordingly. The finite-difference time domain method is used for modeling and implementing simulation, and the results are as follows. The 1-THz orthogonal linearly polarized wave is vertically incident on the coding metasurface. When VO<sub>2</sub> is in the insulating state, the designed metasurface can be regarded as an anisotropic 2 bit coding metasurface to generate dual-polarization orbital angular momentum (OAM) vortex beams. The <i>x</i>-polarized vortex wave has an OAM mode number of 2, and the <i>y</i>-polarized vortex wave possesses an OAM mode number of 1. When VO<sub>2</sub> is in the metallic state, the designed metasurface can be regarded as an anisotropic 1 bit coding metasurface to generate dual-polarization symmetrical beams. Four reflected waves are generated by incident <i>x</i>-polarized waves, and two reflected waves are created by incident <i>y</i>-polarized waves. The proposed method of combining anisotropy material and phase change material realizes the function of generating multiple THz beams in different forms on the same metasurface. The present results provide a reference for the implementation of multi-functional coding metasurface that can be flexibly applied to multiple scenes.

On-chip ultracompact multimode vortex beam emitter based on vertical modes.

Free-space orbital angular momentum (OAM) communication is considered as one of the potential alternative on-chip optical interconnect solutions. The number of OAM modes determines the capacity of high-speed communication. However, existing integrated vortex beam emitters have a constraint relationship between the number of OAM modes and the emitter size, rendering it difficult to emit more OAM modes with a small-sized emitter. In view of the above, this study proposes an on-chip ultracompact multimode vortex beam emitter based on vertical modes, which permits more OAM modes without requiring an increase in the size of the emitter. Vertical modes in large-aspect-ratio waveguides are pointed out to enable multimode microrings with small radii because high-order vertical modes can maintain almost the same horizontal wave vector as that of the fundamental mode. Four-mode and five-mode vortex beam emitters with the same radius of 1.5 µm are designed and the effectiveness of these emitters is verified through simulation. Furthermore, a high-efficiency and low-crosstalk approach for high-order vertical mode coupling by varying the waveguide height is presented. This research not only promotes further integration of on-chip optical interconnection, but also provides a new strategy for optical waveguide mode selection in photonic integrated circuits design.

Simple ring-structured photonic crystal fiber with low nonlinear coefficients and flat dispersion supporting 166 OAM modes

A simple ring-structured photonic crystal fiber (PCF) is designed to support the stable propagation of multiple orbital angular momentum (OAM) modes. The PCF is numerically analyzed and optimized by the finite element method. The results show that the number of OAM modes supported by the PCF reaches 166 in the wavelength range of 1.4 to 1.7 μm. Meanwhile, the confinement loss of the OAM modes is lower than 10 − 8 dB / m, and the smallest dispersion variation is 12.7 ps / ( km · nm ) . Moreover, the mode quality of all of the eigenmodes is higher than 94.1%, and the nonlinear coefficient is lower than 0.7 w − 1 / km. The simple PCF structure with excellent properties has immense application prospects in high-capacity OAM communication.

Direct Light Orbital Angular Momentum Detection in Mid‐Infrared Based on the Type‐II Weyl Semimetal TaIrTe4 (Adv. Mater. 29/2022)

Photodetectors A photodetector based on the type-II Weyl semimetal TaIrTe4 is designed by Dong Sun and co-workers in article number 2201229 to directly detect the orbital angular momentum (OAM) order of the vertex beam in the mid-infrared wavelength. The helical phase gradient of light can be distinguished by a current whose magnitude is proportional to the OAM mode number. This detector can be integrated into a focal plane array that can resolve multiple optical parameters of a target.

Direct Light Orbital Angular Momentum Detection in Mid-Infrared Based on the Type-II Weyl Semimetal TaIrTe4.

The direct photocurrent detection capability of light orbital angular momentum (OAM) has recently been realized with topological Weyl semimetals, but it is limited to the near-infrared wavelength range. The extension of the direct OAM detection capability to the mid-infrared band, which is a wave band that plays an important role in a vast range of applications, has not yet been realized. This is because the photocurrent responses of most photodetectors are neither sensitive to the phase information nor efficient in the mid-infrared region. In this study, a photodetector based on the type-II Weyl semimetal tantalum iridium telluride (TaIrTe4 ) is designed with peculiar electrode geometries to directly detect the topological charge of the OAM using the orbital photogalvanic effect (OPGE). The results indicate that the helical phase gradient of light can be distinguished by a current winding around the optical beam axis, with a magnitude proportional to its quantized OAM mode number. The topologically enhanced responses in the mid-infrared region of TaIrTe4 further help overcome the low responsivity issues and finally render direct OAM detection capability. This study enables on-chip-integrated OAM detection, and thus OAM-sensitive focal plane arrays in the mid-infrared region.

Divergence-degenerate spatial multiplexing towards future ultrahigh capacity, low error-rate optical communications

Spatial mode (de)multiplexing of orbital angular momentum (OAM) beams is a promising solution to address future bandwidth issues, but the rapidly increasing divergence with the mode order severely limits the practically addressable number of OAM modes. Here we present a set of multi-vortex geometric beams (MVGBs) as high-dimensional information carriers for free-space optical communication, by virtue of three independent degrees of freedom (DoFs) including central OAM, sub-beam OAM, and coherent-state phase. The novel modal basis set has high divergence degeneracy, and highly consistent propagation behaviors among all spatial modes, capable of increasing the addressable spatial channels by two orders of magnitude than OAM basis as predicted. We experimentally realize the tri-DoF MVGB mode (de)multiplexing and data transmission by the conjugated modulation method, demonstrating lower error rates caused by center offset and coherent background noise, compared with OAM basis. Our work provides a potentially useful basis for the next generation of large-scale dense data communication.

Low Sidelobe Orbital Angular Momentum Vortex Beams Based on Modified Bayliss Synthesis Method for Circular Array

Electromagnetic orbital angular momentum (OAM) vortex beam patterns generated by conventional methods are always of high sidelobe level, which severely limits its application. Considering the sidelobe suppression abilities of Bayliss synthesis method for difference beams, we present a modified Bayliss synthesis procedure to obtain low sidelobe OAM vortex beams. The Bayliss synthesis method cannot suppress the sidelobe level of difference pattern to the desired value when the element number of linear array is relatively small. By modifying the original zero locations that need to be removed in Bayliss pattern, we can further suppress the sidelobe level of difference pattern. This can be called the modified Bayliss pattern. Finally, by expanding the proposed synthesis method from linear source to circular array, theoretical results show that sidelobe levels of OAM beams can be suppressed to less than −30 dB when OAM mode number varies from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> = 1 to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> = 10. The proposed low sidelobe OAM vortex beam can be applied in antijamming communications of near-field in the future.

Six‐Mode Orbital Angular Momentum Generator Enabled by Helicity‐Assisted Full‐Space Metasurface with Flexible Manipulation of Phase, Polarization, and Spatial Information

AbstractVortex beam carrying orbital angular momentum (OAM) has been experiencing a research upsurge attributed to its excellent communication capability, which also boosts the development of the OAM technology and promotes the application of the OAM generator. However, most of the existing designs of the OAM generators can only produce a small number of diverse OAM modes, and restrict the channel capacity of single OAM generator. Herein, an appealing strategy of six‐mode OAM generator based on helicity‐assisted full‐space metasurface is proposed to generate up to six diverse OAM modes by altering the polarization state, illumination region, and incidence direction of incident waves. Significantly, the designed OAM generator has high communication security because of its great information entropy, and the generated OAM modes possess the characteristics of high purity and low crosstalk which result from the orthogonal polarization states and unequal deflection angles of produced vortex beams. A proof‐of‐concept prototype is constructed to corroborate the validity of our methodology, and the results of simulations and experiments are in excellent agreement with theoretical predictions. This fire‐new OAM generator will possess a promising application prospect in communication systems, and may also provide an efficacious method to design multifunctional devices.

Reconstruction of three-dimensional objects in layered composite structures from multimode orbital angular momentum.

Because of helical phase wavefront distribution, vortex electromagnetic waves are considered to carry more information and additional degrees of freedom than traditional spherical waves. Therefore, a vortex wave carrying orbital angular momentum (OAM) can improve inversion and imaging accuracy. In this work, we revisit the reconstruction of three-dimensional objects in layered composite structures extended with OAM. In forward modeling, the concentric uniform circle array is used to generate electromagnetic vortex beams. To analyze the difference of vortex beams, the electric field radiation pattern and phase pattern distribution of OAM waves with different modes are calculated. Then, the scattered field of layered media illuminated by different OAM beams is determined by the dyadic Green's function and the stabilized biconjugate gradient technique with a fast Fourier transform algorithm. In the inversion, the variational Born iterative method is used to reconstruct targets in layered composite structures, and multiple OAM modes are used to improve the reconstruction results. The numerical results prove that the permittivity of the target can be better reconstructed by using the multiple OAM modes rather than the traditional spherical wave. With the increase of OAM mode number, the reconstructed target parameters are closer to the true value. We expect that our results will provide a better understanding of the OAM and pave the way for the improvement of inversion and optical imaging technology using vortex waves.

UCA-Based OAM Non-Orthogonal Multi-Mode Multiplexing

Electromagnetic waves carrying orbital angular momentum (OAM) can improve the spectral efficiency of communication systems by multiplexing a number of OAM modes. However, since being not able to perform water-filling power allocation and adaptive modulation for each sub-channel like closed-loop multiple-input multiple-output (MIMO) systems, the traditional orthogonal multi-mode OAM multiplexing system usually has poor bit error rate (BER) performance due to the inherent large divergence angle of high-order orthogonal OAM beams. Therefore, in this article we propose a non-orthogonal OAM (NO-OAM) multi-mode multiplexing scheme based on uniform circular array (UCA), which regulates the divergence angles of all non-orthogonal OAM beams to be the same, circumventing the problem that large beam divergence of high-order orthogonal OAM modes results in low received signal-to-noise ratio (SNR) at the receive UCA with a fixed aperture. Mathematical analysis and numerical simulations show that in contrast to the existing uniform concentric circular array (UCCA) beam adjustment scheme, the proposed NO-OAM scheme has slightly better beam adjustment effect but with only one UCA. Moreover, in contrast to the traditional orthogonal OAM multi-mode transmission, the proposed NO-OAM multi-mode multiplexing scheme has asymptotically equivalent channel capacity and much lower BER.

Beam steering of orbital angular momentum vortex wave based on planar phased array

Orbital angular momentum (OAM) vortex electromagnetic waves can provide a new degree of freedom for information modulation at a physical level, which has great prospects of applications in the fields of wireless communication and radar imaging. The application of beam scanning techniques of phased array to OAM vortex electromagnetic wave can increase its communication coverage and expand the detection coverage of vortex radars. Firstly, in this paper, the principle of generating the beam steering vortex electromagnetic beam is discussed and the compensated phase formula for generating beam steering OAM beams is given by planar phased array. Secondly, considering the advantages of phased array antennas in beam scanning and OAM reconfigurability, a planar phased array with 8 × 8 antenna elements at 10 GHz is designed and fabricated. The performances of OAM beam steering and mode reconfigurability are verified. Finally, the performance changes of the deflecting OAM vortex beam at different scanning angles are discussed and analyzed. Simulations and measurements both show that there exist pattern distortion problems when steering angle of OAM beam becomes large. In this paper, the variation of the OAM mode purity is also studied when the scanning angle and the OAM mode number change. The results show that the planar phased array antennas can effectively generate the beam steering OAM vortex beams in a certain angle range. Hence, this paper can provide a reference for the OAM vortex electromagnetic wave communication and the vortex radar in the future.

Extended aperture sample reception method for high-order orbital angular momentum vortex beam mode number measurement.

The traditional phase gradient method can effectively measure the orbital angular momentum (OAM) number of the vortex beam. However, its spatial sampling phase aperture span is strictly restricted within only π radian. In this paper, we presented a more flexible extended aperture sampling reception (EASR) method for the radio frequency (RF) applications, which can break through this restriction condition. It could make the reception and measurement methods about the OAM mode number become more complete and versatile. By converting the higher-order OAM mode to a lower-order OAM mode, the spatial phase aperture span between the adjacent receiving sampling points can realize extensions. We have conducted a comprehensive theoretical analysis and summarized the general guidelines of this EASR method in the main body of the paper. Subsequently, we perform the related numerical simulation calculations to receive and measure the OAM mode number of a high-order mode vortex beam using the EASR method. Simulation results and theoretical analysis are in good agreement.

Probability of orbital angular momentum modes carried by a finite energy frozen wave in turbulent seawater

By developing the spatial coherence radius of a collimated Gaussian beam, we derive the normalized received probability of orbital angular momentum (OAM) modes of the random finite energy frozen wave (FW) in anisotropic weak seawater turbulence based on Rytov theory. We investigate the influences of seawater turbulence and beam parameters on the normalized received probability of OAM modes. This study concludes that the normalized received probability of signal OAM modes increases as the anisotropic factor of the seawater turbulence increases. The rate of dissipation of kinetic energy per unit mass of fluid and the inner scale of turbulence but the normalized received probability of signal OAM modes decreases as the increase of temperature-salinity contribution ratio and the dissipation rate of the mean-squared temperature. For the smaller received diameter of the receiver, larger transverse size and longer signal wavelength, the signal OAM modes achieve the higher normalized received probability. The normalized received probability of signal OAM modes is independent of the quantum number of OAM modes in weak seawater turbulence. The security of signal transmission can be enhanced by designing the position and interval of signals that can be detected along the optical path.