Fractional Orbital Angular Momentum Research Articles

High-Resolution Recognition of Orbital Angular Momentum Modes in Asymmetric Bessel Beams Assisted by Deep Learning

Abstract Fractional orbital angular momentum (OAM) vortex beams present a promising way to increase the data throughput in optical communication systems. Nevertheless, high-precision recognition of fractional OAM with different propagation distances remains a significant challenge. We develop a convolutional neural network (CNN) method to realize high-resolution recognition of OAM modalities, leveraging asymmetric Bessel beams imbued with fractional OAM. Experimental results prove that our method achieves a recognition accuracy exceeding 94.3% for OAM modes, with an interval of 0.05, and maintains a high recognition accuracy above 92% across varying propagation distances. The findings of our research will be poised to significantly contribute to the deployment of fractional OAM beams within the domain of optical communications.

Spatial shaping of low- and high-order harmonics generated using vortex beams

We demonstrate the generation of the low- and high-order harmonic vortex beams from a single spiral phase plate illuminated by different laser wavelengths. The second harmonic (532 nm) originates from the application of the wavefront-structured 1064 nm femtosecond pulses with fractional orbital angular momentum (OAM) during propagation through a lithium triborate crystal, while the third harmonic (500 nm) originates from the application of the wavefront-structured near-IR (1500 nm) femtosecond pulses with integer OAM during propagation through a 150 μm thick fused silica plate. The topological charges (TCs) of the second and third harmonics are measured and compared. The increase in TC and the peculiarities in OAM variations during modification of the polarisation of the incident radiation are analysed and discussed. The two-colour-pump-driven second-harmonic vortex radiation interacted with an Ar gas jet to generate vortex harmonics up to the 14th order with double-lobe complex spatial profiles in the extreme ultraviolet region.

Broadband Generation of Fractional Perfect Optical Vortices via Plasmonic Metasurface

AbstractA fractional perfect optical vortex (FPOV) represents a class of structured light characterized by phase singularities carrying fractional orbital angular momentum (OAM). It manifests a notched annular intensity distribution, and notably, the size of this distribution remains independent of the topological charge. Conventional methods for generating FPOVs involve a series of cascaded bulk components, leading to optical aberrations due to alignment errors and impeding their integration into highly integrated devices. In this work, an experimental demonstration is presented of the broadband generation of FPOVs in the visible spectrum utilizing a monolithic plasmonic metasurface with phase‐only modulation. The metasurface allows for flexible control of various parameters of the FPOVs, including their topological charge, beam radius, ellipticity factor, orientation, and the number of opening gaps. Furthermore, as a proof‐of‐concept, an FPOV pair is utilized to encode a double‐digit hexadecimal number, showcasing the potential of a metasurface array for optical information encryption. This research establishes a highly integrated platform for FPOV generation, with implications for advancing their applications in optical information security.

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%.

原子介质中分数轨道角动量的传播

原子介质中分数轨道角动量的传播

Ultrafast Time Dynamics of Plasmonic Fractional Orbital Angular Momentum.

The creation and manipulation of optical vortices, both in free space and in two-dimensional systems such as surface plasmon polaritons (SPPs), has attracted widespread attention in nano-optics due to their robust topological structure. Coupled with strong spatial confinement in the case of SPPs, these plasmonic vortices and their underlying orbital angular momentum (OAM) have promise in novel light-matter interactions on the nanoscale with applications ranging from on-chip particle manipulation to tailored control of plasmonic quasiparticles. Until now, predominantly integer OAM values have been investigated. Here, we measure and analyze the time evolution of fractional OAM SPPs using time-resolved two-photon photoemission electron microscopy and near-field optical microscopy. We experimentally show the field's complex rotational dynamics and observe the beating of integer OAM eigenmodes at fractional OAM excitations. With our ability to access the ultrafast time dynamics of the electric field, we can follow the buildup of the plasmonic fractional OAM during the interference of the converging surface plasmons. By adiabatically increasing the phase discontinuity at the excitation boundary, we track the total OAM, leading to plateaus around integer OAM values that arise from the interplay between intrinsic and extrinsic OAM.

Topology of Surface Plasmon Polaritons with Integer and Fractional Orbital Angular Momentum

Topology of Surface Plasmon Polaritons with Integer and Fractional Orbital Angular Momentum

Measurement of the integer and fractional topological charge of optical vortex beams by using crossed blades.

Measurement of the topological charge (TC) of vortex beams, including integer and fractional orbital angular momentum, is of great importance in diverse fields. Here we first investigate the diffraction patterns of a vortex beam from crossed blades with different opening angles and positionings on the beam by a simulation and experiment. Then the positions and opening angles of the crossed blades that are sensitive to the variation of TC are selected and characterized. We show that for a specific position of the crossed blades on the vortex beam, the integer TC can be measured directly by counting the bright spots in the diffraction pattern. Moreover, we show experimentally that for other positions of the crossed blades, by calculating the first-order moment of the intensity of the diffraction pattern, the integer TC between -10 and 10 can be obtained. In addition, this method is used to measure the fractional TC and, as an example, the TC measurement is demonstrated for a range between 1 and 2 with 0.1 steps. The result of the simulation and experiment shows good agreement.

Phase-Dislocation-Mediated High-Dimensional Fractional Acoustic-Vortex Communication.

With unlimited topological modes in mathematics, the fractional orbital angular momentum (FOAM) demonstrates the potential to infinitely increase the channel capacity in acoustic-vortex (AV) communications. However, the accuracy and stability of FOAM recognition are still limited by the nonorthogonality and poor anti-interference of fractional AV beams. The popular machine learning, widely used in optics based on large datasets of images, does not work in acoustics because of the huge engineering of the 2-dimensional point-by-point measurement. Here, we report a strategy of phase-dislocation-mediated high-dimensional fractional AV communication based on pair-FOAM multiplexing, circular sparse sampling, and machine learning. The unique phase dislocation corresponding to the topological charge provides important physical guidance to recognize FOAMs and reduce sampling points from theory to practice. A straightforward convolutional neural network considering turbulence and misalignment is further constructed to achieve the stable and accurate communication without involving experimental data. We experimentally present that the 32-point dual-ring sampling can realize the 10-bit information transmission in a limited topological charge scope from ±0.6 to ±2.4 with the FOAM resolution of 0.2, which greatly reduce the divergence in AV communications. The infinitely expanded channel capacity is further verified by the improved FOAM resolution of 0.025. Compared with other milestone works, our strategy reaches 3-fold OAM utilization, 4-fold information level, and 5-fold OAM resolution. Because of the extra advantages of high dimension, high speed, and low divergence, this technology may shed light on the next-generation AV communication.

Rotating speed estimation of spinning objects based on rotational Doppler effect

Rotational Doppler effect is an important phenomenon when the vortex electromagnetic wave carrying orbital angular momentum is used to detect a rotating target. Compared with the traditional plane wave case, rotational Doppler effect enables the vortex electromagnetic wave to detect the spin motion along the rotation axis of target. However, there are still some blind zones when the integer orbital angular momentum beams are used to detect specific spinning objects. To expand the application scope of detection scheme based on the rotational Doppler effect, according to the time-frequency analysis, in this paper we study the method of estimating the rotation speed of spinning objects under the normal incidence and oblique incidence of fractional orbital angular momentum beams. Firstly, based on the ideal scattering point model, the echo models are derived under the normal incidence and oblique incidence of integer orbital angular momentum beam and fractional orbital angular momentum beam, respectively, as well as theoretical time-frequency curves. Then taking the three-dimensional practical object for example, the echo under the incidence of fractional orbital angular momentum beams and its time-frequency graph are achieved by using the momentum method and short-time Fourier transform. The time-frequency ridge and its fluctuation period are extracted from the time-frequency graph, thereby estimating the spinning speed of target. The results show that the fractional orbital angular momentum beams can be used to estimate the rotation speed of spinning objects effectively, whether it is normal incidence or oblique incidence, thereby solving the problem about the detection blind zone of integer orbital angular momentum beams, and improving the applicability in detecting spin motion.

Optical fiber with fractional orbital angular momentum.

A design method for the creation of photons with fractional orbital angular momentum (FOAM) is reported through the use of a metal-wedge optical fiber. The main focus was on a limiting zero-degree metal wedge, the case of light beams carrying ±ℏ2 OAM per photon. We compared this ideal case with a one-degree metal wedge in hopes of encouraging experimentalists to fabricate this type of waveguide. Various intensity and the Poynting vector plots for different modes and varying wedge angles were obtained and analyzed. We found that the Poynting vectors in the transverse direction for the zero and one degree metal wedges were essentially identical. In addition, as the metal wedge angle was increased, the real propagation constant decreased. Furthermore, the metal wedge enables a new method to obtain a local field enhancement in the center of the core of this waveguide, thus providing a wide range of applications in other fields. Finally, we found discrete complex propagation constants leading to discrete leaky modes with potentially an infinite number of these modes.

A Novel Detection Scheme for the Discrete Body of Revolution With Fractional Orbital Angular Momentum Beams

A novel detection scheme with fractional orbital angular momentum (OAM) beams is proposed in this communication, so as to predict the rotational velocity of the discrete body of revolution (DBoR). At first, the echo model of DBoR is derived under the incidence of integer OAM beams. The theoretical derivation shows that some integer OAM modes may not work for the detection of DBoR due to echo cancellation. Then the echo model with fractional OAM modes is also derived. It shows that the echo frequency spectrum with the fractional OAM always includes effective integer OAM modes. Consequently, a novel detection scheme with fractional OAM for DBoR is proposed. It should be noted that all these theoretical derivations are based on ideal scattering points. Finally, 3-D full-wave simulations of a practical DBoR target are conducted with the method of momentum (MoM) and its fast algorithm. Numerical results demonstrate the effectiveness of the proposed detection scheme. It can be used as an efficient tool to analyze the rotation characteristics for DBoR targets.

Experimental implementation of the fractional-vortex Hilbert hotel

The Hilbert hotel is an old mathematical paradox about sets of infinite numbers. This paradox deals with the accommodation of a new guest in a hotel with an infinite number of occupied rooms. Over the past decade, there have been many attempts to implement these ideas in photonic systems. In addition to the fundamental interest that this paradox has attracted, this research is motivated by the implications that the Hilbert hotel has for quantum communication and sensing. In this work, we experimentally demonstrate the fractional vortex Hilbert's hotel scheme proposed by G. Gbur [Optica 3, 222-225 (2016)]. More specifically, we performed an interference experiment using the fractional orbital angular momentum of light to verify the Hilbert's infinite hotel paradox. In our implementation, the reallocation of a guest in new rooms is mapped to interference fringes that are controlled through the topological charge of an optical beam.

Recognition of high-resolution optical vortex modes with deep residual learning

Optical vortex beams with fractional orbital angular momentum (OAM) can greatly enhance the channel capacity in free-space optical communication. However, high precision measurement of fractional OAM modes is always difficult, especially under the influence of atmospheric turbulence (AT). In this work, we identify the high-resolution OAM modes down to 0.01 using an improved residual neural network (ResNet) architecture based convolutional neural network (CNN). Experimentally, using a single cylindrical lens, the light intensity distribution can be readily converted into a diffraction pattern containing significant features trained into a CNN model. For the fractional OAM modes from 5.0 to 5.9 over a long propagation distance of 1500 m, at 0.1 resolution, our model's predicting accuracy is up to 99.07% under strong AT, ${C}_{\mathrm{n}}^{2}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\phantom{\rule{4pt}{0ex}}{\mathrm{m}}^{\ensuremath{-}2/3}$. At 0.01 resolution, the accuracy is as high as 86.98% under intermediate AT, ${C}_{\mathrm{n}}^{2}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{4pt}{0ex}}{\mathrm{m}}^{\ensuremath{-}2/3}$, and exceeds 73.78% under strong AT, ${C}_{\mathrm{n}}^{2}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\phantom{\rule{4pt}{0ex}}{\mathrm{m}}^{\ensuremath{-}2/3}$. So, these results may have great implications in free-space optical communication.

Direct experimental evidence for free-space fractional optical vortex transmutation

The emergence of vortex transmutation has opened new ways for vorticity modulation of optical vortices. Although several approaches have been proposed to realize vortex transmutation, fractional optical vortex (FOV) transmutation remains elusive owing to a lack of effective generation and detection methods. Here we report quantitative experimental evidence for a free-space FOV transmutation rule. The key idea is to combine the advantages of a single optical element, termed as fractional spiral polygonal lenses (FSPLs), with a deep learning approach. The desired wavefront is simultaneously generated and manipulated at the focal plane of the FSPL, and the fractional output vorticity is measured by analyzing a single far-field diffraction pattern. Especially, a deep learning scheme using a Bayesian optimization method is developed for output vorticity prediction with a data recovery rate up to 98.2%. The average error of recognized fractional orbital angular momentum modes is as small as 0.02. We clearly observe the intriguing phenomenon that the central vorticity of FOV is changed following a modulo-n transmutation rule in free space. Our results have important implications for fundamental understanding of FOV systems in free space, and offer a technological foundation for potential applications such as quantum information processing and particle manipulation and transportation.

Recognition of fractional orbital angular momentum modes under scattering with transmission matrix

Vortex beams carrying fractional orbital angular momentum (FOAM) mode show great potential in optical encryption, anisotropic edge enhancement, optical communication, etc. However, the small mode interval of FOAM makes it sensitive to transmission scattering, which distorts the helical phase-front and leads to substantial mode crosstalk. Herein we propose a transmission matrix method to recognize FOAM modes under scattering. By constructing the linear relationship between the input and scattering field, a transmission matrix retrieval algorithm was used to recover the helical phase-front of the vortex beam from its intensity distribution, and FOAM mode was recognized via the phase period. We showed that FOAM modes under scattering are successfully recognized with an accuracy of >99.8%. As a proof-of-concept, a 100 × 100 pixel image was transmitted and recovered in a high scattering. Our results indicate that the transmission matrix method presents a new approach to recognize FOAM modes under scattering, which may benefit various FOAM applications.

Precise measurement of trapping and manipulation properties of focused fractional vortex beams.

Fractional vortex beams (FVBs) were believed to be hard to rotate microparticles at a half-integer topological charge due to the unique radial opening (low-intensity gap) in their intensity ring. However, recent research discovered more symmetric intensity structures with less intensity inhomogeneity of practical FVBs at the focal plane. Here, we experimentally demonstrated the manipulation of trapped microparticles and precisely measured their rotation periods at the focal plane of practical FVBs by using a high-speed camera. We verified that the measured orbital angular momentum (OAM) derived from the collective microparticle rotation is roughly proportional to the fractional OAM of practical FVBs. Furthermore, we also experimentally obtained the trapped microparticles' power spectra under the illumination of FVBs, from which we achieved the average trap stiffness to evaluate the two-dimensional trapping strength of the practical focused FVB intensity ring. Our results provide a new insight and an efficient tool on finely trapping and rotating microparticles and bio-cells by using fractional vortex beams.

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.

Superposition of two fractional optical vortices and the orbital angular momentum measurement by a deep-learning method.

We propose a single diffractive optical element called the composite fractional spiral zone plates to generate superimposed fractional optical vortices. Such an element is composed of two fractional spiral zone plates (FSZPs) through logical AND operation, and the produced beam carries superimposed fractional orbital angular momentum (OAM) states. By controlling the topological charge of the superimposed FSZPs, denoted by l1 and l2, one can flexibly obtain the desired superimposed fractional OAM modes of the generated beam. Especially, a deep-learning model with a densely connected convolutional neural network architecture is utilized to accurately predict the superimposed fractional OAM states of SFOVs. The average recovery rate of the superimposed fractional OAM states based on the training model is over 99%, and the average error is as small as 0.02. This work may pave the way for wide-ranging applications such as smart OAM communication, particle transmission, and even quantum entanglement.

Adaptive demodulation by deep-learning-based identification of fractional orbital angular momentum modes with structural distortion due to atmospheric turbulence

Since the great success of optical communications utilizing orbital angular momentum (OAM), increasing the number of addressable spatial modes in the given physical resources has always been an important yet challenging problem. The recent improvement in measurement resolution through deep-learning techniques has demonstrated the possibility of high-capacity free-space optical communications based on fractional OAM modes. However, due to a tiny gap between adjacent modes, such systems are highly susceptible to external perturbations such as atmospheric turbulence (AT). Here, we propose an AT adaptive neural network (ATANN) and study high-resolution recognition of fractional OAM modes in the presence of turbulence. We perform simulations of fractional OAM beams propagating through a 1-km optical turbulence channel and analyze the effects of turbulence strength, OAM mode interval, and signal noise on the recognition performance of the ATANN. The recognition of multiplexed fractional modes is also investigated to demonstrate the feasibility of high-dimensional data transmission in the proposed deep-learning-based system. Our results show that the proposed model can predict transmitted modes with high accuracy and high resolution despite the collapse of structured fields due to AT and provide stable performance over a wide SNR range.