High-order Orbital Angular Momentum Modes Research Articles

Improving fiber coupling efficiency by shaping the transmission trajectory of the vortex beam

Vortex beams with orbital angular momentum (OAM) have the potential to significantly increase the communication capacity in long-distance free-space optical communication systems. In order to obtain optimal coupling efficiency, few-mode fibers (FMFs) are employed to receive spatial light. This paper presents a computer model that describes the process of coupling vortex beams into FMFs after they have been transmitted via free space. We propose to improve the coupling efficiency by controlling the transmission trajectory of the vortex beam in free space. The coupling efficiency of a vortex beam into FMFs can be enhanced at a specific transmission distance by pre-designing the transmission trajectory of the optical field and tweaking the parameters of the coupling lens and fiber. This paper also examines the coupling correlation between higher-order OAM modes vortex beams and FMF modes. The numerical results of this study show that controlling the radial phase distribution to manage the transmission trajectory of the optical field is an effective and flexible method for improving the efficiency of coupling light between space and fiber. The results of this study can be applied in the domain of free-space optical communications.

Bi-directional high-order orbital angular momentum mode generation using gratings in high numerical aperture fiber

We propose a novel design and theoretically analyse it for bi-directional orbital angular momentum (OAM) mode generation in high numerical aperture (NA) optical fibers using the combination of a long period grating (LPG), a short-period (Bragg) grating and a three-port optical circulator. The proposed design consists only of standard fiber gratings rather than specially designed fibers, such as ring-shaped or other types of fibers, making our model relatively simple. Full-vector true-mode analysis has been used to study the modal characteristics of the supported modes in the high-NA fiber. High-NA optical fibers can effectively relieve the degeneracy of the linearly polarized modes. A circularly polarized (CP) light is injected into a single mode fiber, the output end of which is axially spliced into a high-NA fiber. An appropriately designed raised-cosine apodized tilted LPG (TLPG) is used for broad bandwidth coupling of the fundamental HE11 mode to the co-propagating HE21 mode. The employed TLPG converts the CP fundamental core mode (HE 11x ± iHE 11y ) to ±1 order OAM modes (HE 21even ± iHE 21odd ). Both the CP mode and the generated OAM pass through the circulator in the direction of port 1 to port 2. A second fiber is connected at the output of port 2 and a tilted fiber Bragg grating (TFBG) is used to couple the forward-propagating HE11 core mode with the counter-propagating HE21, EH11 and HE31 core modes. The TFBG reflected higher order (±1 and ±2) OAM modes are transmitted through port 3. We observe that the TFBG has a mode-conversion efficiency of more than 95 % for each mode conversion. The generated vortex beam topological charges have been verified using the coaxial interference method.

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%.

Design of Orbital Angular Momentum Antenna Array for Generating High-Order OAM Modes

Orbital angular momentum (OAM) modes can offer high density and high-capacity communication. The traditional phased array antenna can only produce a limited number of OAM beam modes l, usually less than half of the number of array elements (N): −N/2 < lmax < N/2. An OAM antenna array for generating high-order OAM modes is proposed in this letter. The proposed antenna array consists of a ring patch antenna that can generate vortex waves with OAM mode l = 1 or −1 and a phase-shifting feeding network. By adding different feed excitation signals to each element, the generated beam carries a higher-order mode: l = N or −N, breaking the previous limitations. Near-field measurements were conducted on antenna arrays composed of 3, 4, and 5 elements, revealing a high degree of correspondence between their phase distribution and radiation patterns with numerical simulation results. This alignment further substantiates the practical efficacy of this approach in significantly enhancing the generation of high-order OAM modes within antenna arrays. This advancement improves component utilization efficiency, reduces system complexity, and meets the high demands for spectral resources and channel capacity in future communication applications.

MIMO-free OAM-MDM transmission with a ring-core fiber recirculation loop

We experimentally demonstrate the record long-haul orbital angular momentum (OAM) mode-division multiplexed (MDM) transmission over 300-km assisted by a ring-core fiber (RCF) recirculating loop. The recirculation loop consisting of 50-km RCF is controlled mainly by two acousto-optic switches with opposite states, and the signals are cyclically transmitted in the single-span 50-km RCF to achieve long-haul transmission. The RCF features largely separated OAM mode groups, where the effective refractive index difference between adjacent high-order OAM mode groups is larger than 1.0 × 10-3. Due to the low-crosstalk feature of RCF incorporated into fiber optic links, multiple-input multiple-output (MIMO) equalization technology is not used in the OAM MDM system. We transmit 20-Gbit/s quadrature phase-shift keying signals over two high-order OAM modes, and the transmission performance is characterized. The measured average optical signal-to-noise ratio penalties at a bit-error rate of 1.5 × 10-2 are about 2 dB between single OAM mode transmission and OAM modes multiplexing transmission. The obtained experimental results indicate favorable OAM-based MDM transmission performance in a 300-km recirculating loop link.

Simultaneous Efficient Excitation of Multiple Higher-Order OAM Modes Using a Single Long-Period Fiber Grating

In this paper, a method for the simultaneous generation of multiple higher-order orbital angular momentum (OAM) modes in a few-mode fiber (FMF) using a single long-period fiber grating (LPFG) is proposed and demonstrated. The high diffraction order of the grating is used to achieve the resonant coupling of multiple modes, and the coupling coefficients of different order modes are balanced by a preset-twist method. This solves the two coupling problems of over-coupling for lower-order modes and difficult excitation of higher-order modes faced by multi-order mode generation, and overcomes the challenge of balanced excitation of multiple modes with high coupling efficiency. In the experiment, the simultaneous generation and flexible combination of first-order, second-order and third-order OAM modes are successfully achieved in a six-mode fiber, in which the mode order, resonant wavelength and wavelength interval can be flexibly controlled. By fabricating with grating periods of 2300 μm, 782 μm and 990 μm, respectively, high conversion efficiency of first-order and second-order modes, first-order and third-order modes, second-order and third-order modes can be generated simultaneously. In addition, for the first time, the first-order, second-order and third-order modes are generated simultaneously at a grating period of 1630 μm with conversion efficiencies of 98.61%, 99.11% and 98.89%, respectively. The mode profiles and interference patterns of different order modes show that multiple higher-order OAM modes with insertion loss less than 1 dB and mode purity over 95% are successfully generated.

Negative curvature fiber for suppressing high-order radial OAM modes transmission

The combination of terahertz (THz) wave and the orbital angular momentum (OAM) multiplexing technology can further improve the communication capacity. Compared to other outer cladding structures, the negative curvature structure has been proven to provide stronger confinement effect on electromagnetic waves. Here, we propose a novel polymer (COC TOPAS) fiber which consists a central hollow-core, annular region and single layer negative curvature circle tubes as outer cladding for terahertz OAM modes transmission. The mode map is established by mathematical analysis of cut-off conditions for the vector modes, and the excitation of high-order radial modes in the fiber is successfully suppressed. In addition, the effective refractive index, confinement loss, effective mode area, mode purity and dispersion characteristics of the fiber are investigated under the condition of ‘single mode’ operation in the frequency range of 2.0–3.0 THz.

Full C-band covered and DWDM channelized high channel-count all-fiber orbital-angular-momentum mode generator based on the fiber gratings.

To generate the orbital-angular-momentum (OAM) modes at multiple wavelengths, which exactly fit with the dense-wavelength-division-multiplex (DWDM) channel grids, is important to the DWDM-based OAM mode-division-multiplex (MDM) fiber communication system. In this study, a full C-band covered and DWDM channelized OAM mode generator is firstly proposed and experimentally demonstrated, which is realized especially by using a broadband helical long-period fiber grating (HLPG) combined with a phase-only sampled multichannel fiber Bragg grating (MFBG). As a proof-of-concept example, the DWDM channelized two complementary 51-channel OAM mode generators have been successfully demonstrated, each of which has a channel spacing of 100 GHz (∼0.8 nm), an effective bandwidth of ∼40 nm, a high azimuthal-mode conversion efficiency of 90%, and high uniformities in both inter- and intra-channel spectra as well. To the best of our knowledge, this is the first time for proposal and experimental demonstration of such a high channel-count and DWDM channelized first-order OAM mode (l = 1) generator, which can also be used for multichannel higher-order OAM mode generation as long as the utilized HLPG is capable of generating a broadband higher-order OAM mode. The proposed device has potential applications to DWDM-based OAM fiber communications, OAM comb lasers, OAM holography, and OAM sensors as well.

Mode-group selective photonic lanterns for multiplexing multi-order orbital angular momentum modes.

The lack of research on photonic lanterns multiplexing multi-order orbital angular momentum (OAM) modes hinders the development of OAM space division multiplexing systems. In this paper, an annular multicore photonic lantern (AMCPL) for multiplexing several OAM mode groups is proposed and demonstrated. Comprehensive simulations are carried out to investigate the effect of the multicore arrangements on the crosstalk (XT) between different OAM mode groups. Further optimization provides an inverted multicore arrangement of the OAM AMCPL with balanced XT between high-order OAM mode groups with topological charges |l| = 2 to 5 for the first time, of which the highest XT between target mode groups does not exceed -27.20 dB at wavelengths from 1300 nm to 1600 nm, and mode conversion efficiencies of all target mode groups exceed 99.5%. Furthermore, a quantum interpretation is given to reveal the characteristics of the evolution of the supermodes along the taper of the OAM AMCPL, which has not been reported.

Low loss side-polished pumping coupler for high order OAM modes amplification.

An all-fiber fiber coupler was demonstrated for pumping orbital angular momentum (OAM) modes amplification, which was fabricated by side-polishing and bonding a ring-core erbium-doped fiber (RC-EDF) and a pre-tapered side-polished single-mode fiber (SMF). With the selected phase-matching condition at 976 nm, the pumping laser was coupled into the RC-EDF from the SMF with optimized high efficiency, whereas the 1st to 3rd-order OAM mode signals were transmitted with the low insertion loss in the RC-EDF over a broadband wavelength range from 1530 to 1565 nm. This all-fiber wavelength division multiplexing coupler was optimized by the polished length and depth of the two coupled fibers. The insertion loss for the OAM signal modes was obtained lower than 0.58 dB with the pump power coupling ratio of above 90%. The proposed side-polished pumping coupler technique can ensure high-order OAM modes amplification, paving the way for the all-fiber optical amplifier in high-capacity modal-division multiplexing fiber communication systems.

Extending orbital angular momentum multiplexing to radially high orders for massive mode channels in fiber transmission.

Orbital angular momentum (OAM) beams with different angular indices l have the potential to greatly increase communication capacity. However, the finite aperture of optical systems limits the value of the angular index. In order to fully use the orthogonal mode channels supported in the fiber for high-capacity communications, we propose extending the radial indices p of OAM modes as an additional multiplexing dimension. In this paper, we introduce spatially discrete multiple phase planes to multiplex the angular and radial OAM modes simultaneously. Due to the orthogonal property of the central symmetric OAM modes, a two-dimensional (2D) input Gaussian beams array can be converted to coaxial OAM modes through Cartesian to log-polar coordinate transformation by inverse design. For a proof-of-concept demonstration, a 10-mode multiplexer for high-order radial OAM modes was designed using five phase planes. The fabricated multiplexer generated high-quality multiplexed OAM modes with a loss of less than 5.4 dB. The multiplexed OAM modes were coupled into a specially designed ring-core fiber by mode-field matching, achieving stable mode transmission in 2 km fiber. The approach provides a scalable technology to increase the number of transmission channels and could lead to the practical applications of OAM multiplexing in communication.

Multiple core modes conversion using helical long-period fiber gratings.

We propose and demonstrate the fabrication of an all-fiber mode converter enabling simultaneous generation of multiple high-order core modes, which is realized by inscribing a helical long-period grating (HLPG) in a few-mode fiber (FMF) using a femtosecond laser. Helical refractive index modulation is introduced by continuously irradiating the core region with a highly focused femtosecond laser, while the fiber moves in a spiral path through a three-dimensional translation stage. Mode conversion from the LP01 mode to high-order core modes, including LP11, LP21, LP31, LP02, LP12, and LP41 modes, is achieved by controlling the inscription pitch of the grating. Moreover, first-, second-, third-, and fourth-order orbital angular momentum (OAM) modes can be directly generated using the HLPGs, and multiple OAM modes of different topological charges can be simultaneously excited using a single high diffraction order HLPG. This approach offers a new option for implementing with high-integration high-order mode converters or OAM mode generators.

Helical Circular Array Configurations for Generation of Orbital Angular Momentum Beams

The vortex electromagnetic waves carrying the orbital angular momentum (OAM) are an increasing subject of study, and the design of a system capable of generating such waves is also of crucial importance. In this letter, a helical circular array (HCA) has been proposed to generate OAM radio beams. The proposed HCA has a more straightforward and more feasible scheme when compared to uniform circular arrays (UCAs) that require additional phase-shifting devices to form inter-element phases. The heights of the proposed HCA elements along the z-axis are exploited to generate the different OAM modes. For the high-order OAM modes, the height of the HCA is made more compact with the help of the proposed helical circular subarray (HCSA) configurations with spiral phase positions providing a linear phase delay with the azimuth angle. In addition, at high mode values, the HCSA structure creates a smoother OAM vortex beam than HCA. The full-wave simulation results show that the proposed HCA scheme can be used to generate vortex electromagnetic waves with a spiral phase wavefront structure.

Co-Modulation of Spin Angular Momentum and High-Order Orbital Angular Momentum Based on Anisotropic Holographic Metasurfaces

In this communication, a new method for modulating spin angular momentum (SAM) and orbital angular momentum (OAM) based on anisotropic holographic metasurfaces is proposed, which can realize the co-modulation of SAM, high order OAM, and beam’s direction simultaneously. The tensor unit adopts an ellipse patch with three adjustable parameters without slotting, and a design and analysis method suitable for this kind of tensor unit is proposed based on the two-dimensional effective impedance database for geometrical size mapping. Based on the tensor unit and proposed methods, the vortex beams with a single SAM state, a single high order OAM mode, and different directions are generated at 22 GHz. Then, the deflected vortex beams with the same SAM state and mixed OAM modes, or the deflected vortex beams with different SAM states and OAM modes are realized using a single feed and a single metasurface integrated for the first time. Simulation and experimental measurement results show that the OAM mode purity can reach more than 80% of the theoretical best value in the main SAM state. The proposed design methods and the device can achieve arbitrary modulation of SAM and OAM, providing a solution for combining and applying the two to multiplexing communications.

High-Order OAM Mode Generator Using Multi-Cascaded Long-Period Fiber Gratings

We propose and demonstrate the inscription of multi-cascaded long-period fiber gratings (LPFGs) in a few-mode fiber using a CO2-laser. The multi-cascaded LPFGs containing three gratings were fabricated successfully. The first LPFG was used to realize the mode conversion from LP01 mode to LP11 mode, the second one was used to convert LP11 mode to LP21 mode, and the third one achieved the higher-order mode conversion from LP21 mode to LP31 mode. The second-order and third-order orbital angular momentum (OAM) modes can be generated using the cascaded LPFGs with the second and third gratings, respectively. The multi-cascaded LPFGs have the promising potential to be adopted as mode converters and mode scramblers in the mode division multiplexing system thanks to the flexible mode conversion among different higher-order modes.

Generation of all-fiber third-order orbital angular momentum modes based on femtosecond laser processing of long-period grating

The generation of orbital angular momentum (OAM) modes is very important, for they have a variety of applications such as in optical tweezers, quantum optics, and optical communication systems. Particularly, how can high-order OAM modes be generated efficiently in fibers with the advantage of low cost and compatible with fiber system? The Traditional method for first order to third order OAM is based on long period fiber grating (LPFG) fabricated by carbon dioxide laser. However, high power and large focused spot of carbon dioxide laser are unfavorable for stable and repeatable generation of higher-order OAM, which needs the LPFG with small grating pitch. In order to solve this problem, a third-order OAM mode converter based on femtosecond microfabrication is proposed and fabricated for the first time. With the advantage of 4.4 μm focused spot size near the core, lower power and lower heat absorption efficiency, this method can be more stable and promising. Therefore, we first carry out the mode filed analysis and simulate the intensity and phase profiles of the superposed mode field in LP odd-even mode on different scales and phases patterns to obtain OAM mode. Second, we use the coupled-mode theory to analyze and simulate the transmission spectrum of LPFG, which guides the setting of the grating parameters such as the grating pitch, the depth of modulation and the length of the grating. By experimental verification, an asymmetric modulated long-period fiber grating with a pitch setting to 194 μm is fabricated on a six-mode fiber. The fundamental mode can be converted into the third-order angular linear polarization mode LP<sub>31</sub> mode with 98% mode conversion efficiency near 1550 nm, and further converted into the OAM<sub>±3</sub> modes by superposition of the odd and even LP<sub>31</sub> mode with ±π/2 phase difference. At the same time, this fiber grating can also generate LP<sub>12</sub> mode with 90% mode conversion efficiency near 1325 nm. Then we can take the same approach to transform LP<sub>12</sub> mode into OAM modes with angular first-order as well as radial second-order. The experimental result is consistent with the simulation result. Thus, this scheme provides an idea for generating the high-order OAM modes in all-fiber systems by using only one grating with high repeatability.

Helically twisted double-cladding-three-core photonic crystal fiber for generation of orbital angular momentum

Aiming at the shortcomings of helically twisted single-cladding-few-core photonic crystal fibers in generating orbital angular momentum (OAM), the double-cladding and three-core structures with non-uniform inner and outer air holes are introduced into a photonic crystal fiber for the first time and the generation of high-order OAM modes through helical twisting is realized. The fiber is expected to reduce the losses of the generated OAM modes by introducing a specially designed double-cladding structure, while the three cores distributed in a regular triangle around the center are expected to increase the number of generated OAM modes. On the basis of optical transformation theory, the optical fiber is systematically analyzed by the finite element method. It is found that with the twist rate <i>α</i> = 7853.98 rad/m, the generated OAM modes include “OAM<sub>–4,1</sub>, OAM<sub>+9,1</sub>, OAM<sub>+10,1</sub>, OAM<sub>+11,1</sub>, OAM<sub>+13,1</sub>”, where +13 is the highest order in the OAM modes currently generated by using helically twisted fibers. And the losses of OAM modes are all less than 1.64×10<sup>–3</sup> dB/m, which is at least two orders of magnitude lower than the lowest OAM mode loss reported in the existing references (Napiorkowski M, Urbanczyk W S 2018 <i>Opt. Express</i> <b>26</b> 12131), and their purity is greater than 93%. Further studies show that the generation of orbital angular momentum depends on the resonant coupling between the core supermode and the ring-core mode, and the parity of the order of the generated OAM modes is related to the polarization direction of the fiber core supermode and the ring-core mode.

Propagation Properties of Vortex Beams in a Helically Twisted Photonic Bandgap Fiber

We propose a helically twisted hollow-core photonic bandgap fiber (PBGF) for orbital angular momentum (OAM) generation. Results demonstrate that this fiber can effectively separate and transmit higher-order OAM modes while reducing crosstalk. The mode effective refractive index curves as a function of wavelength and the transmission characteristics of OAM are investigated in this letter. We show that this fiber has the potential to be used in OAM generators, light-controlling devices, and all-fiber optical communication applications.

High-efficiency broadband third-order OAM mode converter based on a multi-period preset-twist long-period fiber grating.

All-fiber mode converters for generating orbital angular momentum (OAM) beams have many applications in optical communications, optical sensing and lasers. Currently, it is a great challenge to use a long-period fiber grating (LPFG) to broadband excite high-order OAM modes above the second-order. Here, we demonstrate a preset-twist LPFG fabrication method, which introduces asymmetry in the refractive index modulation area, for efficient generation of third-order modes. Through optimization, the generation of third-order OAM modes with 99.55% conversion efficiency, 0.81 dB insertion loss, and over 99% purity is achieved with only 40 pitch number. In addition, a multi-period preset-twist LPFG is proposed and demonstrated to achieve the excitation of broadband third-order mode with conversion efficiency of more than 99%, insertion loss of less than 1 dB, and mode purity of more than 90%. The 15 dB bandwidth (96.8% conversion efficiency) of the LPFG is 109 nm in the wavelength range from 1475 nm to 1584 nm, and the 20 dB bandwidth (99% conversion efficiency) of the LPFG is 92 nm from 1488 nm to 1580 nm. To the best of our knowledge, this is the first time to generate efficient and broadband third-order mode using a long-period fiber grating.

Generation, Transmission, and Amplification of OAM Modes in the PbSe-Doped Ring-Core Fiber Carrying 3D Printed Spiral Phase Plate

Vortex beams carrying orbital angular momentum (OAM) have increasingly attracted attention in the field of optical communication. However, transmission is still an issue due to transmission loss, especially in optical fibers. In this work, we proposed, designed, and fabricated micro spiral phase plates (SPPs) directly on an end facet of a piece of PbSe-doped ring-core fiber (RCF) through two-photon polymerization, realizing the integration of OAM beam generation, transmission, and amplification. The prepared RCF comprises a double-clad structure with a core-clad refractive index difference of 2.2% and the fluorescence range is 1150 nm–1700 nm. The intensity distribution of the OAM beam and the spiral interference fringes were obtained, which indicated that the OAM mode (|l|=1, 2, 3, 4) was generated and transmitted directly within the fiber. The small-signal amplification of four OAM modes was accomplished at 1550 nm under a pump power of 634 mW. The on–off gain is >13.2 dB for all modes and the differential mode gain (DMG) is <1.7 dB. The SPP-carrying RCF structure demonstrates the integration of generation, transmission, and amplification of higher-order OAM modes in all-fiber systems.