Fractional Orbital Angular Momentum Research Articles

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.

Machine learning based accurate recognition of fractional optical vortex modes in atmospheric environment

Optical vortex beam with fractional orbital angular momentum (OAM) has great potential to increase the capacity of optical communication and information processing in classical and quantum regimes. However, atmospheric turbulence (AT) in free space distorts the helical phase-front of vortex beams and causes the mode diffusion, seriously hindering the practical application. Herein, using a convolutional neural network approach with an improved residual neural network architecture, we overcome the hurdle to give the accurate recognition of the fractional OAM in the AT. As demonstrated on the petal interference patterns, a type of hybrid beams carrying double OAM modes is utilized to provide two controllable degrees of freedom for greater recognition of more subtle OAM modes, e.g., the fractional topological charge number l and the angular ratio n. Our studies show that with various l and n, the recognition accuracy of OAM over 20 000 images is as high as 85.30% even under the strong AT parameter (Cn2 = 5 × 10−14 m−2/3) and the long propagation distance (z = 1500 m). Our findings represent a remarkable achievement toward highly accurate recognition of fractional OAM with broad bandwidth in the atmospheric environment, expanding the applications for the general interest of machine learning based OAM optical communication.

Generation of perfect helical Mathieu vortex beams.

We introduced a kind of novel perfect optical vortex beam, which we termed herein as perfect helical Mathieu vortex (PHMV) beams. The theoretical mechanism regarding the construction of PHMV beams was divided into two parts: generation of helical Mathieu (HM) beams using the stationary phase method and then Fourier transform of HM beams into the PHMV beams. Accordingly, the experimental system for generating PHMV beams was built as follows. Based on the complex amplitude modulation method, HM beams of different orders and ellipticity were generated using an amplitude-type spatial light modulator (SLM) and a radial-helical phase mask. Subsequently, an achromatic Fourier transform lens was illuminated using the HM beams, and the PHMV beams were presented on the focal plane after the Fourier transform lens. The experimental results were consistent with theoretical predictions. Compared with the classical perfect optical vortex (POV) beams, the PHMV beams still retained the property of ring radius independent of topological charge values. The distribution pattern of the PHMV beams can be controlled by the topological charges and elliptical parameters. Furthermore, two important optical properties of the PHMV beams were theoretically elucidated. First, we proved that the PHMV beams carry a fractional order orbital angular momentum (OAM). Second, we found that the complex amplitudes of any two PHMV beams with the same elliptical parameter but different order numbers are orthogonal to each other.

Recognizing fractional orbital angular momentum using feed forward neural network

Fractional vortex beam (FVB) possessing helical phase can be applied in the shift-keying communication due to its fractional orbital angular momentum (FOAM) mode, which theoretically allows an infinite increase of the transmitted capacity. However, the discontinuity of spiral phase makes FVB more likely to be disturbed in turbulence environment, and the precise measurement of distorted FOAM modes is crucial for practical FOAM-based communication application. Here, we proposed a FOAM mode recognition method with feedforward neural network (FNN). Employing the diffraction preprocessing of a two-dimensional fork grating, the original optical features of FVBs can be extended along the far-field diffraction order, endowing FNN more feature information and saving calculation time, and enlarging the detection range to conjugate FOAM modes. The simulation results show that the 9-layer FNN can identify FOAM mode with interval of 0.1 with an accuracy of 99.1% under the turbulences of Cn2=1×10-14m-2/3 and Δz=10m. Furthermore, we experimentally constructed a 102-ary FOAM shift-keying communication link to transmit gray image, and the signals are successfully demodulated by the FNN model with the pixel-error-rate of 0.07160. It is anticipated that the proposed FNN-based FOAM recognition method will break the limitation of precision measurement under turbulence environment in practical FOAM applications.

Fractional orbital angular momentum conversion in second-harmonic generation with an asymmetric perfect vortex beam.

This Letter demonstrates the nonlinear conversion of asymmetric perfect vortex (APV) beams with fractional orbital angular momentum (OAM). By controlling the amplitude and phase of the fundamental light field, we create APVs whose global OAM demonstrates a one-to-one correspondence of the charge numbers for fractional OAM values. The results show that the OAM of the second-harmonic generation fields follow the OAM conservation law. The nonlinear interactions of multiple OAM beams with the APVs are also investigated as they relate to the nonlinear frequency conversion and are shown to exhibit unique frequencies as a result of the Doppler frequency tagged OAM values.

A Novel Demultiplexing Scheme for Vortex Beams in Radio Communication Systems

The orbital angular momentum (OAM) based communication is a promising technology in the wireless communication system for its improving spectrum efficiency. However, for the OAM demultiplexing, it requires a very large aperture size in the receiving end due to the OAM beam divergence and the amplitude null in the beam center, which restricts the full development of OAM based communication. In this paper, we propose a novel partial arc sampling receiving (PASR) scheme based on the augmented dynamic mode decomposition (ADMD) to solve this issue. We explore the use of the phase delay coordinates in the conventional DMD to sort the arbitrary OAM modes with arc sampling receiving. Simulation results demonstrate the accuracy and robustness of the proposed approach in sorting both integral and fractional OAM modes with the PASR scheme. Our work offers a practical approach for demultiplexing OAM beams in radio communication systems with fewer receiving devices, especially for the long-distance transmission case.

Electromagnetic Vortex Enhanced Imaging Using Fractional OAM Beams

Electromagnetic (EM) vortex can realize high resolution imaging in forward-looking observation geometry without relative motion between the radar system and targets. However, the current research about EM vortex imaging only exploits integral orbital angular momentum (OAM) beams, which limit the application in the real scene with the existence of noise. An EM vortex enhanced imaging method based on fractional OAM beams is proposed against noise effect in this letter. Firstl the generation method of fractional OAM beams with phase distribution of nonintegral OAM mode is proposed using uniform circular array, and the corresponding features are analyzed. Subsequently, the imaging model and scheme with fractional OAM beams are provided and the principle for enhancing imaging performance is derived. Finally, results by Monte Carlo simulations demonstrate that the proposed vortex imaging method based on fractional OAM beams is robust against noise effect and can achieve better imaging performance in low signal-to-noise ratio (SNR) environment, which is of prospect for overcoming the shortage of poor imaging performance in low OAM order and complex noise scenario. This letter benefits the development of EM vortex imaging.

High-Precise Fractional Orbital Angular Momentum Probing With a Fiber Grating Tip

Optical orbital angular momentum (OAM), carried by optical vortices, is a fundamental property of light that grabs broad interests. The detection of OAM modes, including fractional OAM is of great importance in diverse fields. Here, we firstly propose and develop the limited integer-component measurement method to determine the fractional topological charge (TC) of OAM states. This method indicates that a 2-integer-mode responsive device could be applied for the detection of fractional TC. An orthogonal long-period fiber grating (OLPFG) element is used as a fractional OAM TC probe to verify the Applicability. We experimentally demonstrate the fractional TC detection, ranging from −1 to 0, and recognize different fractional OAM modes with the minimum TC interval of 0.01. This scheme provides a concise, precise, continuous, and fiber-compatible fractional TC detection method that might have great potential in micro-detection, optical communication, quantum information, and chiral sensing applications.

Polarization‐Engineered Noninterleaved Metasurface for Integer and Fractional Orbital Angular Momentum Multiplexing

AbstractVortex beam carrying orbital angular momentum (OAM) has been widely explored in optical and microwave regions attributed to its potential characteristics in communication systems. For circular polarization incidence, Pancharatnam–Berry (PB) phase is a direct resource to generate phase gradient along the azimuthal direction required by specific OAM mode. The main drawback of PB phase is that it only affects cross‐polarized fields and keeps the copolarized part unmodulated. Here, a paradigm‐shift perspective of noninterleaved metasurfaces is proposed, which can simultaneously generate separate multiple integer and fractional OAM modes occupying both copolarized and cross‐polarized output channels. The scheme is validated by a series of experimental demonstrations in the microwave regime. By adjusting the polarization states of both input and receiving ends, different integer and fractional OAM modes are demonstrated in the full transmission channels. The results offer a unique recipe to enhance information capacity of metasurfaces and trigger versatile electromagnetic (EM) wave function integrations for advanced compact systems. A variety of applications can be readily expected in spin‐selective optics, spin‐Hall metadevices, and multitask metasurfaces operating in both reflection and transmission modes.

Ultrafast control of fractional orbital angular momentum of microlaser emissions

On-chip integrated laser sources of structured light carrying fractional orbital angular momentum (FOAM) are highly desirable for the forefront development of optical communication and quantum information–processing technologies. While integrated vortex beam generators have been previously demonstrated in different optical settings, ultrafast control and sweep of FOAM light with low-power control, suitable for high-speed optical communication and computing, remains challenging. Here we demonstrate fast control of the FOAM from a vortex semiconductor microlaser based on fast transient mixing of integer laser vorticities induced by a control pulse. A continuous FOAM sweep between charge 0 and charge +2 is demonstrated in a 100 ps time window, with the ultimate speed limit being established by the carrier recombination time in the gain medium. Our results provide a new route to generating vortex microlasers carrying FOAM that are switchable at GHz frequencies by an ultrafast control pulse.

Evolution of vortices created by conical diffraction in biaxial crystals versus orbital angular momentum

Light states evolution versus their fractional orbital angular momentum (OAM) has been analyzed in the conical diffraction process occurring through biaxial crystals. Experimental results are provided by a non-degenerate cascade of KGd(WO$_2$)$_4$ and Bi$_2$ZnOB$_2$O$_6$ biaxial crystals. The continuous $0\to 1\to 2$ $\hbar$/photon increasing of the fractional OAM in passing through integer values was operated with the help of the spin-orbit coupling in the Bi$_2$ZnOB$_2$O$_6$ crystal. The phase of the state light and its vortices were visualized by interference patterns with a reference beam. The evolution of the fractional OAM value is accompanied by a continuous evolution of pairs of vortices with opposite signs and linked by a $-\pi/+\pi$ discontinuous phase line. The phase pattern evolution around half-integer OAM is observed to be continuous. In other cases, the evolution can be interrupted by the breaking of a $-\pi/+\pi$ discontinuous phase line and a new pair of vortices with opposite charges is born.

Spectral control of the orbital angular momentum of a laser beam based on 3D properties of spiral phase plates fabricated for an infrared wavelength.

This paper examines the spectral properties of a spiral phase plate (SPP) generating orbital angular momentum (OAM) beams. A simple method is proposed for calculating the resulting OAM by measuring only two maximum expansion coefficients. A comparative numerical simulation of the proposed and traditional methods is performed. An SPP is fabricated for generation of an OAM with integer values at infrared and visible wavelengths. Qualitative experimental studies of the changes in a generated OAM with a change in the operating wavelength are performed using the spatial filtering method. The experimental results are found to agree with the results of numerical simulation. Beams with integer and fractional OAM values are obtained experimentally by changing the wavelength.

Investigation of the sum of orbital angular momentum generated by conical diffraction

The conical diffraction (CD) of a wave propagating along the optical axis of a biaxial crystal is an intriguing phenomenon with current applications including imaging and optical communications. The emerging light can have a fractional or integer orbital angular momentum (OAM) along the propagation direction per unit thickness of a transverse section. The measurement of the OAM of a beam is not an easy task, particularly for non-integer values. We operated the CD of 1053 and 1047 nm beams with a KGd(WO2)4 crystal, in various input and output polarization states. Then, the sum-frequency was obtained with a KTiOPO4 crystal located near the second Raman spike. The integer or fractional OAM of both the fundamental and sum-frequency waves were visualized with the cylindrical lens method. All the experimental patterns, far field, near field and field in the focal plane of the cylindrical lens, are quite well described by a self-consistent model based on plane wave propagation and their interferences. The sum of the OAM due to quadratic nonlinear conversion is evidenced from experimental and calculated patterns.

Multistable circular currents of polariton condensates trapped in ring potentials.

We demonstrate the formation and trapping of different stationary solutions, oscillatory solutions, and rotating solutions of a polariton condensate in a planar semiconductor microcavity with a built-in ring-shaped potential well. Multistable ring-shaped solutions are trapped in shallow potential wells. These solutions have the same ring-shaped density distribution but different topological charges, corresponding to different orbital angular momentum (OAM) of the emitted light. For stronger confinement potentials, besides the fundamental modes, higher excited (dipole) modes can also be trapped. If two modes are excited simultaneously, their beating produces a complex oscillation or rotation dynamics. When the two modes have the same OAM, a double-ring solution forms for which the density oscillates between the inner and the outer ring. When the two modes have different OAM, a rotating solution with fractional OAM is created.

Interaction of fractional orbital angular momentum in two-wave mixing processes

Nonlinear mixing of optical vortices carrying arbitrary fractional orbital angular momentum was studied. The selection rule for the generated field is extended for the case where non-integer vortices interacts in two-wave mixing processes. We experimentally observe, step by step, the evolution of the birth of a vortex and the formation of higher radial orders in a non-collinear two-wave mixture at the Fraunhofer zone. This is possible due the constrains on the radial order p and the topological charge l in the normalized overlap integral, allowing us to access states where both vortex and external ring are not fully formed. A theoretical model was presented together with numerical and experimental results.

Purity and efficiency of hybrid orbital angular momentum-generating metasurfaces

Controlling light with subwavelength-designed metasurfaces (MSs) has allowed for the arbitrary creation of structured light by precisely engineered matter. We report on the purity and conversion efficiency of hybrid orbital angular momentum (OAM)-generating MSs. We use a recently reported method to design and fabricate meta-surfaces that exploit generalized spin-orbit coupling to produce vector OAM states with asymmetric OAM superpositions, e.g., 1 and 5, coupled to linear and circular polarization states, fractional vector OAM states with OAM values of 3.5 and 6.5, and also the common conjugate spin and OAM of ±1 as reported in previous spin-orbit coupling devices. The OAM and radial modes in the resulting beams are quantitatively studied by implementing a modal decomposition approach, establishing both purity and conversion efficiency. We find conversion efficiencies exceeding 75% and purities in excess of 95%. A phase-flattening approach reveals that the OAM purity can be very low due to the presence of undesired radial components. We characterize the effect and illustrate how to suppress the undesired radial modes.

CUCA Based Equivalent Fractional Order OAM Mode for Electromagnetic Vortex Imaging

An equivalent fractional order orbital angular momentum (OAM) mode based on concentric uniform circular array (CUCA) is proposed in this paper. It is known that the azimuthal resolution of electromagnetic vortex imaging is closely related to the number of OAM modes. Although the multiple-in-multiple-out (MIMO) scheme gives better azimuthal resolution than the multiple-in-single-out (MISO) scheme, it suffers aliasing problem, which means the scattering points with their azimuthal difference larger than 180 degree can not be separated correctly. One possible way to solve this is adding fractional modes in MIMO scheme, but unfortunately, fractional modes are unstable and can not transmit to far field. In this paper, an equivalent fractional order OAM mode is introduced to deal with the problem to achieve higher azimuthal resolution by MIMO scheme. The transmitted and received modes are set to be two adjacent integer modes to realize an equivalent fractional mode. Since the radiation patterns generated by uniform circular array (UCA) for different modes are not aligned, concentric uniform circular array (CUCA) is applied and optimized to overcome this shortage. Simulation results demonstrate the validity of the proposed method.

Kummer laser beams with a transverse complex shift

Here, we study asymmetric Kummer beams, whose complex amplitude is proportional to the Kummer function (a degenerate hypergeometric function). These beams are exact solutions of the paraxial equation (Schrödinger-type equation) and are obtained from the conventional symmetric hypergeometric beams by complex shift of the transverse coordinates. On propagation, the asymmetric Kummer beams change their intensity weakly and rotate around the optical axis. These beams are an example of vortex laser beams with a fractional orbital angular momentum (OAM), which depends on four parameters: the vortex topological charge, the shift magnitude, the logarithmic axicon parameter, and the degree of the radial factor. Changing these parameters, it is possible to control the beam OAM, continuously increasing or decreasing it.

Propagation property of Laguerre-Gaussian beams carrying fractional orbital angular momentum in an underwater channel

In the paper, we experimentally demonstrate the propagation property of Laguerre-Gaussian (LG) beams carrying fractional orbital angular momentum (FOAM) in an underwater environment. The effects of topological charge (TC), temperature gradient, and salinity on the transmission of the LG-FOAM beam in underwater turbulence are analyzed, and the optimum interval of TC for FOAM communication and their help for the improvement of system capacity are discussed. The results show that both the salinity and the temperature gradient have serious impacts on the beam, and meanwhile, the temperature gradient plays a heavier influence. Although the detection probability of one FOAM mode at the receiver side is lower than that nearest integer OAM mode, in the case of that topological charges used are limited, the interval-based mode-multiplexed communication using FOAM can increase the channel capacity.