Spiral Phase Distribution Research Articles

Focused polarization ellipse field singularities: interaction of spin-orbital angular momentum and the formation of optical Möbius strips

We study here the intensity distribution and formation of optical polarization Möbius strips by tightly focusing of C-point singularity beams. These beams are characterized by a central circular polarization point (C-point) surrounded by a spatially varying elliptic polarization. Under tight focusing conditions, the different polarization components of the beam interfere and exhibit clear difference between left-handed and right handed input beams. The transverse polarization distribution at the focal plane is similar to the input distribution for left-handed lemon beam, but exhibits 180° rotation for right handed lemon beam. Moreover, the longitudinal polarization component exhibits spiral phase distribution, owing to spin-orbit angular momentum conversion at the focal plane, with opposite winding directions for the left-handed and right-handed input beams. We show that the shape of the resulting Möbius strip is determined by the helicity of the C-point and by the polarization singularity index, which is the contour integral of polarization ellipse angle around the singularity. It is found that inverting the helicity leads to 180° rotation in the focal plane intensity distribution, accompanied by handedness inversion for the polarization ellipses. The number of separatrices in the input polarization distribution is equivalent to the number of twist points of the Möbius strip in the focal plane, as well as to the number of intensity zeros in the z-component of the focused field. These phenomena are observed for beams with a bright C-point, but also for dark C-point, in which the electric field is zero at the center of the beam.

Versatile generation and manipulation of phase-structured light beams using on-chip subwavelength holographic surface gratings

Abstract Phase-structured light beams carrying orbital angular momentum (OAM) have a wide range of applications ranging from particle trapping to optical communication. Many techniques exist to generate and manipulate such beams but most suffer from bulky configurations. In contrast, silicon photonics enables the integration of various functional components on a monolithic platform, providing a way to miniaturize optical systems to chip level. Here, we propose a series of on-chip subwavelength holographic waveguide structures that can convert the in-plane guided modes into desired wavefronts and realize complex free-space functions, including the generation of complex phase-structured light beams, arbitrarily directed vortex beam emission and vortex beam focusing. We use a holographic approach to design subwavelength holographic surface gratings, and demonstrate broadband generation of Laguerre–Gaussian (LG) and linearly polarized (LP) modes. Moreover, by assigning appropriate geometric phase profiles to the spiral phase distribution, the off-chip vortex beam manipulation including arbitrarily directed emission and beam focusing scenarios can be realized. In the experiment, directed vortex beam emission is realized by using a fabricated tilt subwavelength holographic fork grating. The proposed waveguide structures enrich the functionalities of dielectric meta-waveguide structures, which can find potential applications in optical communication, optical trapping, nonlinear interaction and imaging.

Plane Spiral OAM Mode-Group Orthogonal Multiplexing Communication Using Partial Arc Sampling Receiving Scheme

A variety of novel orbital angular momentum (OAM)-based communication or sensing systems have attracted much attention over the past decade, the superiority is brought about by nothing other than its orthogonality or vorticity. Plane spiral OAM (PSOAM) mode-group (MG) technique as a reconfigurable beamforming method can be used for building a multiple-in-multiple-out (MIMO) system to achieve the reduction in subchannel correlation, which benefits from the spiral phase distribution within the mainlobe. However, the demultiplexing process still depends on the MIMO algorithm, in which the receiver complexity is same as the conventional MIMO systems. In this article, a PSOAM MG orthogonal multiplexing communication link at the X-band using partial arc sampling receiving (PASR) scheme has been demonstrated experimentally. The MG channels have a good isolation of about 15 dB, and the existing performance can ensure the reliable 16-QAM wireless transmission. Besides, a real-time dual-channel video transmission experiment has been carried out to verify the channel isolation caused by MG’s orthogonality intuitively. More importantly, the demultiplexing procedure using the PASR scheme can be implemented by simple analog phase shifting operation with a lower receiver complexity compared with the conventional MIMO systems.

Electromagnetic Radiation Force of Vortex Electromagnetic wave exerted on a perfect electromagnetic conductor (PEMC) Sphere

In this manuscript, the electromagnetic (EM) radiation force (RF) exerted on a perfect electromagnetic conductor (PEMC) sphere by a vortex electromagnetic (VEM) wave with spiral phase distribution had been investigated. The analytical formulation of EM fields is being done in the framework of Mie theory, while the field expressions are being modeled considering the features of VEM wave for PEMC sphere. Initially, the incident field coefficients are evaluated using definite integrals. The scattering coefficients are then determined by imposing boundary conditions at the surface of PEMC sphere i.e., at 𝑟=𝑎, leading to a linear system of equations computed via solving matrix. So, a lengthy calculation yields undetermined scattered field coefficients relative to incident field coefficients. The cross-section (𝑄) factors i.e., scattering (𝑄𝑠𝑐𝑎) and extinction (𝑄𝑒𝑥𝑡) have been computed. The influence of sphere size parameter (𝜌) and beam waist radius (𝑤0) versus scattering angle (𝛼°) for the RF along with 𝑄𝑠𝑐𝑎 has been numerically analyzed. As no loss of energy occurs inside PEMC sphere so absorption ((𝑄𝑎𝑏𝑠)=0), by virtue of the energy conservation principle then, 𝑄𝑒𝑥𝑡=𝑄𝑠𝑐𝑎. Under specific condition, we implemented present results on 𝑄𝑠𝑐𝑎 towards light without orbital angular momentum (OAM) i.e., (𝑙=0) and plane wave for the PEMC sphere. The research work has potential applications towards particle manipulation, optical technology, and optical tweezers.

Forward-Looking Imaging Based on the Linear Wavefront of the Modulated Field

The vortex electromagnetic wave improves the range-azimuth forward-looking imaging performance with its spiral spatial phase distribution. However, the beam of the vortex electromagnetic wave is divergent, which makes it difficult to detect the targets near the center of the beam. In addition, the vortex electromagnetic wave only has the phase change in the azimuth direction and can hardly estimate the elevation position of the targets. In this paper, a linear wavefront control method based on the amplitude weighting of the array antenna is proposed. The modulated field has a phase gradient in both azimuth and elevation directions and has a maximum radiation intensity in the center of the beam. The imaging model based on the modulated field is theoretically derived and simulations are conducted to demonstrate the imaging performance. The modulated field constructed by the linear array can realize range-azimuth two-dimensional imaging with azimuth resolution of 1/5 beam width. The modulated field constructed by the circular array can realize range-azimuth-elevation three-dimensional imaging, and the resolution of the azimuth and elevation directions is 1/3 of the beam width.

Experimental generation and orbital angular momentum properties of focused field for vector vortex beams on Hybrid-order Poincaré sphere

Due to the anisotropic spatial polarization state and spiral phase distribution, the orbital angular momentum (OAM) of vector vortex beams (VVBs) has attracted increasingly attention in recent years. In this paper, the Hybrid-order Poincaré sphere VVBs are constructed by orthogonal left-handed (L-H) and right-handed (R-H) circularly polarized vortexes. The vector vortex light fields of different orders at the focal plane are collected and analyzed experimentally. Based on the vector diffraction integral theory, the effects of the topological charge and polarization order for VVBs, as well as the initial phase difference for L-H and R-H components on the OAM properties of focused field for the longitudinal component are investigated numerically. It is found that the OAM density distribution of the longitudinal component shows inner and outer two layers on the whole, and the layers mainly concentrate the corresponding L-H and R-H components respectively. Meanwhile, the signs of the topological charges for L-H and R-H components determine the positive and negative distributions of the inner and outer OAM density respectively. When the initial phase difference of L-H and R-H components ϕ0 changes in the range of 0–2π, the OAM density rotates the angle ϕ0/2 along the clockwise. However, the OAM of the longitudinal component does not change with ϕ0, and increases as the polarization order m increases when the topological charge of VVBs l>2. The results could be helpful to further explore the applications of the OAM for VVBs in the fields of optical detection and communication.

Experimental Study of Plane Spiral OAM Mode-Group Based MIMO Communications

Spatial division multiplexing using conventional orbital angular momentum (OAM) has become a well-known physical layer transmission method over the past decade. The mode-group (MG) superposed by specific single-mode plane spiral OAM (PSOAM) waves has been proved to be a flexible beamforming method to achieve the azimuthal pattern diversity, which inherits the spiral phase distribution of conventional OAM wave. Thus, it possesses both beam directionality and vorticity. In this article, it is the first time to show and verify a novel PSOAM MG based multiple-in–multiple-out (MG-MIMO) communication link experimentally in a line-of-sight (LoS) scenario. A compact multimode PSOAM antenna is demonstrated experimentally to generate multiple-independent controllable PSOAM waves, which can be used for constructing MGs. After several proof-of-principle tests, it has been verified that the beam directionality gain of MG can improve the receiving signal-to-noise ratio (SNR) level in an actual system. Meanwhile, the vorticity can provide another degree of freedom (DoF) to reduce the spatial correlation of MIMO system. Furthermore, a tentative long-distance transmission experiment operated at 10.2 GHz has been performed successfully at a distance of 50 m with a single-way spectrum efficiency of 3.7 bits/s/Hz/stream. The proposed MG-MIMO may have potential in the long-distance LoS backhaul scenario.

A Non-Uniform Travelling-Wave Current Source Model for Designing OAM Antenna: Theory, Analysis and Application

Orbital angular momentum (OAM) has become a research hotspot in radar, communication, and other fields because of its spatial spiral phase distribution in azimuthal domain. However, it encounters some problems in practical application scenarios owing to its inherent defects. Recently, several particular OAM waves and novel antenna structures have been proposed to make up for its defects or optimize its characteristics. However, there lack a universal and systematic theoretical analysis for these schemes. In this paper, the non-uniform travelling-wave current source (NTCS) model for OAM generation is proposed. This model is universal and suitable to be applied to many proposed antennas. The far field pattern and OAM spectrum distribution are theoretically derived based on the uniform travelling-wave source model. Bridged by the OAM spectrum analysis, an application-oriented antenna design process is presented. A PSOAM MG antenna optimal for the MIMO system is designed as an example. This work not only unifies the generation model of different OAM waves, but also provides a new view for the OAM based antenna design.

Velocity measurement of an arbitrary three-dimensional moving object by using a novel modulated field

The rotational Doppler effect caused by vortex beam carrying orbital angular momentum is recently used to estimate the rotational velocity of the object. However, the vortex beam only has the spiral phase distribution in one dimension, which means that only the rotational movement of the object would introduce the frequency shift. Also, the vortex beam has a spatial amplitude distribution of doughnut-shaped, which is not suitable for many application scenarios. To simultaneously measure the velocity of an arbitrary three-dimensional moving object, we propose theoretically and demonstrate experimentally an effective method by constructing a novel modulated field. Different from the plane wave and the vortex beam, the modulated field has linear phase distribution in azimuth and elevation directions. In addition, the modulated field has the maximal radiation intensity in the center, which avoids the beam divergence of the vortex beam. By decomposing the frequency shift caused by the radial, azimuth and elevation movements, we realize the velocity measurement in three dimensions. Experiments in a microwave system show that the estimated velocity errors are lower than 6.0%.

Measurement of real phase distribution of a vortex beam propagating in free space based on an improved heterodyne interferometer

This paper proposes an improved heterodyne interferometer to measure the real phase distribution of vortex beams propagating in free space. The fundamental mode Gaussian beam passes through the vortex phase plate and has one or more phase transitions of 2π along the angular direction. Such vortex beams undergo phase distortion during transmission, and their complex phase distribution is difficult to measure. The improved heterodyne interferometer proposed in this study successfully measures the phase distortion, demonstrating high spatial resolution and phase measurement accuracy. Both the theoretical and the experimental results show that in the process of free space propagation, the phase jump intersection boundary transforms from a straight line into a twisted line and that the phase distribution gradually becomes a spiral phase distribution followed by a ring intensity distribution corresponding to further increase in the propagation distance. The proposed method is estimated to be capable of predicting the variation of the vortex beams based on the research conducted on the interaction between the vortex beams and the atmospheric turbulence.

Soft-X-Ray Vortex Beam Detected by Inline Holography

We demonstrate the in-line holography for soft x-ray vortex beam having an orbital angular momentum. A hologram is recorded as an interference between a Bragg diffraction wave from a fork grating and a divergence wave generated by a Fresnel zone plate. The obtained images exhibit fork-shaped interference fringes, which confirms the formation of the vortex beam. By analyzing the interference image, we successfully obtained the spiral phase distribution. The results demonstrate that the in-line holography technique is promising for the characterization of topological magnets, such as magnetic skyrmions.

Vortex beam and its application in optical tweezers

Vortex beams are beams with a spiral phase distribution and zero central light intensity. In recent years, it has been widely studied and applied. This article first analyses the characteristics of the vortex beam from a theoretical perspective, and then introduces the application of the vortex beam to optical tweezers.

Generation of E-band metasurface-based vortex beam with reduced divergence angle

Vortex beams carrying orbital angular momentum (OAM) have attracted considerable attention for the development of high-capacity wireless communication systems due to their infinite sets of orthogonal modes. However, the practical applications of Laguerre-Gaussian type vortex beams are limited due to the fact that the divergence angle increases as the order of the OAM mode increases. In this work, we present metasurfaces that generate vortex beams carrying OAM modes with reduced divergence angles in the E-band frequency range. The metasurfaces were designed using eight different meta-atom phase elements, including a spiral phase distribution for OAM modes l = 1 and 2, a phase gradient array to avoid interference with the source beam, and a lens pattern array to reduce the divergence angle. Through simulation and experimental measurement, it was confirmed that the divergence angle of the vortex beam generated by the metasurface with the lens pattern was reduced from 13° to 9° and 14° to 11° for OAM modes l = 1 and 2, respectively, in comparison with the metasurface without the lens pattern. Our results provide new design methods for various applications based on OAM multiplexing especially in high frequency E-band range.

Generation of Orbital Angular Momentum Beam With Circular Polarization Ceramic Antenna Array

Orbital angular momentum (OAM) beams can be generated at many microwave frequencies by using antenna array. However, the complexity of the system and inability to transmit over long distances limit the applications of OAM beams in the radio domain. Here, a significantly simplified global positioning system (GPS) ceramic antenna array is employed to generate OAM beams without the assistance of phase shifting devices. Simulation of the GPS ceramic antenna array verifies that the OAM beams with the mode of ±1 show small divergence angle and very standard spiral phase distribution. To test the transmission capability of the proposed antenna array, a measurement system that can detect the one-dimension spatial distribution of electromagnetic characteristic for the OAM beams is set up. Even considering the enormous loss in cables and power divider, the receiving antenna still can receive the electromagnetic characteristic of the OAM beams at a place more than 2 m away from the antenna array. Experimental results presented in this paper demonstrate the excellent performance of the OAM beams when generated with the proposed ceramic antenna array configuration.

Dual-band vortex beam generation with different OAM modes using single-layer metasurface.

Recently, considerable attention has been focused on orbital angular momentum (OAM) vortex wave, owing to its prospect of increasing communication capacity. Here, a single-layer metasurface is proposed to realize vortex beams with different OAM modes and polarizations carried at two distinctive bands. Both the resonant and geometric (Pancharatnam-Berry) phase cells are adopted to construct this metasurface for generating the desired phase profile, and each type of phase modulation cell can independently control the vortex beam at different frequencies. When a linearly-polarized wave is incident onto our metasurface, the resonant phase cells with spiral phase distribution can achieve OAM beam with topological charge of + 1 at 5.2 GHz. And under illumination of left-handed circular polarized (LHCP) wave, the rotated geometric phase cells assist the metasurface to generate the deflected OAM beam with topological charge of + 2 at 10.5~12 GHz. Both simulated and experimental results demonstrate good performance of the proposed single-layer metasurface at the above two frequency bands.

Generating optical vortex with large topological charges by spiral phase plates in cascaded and double-pass configuration

Spiral phase plate (SPP), as a kind of optical component for generating optical vortex (OV), has the ability to convert the traditional non-singular beams into OV with spiral phase distribution. However, due to the demanding of machining accuracy, the production of high quality SPPs with large topological charges (TCs) is usually complicated and expensive. An approach to generate OV with large TCs based on low-order SPPs is presented. In the proposed scheme, the addition of TCs is realized by cascading multiple SPPs, and the double-pass configuration is employed to implement doubling of TCs. Based on the combination of cascaded and double-pass configuration, an OV with TCs as high as 28 is generated, using two SPPs of TCs 6 and 8, respectively. The method of alignment and the alignment deviation is discussed.

Realization of Beam Steering Based on Plane Spiral Orbital Angular Momentum Wave

A new form of plane spiral orbital angular momentum (PS-OAM) carrying wave with the spiral harmonics of exp(− $jl\varphi$ ) as a complete set of eigenmodes is proposed to realize beam steering. Such a wave possesses the fundamental characteristics of an OAM-carrying wave, i.e., a spiral phase distribution, yet propagates along transverse directions. Hence, it owes unique advantages for use in realizing desired radiation beams, while avoids the puzzles encountered by traditional OAM-carrying beams. Various OAM mode grouping using the superposition of PS-OAM waves are demonstrated here via theoretical calculations as well as experimental verifications. The generation methods for PS-OAM waves are also proposed and experimentally validated to authenticate the feasibility. Both the calculated and experimental results show that the PS-OAM grouping is capable of providing a practical realization of eigenmode beamforming.

Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate

Cylindrical vector (CV) beams have found increasing applications in physics, biology, and chemistry. To generate CV beams, interferometric technique is popularly adopted due to its flexibility. However, most interferometric configurations for the generation of CV beams are faced with system instability arising from external disturbance, limiting their practical applications. A common-path interferometer for the generation of radially and azimuthally polarized beams is proposed to improve the system stability. The optical configuration consists of a vortex phase plate acting to tailor the phase profile and a cube nonpolarizing beamsplitter to split the input beam into two components with mirror-like spiral phase distribution. The generated CV beams show a high quality in polarization and exhibit a better stability of beam profile than those obtained by noncommon-path interferometric configurations.

Theoretical analysis and experimental verification on optical rotational Doppler effect.

We present a theoretical model to sufficiently investigate the optical rotational Doppler effect based on modal expansion method. We find that the frequency shift content is only determined by the surface of spinning object and the reduced Doppler shift is linear to the difference of mode index between input and output orbital angular momentum (OAM) light, and linear to the rotating speed of spinning object as well. An experiment is carried out to verify the theoretical model. We explicitly suggest that the spatial spiral phase distribution of spinning object determines the frequency content. The theoretical model makes us better understand the physical processes of rotational Doppler effect, and thus has many related application fields, such as detection of rotating bodies, imaging of surface and measurement of OAM light.

Application of spatial light modulators for generation of laser beams with a spiral phase distribution

Application of spatial light modulators for generation of laser beams with a spiral phase distribution