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14 pages, 6358 KiB  
Article
Practical Performance Analysis of MDI-QKD with Orbital Angular Momentum on UAV Relay Platform
by Dan Wu, Jiahao Li, Lan Yang, Zhifeng Deng, Jie Tang, Yuexiang Cao, Ying Liu, Haoran Hu, Ya Wang, Huicun Yu, Jiahua Wei, Huazhi Lun, Xingyu Wang and Lei Shi
Entropy 2024, 26(8), 635; https://doi.org/10.3390/e26080635 - 27 Jul 2024
Viewed by 1074
Abstract
The integration of terrestrial- and satellite-based quantum key distribution (QKD) experiments has markedly advanced global-scale quantum networks, showcasing the growing maturity of quantum technologies. Notably, the use of unmanned aerial vehicles (UAVs) as relay nodes has emerged as a promising method to overcome [...] Read more.
The integration of terrestrial- and satellite-based quantum key distribution (QKD) experiments has markedly advanced global-scale quantum networks, showcasing the growing maturity of quantum technologies. Notably, the use of unmanned aerial vehicles (UAVs) as relay nodes has emerged as a promising method to overcome the inherent limitations of fiber-based and low-Earth orbit (LEO) satellite connections. This paper introduces a protocol for measurement-device-independent QKD (MDI-QKD) using photon orbital angular momentum (OAM) encoding, with UAVs as relay platforms. Leveraging UAV mobility, the protocol establishes a secure and efficient link, mitigating threats from untrusted UAVs. Photon OAM encoding addresses reference frame alignment issues exacerbated by UAV jitter. A comprehensive analysis of atmospheric turbulence, state-dependent diffraction (SDD), weather visibility, and pointing errors on free-space OAM-state transmission systems was conducted. This analysis elucidates the relationship between the key generation rate and propagation distance for the proposed protocol. Results indicate that considering SDD significantly decreases the key rate, halving previous data results. Furthermore, the study identifies a maximum channel loss capacity of 26 dB for the UAV relay platform. This result is pivotal in setting realistic parameters for the deployment of UAV-based quantum communications and lays the foundation for practical implementation strategies in the field. Full article
(This article belongs to the Special Issue Progress in Quantum Key Distribution)
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<p>Schematic diagram of ground-to-UAV MDI-QKD scenarios.</p>
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<p>Schematic diagram of state-dependent diffraction.</p>
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<p>The wavefronts and intensity profiles of OAM modes <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> </mrow> </semantics></math> and 3. The OAM mode with a nonzero order has a donut-shaped intensity profile. The size of the ring in the intensity profile grows with <span class="html-italic">l</span>.</p>
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<p>Schematic diagram of OAM-MDI-QKD.</p>
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<p>Link loss against propagation distance of different OAM orders <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>7</mn> <mo>,</mo> </mrow> </semantics></math> and 9.</p>
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<p>Probability of receiving adjacent OAM modes versus the ratio of the telescope diameter <math display="inline"><semantics> <msub> <mi>D</mi> <mi>r</mi> </msub> </semantics></math> to the Fried parameter <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>.</p>
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<p>(<b>a</b>) Transmission efficiency against distance at different atmospheric turbulence strengths. (<b>b</b>) Key rate versus distance at different atmospheric turbulence strengths.</p>
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<p>(<b>a</b>) Weather visibility versus attenuation at different wavelengths <math display="inline"><semantics> <mi>λ</mi> </semantics></math> = 550 nm, 690 nm, 850 nm, and 1550 nm. (<b>b</b>) Relationship between weather visibility, propagation distance, and transmission efficiency at the operational wavelength of 1550 nm.</p>
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<p>(<b>a</b>) Variation of the link loss as a function of the propagation distance for different effects. (<b>b</b>) Variation of the key rate as a function of the propagation distance for different effects.</p>
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11 pages, 853 KiB  
Article
A Terahertz Programmable Digital Metasurface Based on Vanadium Dioxide
by Tianrui Pan, Chenxi Liu, Shuang Peng, Haiying Lu, Han Zhang, Xiaoming Xu and Fei Yang
Photonics 2024, 11(6), 527; https://doi.org/10.3390/photonics11060527 - 1 Jun 2024
Viewed by 870
Abstract
Metasurfaces can realize the flexible manipulation of electromagnetic waves, which have the advantages of a low profile and low loss. In particular, the coding metasurface can flexibly manipulate electromagnetic waves through controllable sequence encoding of the coding units to achieve different functions. In [...] Read more.
Metasurfaces can realize the flexible manipulation of electromagnetic waves, which have the advantages of a low profile and low loss. In particular, the coding metasurface can flexibly manipulate electromagnetic waves through controllable sequence encoding of the coding units to achieve different functions. In this paper, a three-layer active coding metasurface is designed based on vanadium dioxide (VO2), which has an excellent phase transition. For the designed unit cell, the top patterned layer is composed of two split square resonant rings (SSRRs), whose gaps are in opposite directions, and each SSRR is composed of gold and VO2. When VO2 changes from the dielectric state to the metal state, the resonant mode changes from microstrip resonance to LC resonance, correspondingly. According to the Pancharatnam-Berry (P-B) phase, the designed metasurface can actively control terahertz circularly polarized waves in the near field. The metasurface can manipulate the order of the generated orbital angular momentum (OAM) beams: when the dielectric VO2 changes to metal VO2, the order l of the OAM beams generated by the metasurface changes from −1 to −2, and the purity of the generated OAM beams is relatively high. It is expected to have important application values in terahertz wireless communication, radar, and other fields. Full article
(This article belongs to the Special Issue Emerging Trends in Metamaterials and Metasurfaces Research)
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<p>Schematic diagram of the unit cell. (<b>a</b>) The top view and (<b>b</b>) the side view of the unit cell.</p>
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<p>The distributions of electric field intensity and equivalent structural diagrams for the top patterned layer of the unit cell. For the unit cells with <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math> in (<b>a</b>) the dielectric state and (<b>c</b>) the metal state, the corresponding distribution of electric field intensity in the top patterned layer is given. Equivalent structural diagrams of the top layer of the unit cell with (<b>b</b>) the dielectric <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math> and (<b>d</b>) the metal <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
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<p>The reflection characteristics of the unit cells. The reflection amplitude and phase of the unit when <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is in (<b>a</b>) the dielectric state and (<b>b</b>) the metal state for different values of rotation angle <math display="inline"><semantics> <mi>α</mi> </semantics></math>, and the incident wave is the RCP wave in the −<span class="html-italic">z</span> direction.</p>
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<p>The reflection characteristics of the unit cell when <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is in the two different states. For <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math> in the dielectric state, <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math> in the metal state, and without <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, the (<b>a</b>) reflection amplitude and (<b>b</b>) reflection phase of the unit cell (the case of rotation angle <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 0°).</p>
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<p>The schematic diagram of four coding units and their corresponding coding states (“0” or “1”) at a low and a high temperature. (<b>a</b>) Four coding units “0”, “1”, “2”, and “3”; (<b>b</b>) at a low temperature, the coding states for four coding units (the blue part represents the dielectric <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math>); (<b>c</b>) at a high temperature, the coding states for four coding units (the red part represents the metal <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math>).</p>
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<p>Phase distribution of the metasurfaces with the function of generating <span class="html-italic">l</span> = −1 and <span class="html-italic">l</span> = −2 OAM beams (<span class="html-italic">l</span> is the order of the generated OAM beams). Theoretical phase distribution of the metasurfaces generating the (<b>a</b>) <span class="html-italic">l</span> = −1 OAM beam and (<b>d</b>) <span class="html-italic">l</span> = −2 OAM beam; compensation phase distribution of the metasurfaces generating the (<b>b</b>) <span class="html-italic">l</span> = −1 OAM beam and (<b>e</b>) <span class="html-italic">l</span> = −2 OAM beam; phase distribution of the phase-compensated metasurfaces generating the (<b>c</b>) <span class="html-italic">l</span> = −1 OAM beam and (<b>f</b>) <span class="html-italic">l</span> = −2 OAM beam.</p>
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<p>Phase distributions of OAM beams with different orders. Theoretical phase distributions of the (<b>a</b>) <span class="html-italic">l</span> = −1 OAM beam and (<b>c</b>) <span class="html-italic">l</span> = −2 OAM beam; 1-bit coding phase distribution of the (<b>b</b>) <span class="html-italic">l</span> = −1 OAM beam and (<b>d</b>) <span class="html-italic">l</span> = −2 OAM beam.</p>
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<p>The arrangement of the designed OAM manipulation metasurface. The arrangement of (<b>a</b>) 1-bit coding units and (<b>b</b>) units with and without <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
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<p>Near-field simulation results of the designed OAM-manipulating metasurface. For the metasurface, when <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is in the dielectric state, near-field normalization (<b>a</b>) amplitude and the (<b>b</b>) phase and (<b>c</b>) mode purity of the generated <span class="html-italic">l</span> = −1 OAM beam. When <math display="inline"><semantics> <mrow> <mi>V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is in the metal state, the near-field normalization (<b>d</b>) amplitude and (<b>e</b>) phase and (<b>f</b>) mode purity of the generated <span class="html-italic">l</span> = −2 OAM beam.</p>
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11 pages, 380 KiB  
Article
Quantum Limit for the Emittance of Dirac Particles Carrying Orbital Angular Momentum
by Alessandro Curcio, Alessandro Cianchi and Massimo Ferrario
Particles 2024, 7(1), 264-274; https://doi.org/10.3390/particles7010015 - 17 Mar 2024
Viewed by 1324
Abstract
In this article, we highlight that the interaction potential confining Dirac particles in a box must be invariant under the charge conjugation to avoid the Klein paradox, in which an infinite number of negative-energy particles are excited. Furthermore, we derive the quantization rules [...] Read more.
In this article, we highlight that the interaction potential confining Dirac particles in a box must be invariant under the charge conjugation to avoid the Klein paradox, in which an infinite number of negative-energy particles are excited. Furthermore, we derive the quantization rules for a relativistic particle in a cylindrical box, which emulates the volume occupied by a beam of particles with a non-trivial aspect ratio. We apply our results to the evaluation of the quantum limit for emittance in particle accelerators. The developed theory allows the description of quantum beams carrying Orbital Angular Momentum (OAM). We demonstrate how the degeneracy pressure is such to increase the phase–space area of Dirac particles carrying OAM. The results dramatically differ from the classical evaluation of phase–space areas, that would foresee no increase in emittance for beams in a coherent state of OAM. We discuss the quantization of the phase–space cell’s area for single Dirac particles carrying OAM, and, finally, provide an interpretation of the beam entropy as the measure of how much the phase–space area occupied by the beam deviates from its quantum limit. Full article
(This article belongs to the Special Issue Feature Papers for Particles 2023)
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<p><b>Left</b>: Cylindrical coordinates system for this paper. <b>Right</b>: Cylindrical box with transverse radius <span class="html-italic">R</span> and axial length <span class="html-italic">L</span>.</p>
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<p>Occupation of states in the <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>ρ</mi> </msub> <mo>−</mo> <mi>φ</mi> </mrow> </semantics></math> sub-space. The drawn line defines the Fermi level, as the line of maximal transverse momenta.</p>
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<p>Value of <math display="inline"><semantics> <msub> <mi>σ</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> </msub> </semantics></math> for different OAM states.</p>
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<p>Value of <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> </msub> </semantics></math> for different OAM states.</p>
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<p>Value of transverse phase–space correlation for different OAM states.</p>
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13 pages, 3535 KiB  
Article
The Spiral Spectrum of a Laguerre–Gaussian Beam Carrying the Cross-Phase Propagating in Weak-to-Strong Atmospheric Turbulence
by Yunxiao Li, Zhao Zhang, Ruyi Li, Dong Xu, Hao Zhang, Yangjian Cai and Jun Zeng
Photonics 2024, 11(2), 148; https://doi.org/10.3390/photonics11020148 - 4 Feb 2024
Cited by 1 | Viewed by 1371
Abstract
In communication links, the presence of atmospheric turbulence leads to crosstalk between the orbital angular momentum (OAM) states, thereby limiting the performance of information transmission. Thus, knowledge of the effect of turbulence on the spiral spectrum (also named the OAM spectrum) is of [...] Read more.
In communication links, the presence of atmospheric turbulence leads to crosstalk between the orbital angular momentum (OAM) states, thereby limiting the performance of information transmission. Thus, knowledge of the effect of turbulence on the spiral spectrum (also named the OAM spectrum) is of utmost importance in the field of optical communications. However, most of the existing studies are limited to weak turbulence calculation models. In this paper, based on the extended Huygens–Fresnel integral, the analytical expression is derived for the mutual coherence function of a Laguerre–Gaussian beam carrying the cross-phase and propagating through weak-to-strong anisotropic Kolmogorov atmospheric turbulence; subsequently, the analytical expression is used to study the behavior of the spiral spectrum. The discrepancies in the spiral spectrum between weak and strong turbulence are comparatively studied. The influences of the cross-phase and the anisotropy of turbulence on the spiral spectrum are investigated through numerical examples. Our results reveal that the cross-phase determines the distribution of the spiral spectrum. The spiral spectrum can be tuned to multiple OAM modes through the adaptation of the cross-phase coefficient. Moreover, increasing the cross-phase coefficient can reduce both the discrepancies of the spiral spectrum under two computational methods and the effects of the anisotropic factors of turbulence on the spiral spectrum. Full article
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<p>Schematic diagram of (<b>a</b>) the single-phase screen perturbation method propagation system and (<b>b</b>) the extended Huygens–Fresnel method propagation system. (<b>c</b>,<b>d</b>) Schematic for the Kolmogorov cascade theory of turbulence. (<b>c</b>) Isotropic turbulence. (<b>d</b>) Anisotropic turbulence. <span class="html-italic">L</span><sub>0</sub> and <span class="html-italic">l</span><sub>0</sub> denote the outer and inner scales of turbulence, respectively. Turbulent cells (eddies) between the scale size <span class="html-italic">L</span><sub>0</sub> and <span class="html-italic">l</span><sub>0</sub> form the inertial subrange. <span class="html-italic">r</span>, <span class="html-italic">R<sub>a</sub></span>, <span class="html-italic">R<sub>b</sub></span> and <span class="html-italic">R<sub>c</sub></span> denote the semi-principal axes of turbulent cells in different directions, respectively.</p>
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<p>The effect of the cross-phase on the spiral spectrum and of an LG beam in the source plane. (<b>a</b>) <span class="html-italic">u</span> = 0 m<sup>−2</sup>; (<b>b</b>) <span class="html-italic">u</span> = 5 × 10<sup>3</sup> m<sup>−2</sup>; (<b>c</b>) <span class="html-italic">u</span> = 4 × 10<sup>4</sup> m<sup>−2</sup>; (<b>d</b>) <span class="html-italic">u</span> = 5 × 10<sup>4</sup> m<sup>−2</sup>.</p>
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<p>Spiral spectrum of an LG beam carrying the cross-phase with different factors <span class="html-italic">u</span> in weak-to-strong isotropic turbulence (<span class="html-italic">μ<sub>x</sub> = μ<sub>y</sub> = μ<sub>z</sub></span> = 1) using different propagation models. Method A corresponds to the single-phase screen perturbation (SPSP) propagation model; Method B corresponds to the extended Huygens–Fresnel (eHF) propagation model. (<b>a1</b>–<b>d1</b>) <span class="html-italic">u</span> = 0 m<sup>−2</sup>; (<b>a2</b>–<b>d2</b>) <span class="html-italic">u</span> = 5 × 10<sup>3</sup> m<sup>−2</sup>; (<b>a3</b>–<b>d3</b>) <span class="html-italic">u</span> = 4 × 10<sup>4</sup> m<sup>−2</sup>.</p>
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<p>Variation in <span class="html-italic">P<sub>m</sub></span><sub>=<span class="html-italic">l</span></sub> of an LG beam carrying the cross-phase with different factors <span class="html-italic">u</span> in isotropic turbulence (<span class="html-italic">μ<sub>x</sub> = μ<sub>y</sub> = μ<sub>z</sub></span> = 1) as a function of propagation distance <span class="html-italic">z</span>. A: single-phase screen perturbation propagation model; B: extended Huygens–Fresnel propagation model.</p>
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<p>Spiral spectrum of an LG beam carrying the cross-phase in anisotropic turbulence with different values of <span class="html-italic">μ<sub>x/</sub>μ<sub>y</sub></span> for <span class="html-italic">u</span> = 5 × 10<sup>3</sup> m<sup>−2</sup>. (<b>a1</b>–<b>d1</b>) <span class="html-italic">z</span> = 500 m; (<b>a2</b>–<b>d2</b>) <span class="html-italic">z</span> = 1500 m; (<b>a3</b>–<b>d3</b>) <span class="html-italic">z</span> = 3000 m.</p>
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<p>Variation in <span class="html-italic">P<sub>m</sub></span><sub>=<span class="html-italic">l</span></sub> of an LG beam carrying the cross-phase with different factors <span class="html-italic">u</span> in anisotropic turbulence with different values of <span class="html-italic">μ<sub>x/</sub>μ<sub>y</sub></span> as a function of propagation distance <span class="html-italic">z</span>. (<b>a</b>) <span class="html-italic">u</span> = 0 m<sup>−2</sup>; (<b>b</b>) <span class="html-italic">u</span> = 5 × 10<sup>3</sup> m<sup>−2</sup>; (<b>c</b>) <span class="html-italic">u</span> = 4 × 10<sup>4</sup> m<sup>−2</sup>.</p>
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24 pages, 4888 KiB  
Review
Research Progress on Router Devices for the OAM Optical Communication
by Binbin Wang, Xizheng Zhang, Jinlong Tian, Badreddine Merabet, Zhixiang Li, Syed Afaq Ali Shah, Yi Lei, Bingyi Liu, Kai Guo and Zhongyi Guo
Sensors 2024, 24(3), 944; https://doi.org/10.3390/s24030944 - 1 Feb 2024
Cited by 4 | Viewed by 2230
Abstract
Vortex beams carrying orbital angular momentum (OAM) provide a new degree of freedom for light waves in addition to the traditional degrees of freedom, such as intensity, phase, frequency, time, and polarization. Due to the theoretically unlimited orthogonal states, the physical dimension of [...] Read more.
Vortex beams carrying orbital angular momentum (OAM) provide a new degree of freedom for light waves in addition to the traditional degrees of freedom, such as intensity, phase, frequency, time, and polarization. Due to the theoretically unlimited orthogonal states, the physical dimension of OAM is capable of addressing the problem of low information capacity. With the advancement of the OAM optical communication technology, OAM router devices (OAM-RDs) have played a key role in significantly improving the flexibility and practicability of communication systems. In this review, major breakthroughs in the OAM-RDs are summarized, and the latest technological standing is examined. Additionally, a detailed account of the recent works published on techniques related to the OAM-RDs has been categorized into five areas: channel multicasting, channel switching, channel filtering, channel hopping, and channel adding/extracting. Meanwhile, the principles, research methods, advantages, and disadvantages are discussed and summarized in depth while analyzing the future development trends and prospects of the OAM-RDs. Full article
(This article belongs to the Special Issue Novel Technology in Optical Communications)
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<p>Principle or experimental setup of OAM-RDs based on OAM channel multicasting (I); (<b>a</b>) experimental setup for OAM-mode multicasting [<a href="#B104-sensors-24-00944" class="html-bibr">104</a>], Col: Collimator; (<b>b</b>) the concept of tunable OTDL system using the modal-dependent delays [<a href="#B107-sensors-24-00944" class="html-bibr">107</a>]; (<b>c1</b>,<b>c2</b>) the multiplexed vortex state array [<a href="#B108-sensors-24-00944" class="html-bibr">108</a>]: (<b>c1</b>) depicts the concept of generating a multiplexed vortex state array using a phase-only hologram, and (<b>c2</b>) shows the experimental setup, BS, and beam splitter; L1~L4, lenses; CCD1&amp;CCD2, infrared CCD camera; AS, aperture stop.</p>
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<p>Working principle and experimental setup of OAM-RDs based on OAM channel multicasting (II) [<a href="#B109-sensors-24-00944" class="html-bibr">109</a>]: (<b>a</b>) principle of OAM neural communication, and (<b>b</b>) experimental setup.</p>
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<p>Principle or experimental setup of OAM-RDs based on OAM channel switching(I) (<b>a</b>) Functional block diagram of the 2 × 2 OAM-based switch [<a href="#B122-sensors-24-00944" class="html-bibr">122</a>]; (<b>b</b>) experimental setup of reconfigurable 4 × 4 OAM mode switching, space switching, and joint OAM mode and space switching [<a href="#B123-sensors-24-00944" class="html-bibr">123</a>]; (<b>c</b>) the schematic diagram of multi-channel MSI [<a href="#B118-sensors-24-00944" class="html-bibr">118</a>]; (<b>d</b>) experimental setup for the mode generation, dynamic switching, and detection between OAM modes. OC, 50:50 optical coupler; PC, polarization controller; H, holder; R, rotator; Obj, objective; ATT, attenuator; BS, beam splitter; Col, collimator; SLM, spatial light modulator; CCD, charge-coupled device [<a href="#B118-sensors-24-00944" class="html-bibr">118</a>].</p>
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<p>Principle or experimental setup of OAM-RDs based on OAM channel switching(II): (<b>a</b>) schematic of OAM-RD for intra-datacenter optical interconnects [<a href="#B124-sensors-24-00944" class="html-bibr">124</a>]; (<b>b1</b>,<b>b2</b>) the reconfigurable optical switching based on OAM [<a href="#B126-sensors-24-00944" class="html-bibr">126</a>]; (<b>b1</b>) dual-area mirror and principle of separating multiplexed beams; and (<b>b2</b>) principle of OAM-based optical switching.</p>
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<p>Principle or experimental setup of OAM-RDs based on OAM channel filtering: (<b>a</b>) the tunable mode-blocking filter [<a href="#B134-sensors-24-00944" class="html-bibr">134</a>]. (<b>b</b>) Schematic diagram of OAM filter based on multiple-beam interference [<a href="#B136-sensors-24-00944" class="html-bibr">136</a>]. (<b>c</b>) Schematic diagram of the transmission loss in the righthanded CLPG [<a href="#B137-sensors-24-00944" class="html-bibr">137</a>].</p>
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<p>Principle or experimental setup of OAM-RDs based on OAM channel hopping: (<b>a</b>) spatial domain channel hopping principle based on OAM mode [<a href="#B145-sensors-24-00944" class="html-bibr">145</a>]; (<b>b</b>) the schematic diagram MFH system model [<a href="#B146-sensors-24-00944" class="html-bibr">146</a>].</p>
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<p>Principle or experimental setup of OAM-RD for OAM channel adding/extracting: (<b>a</b>) concept of OAM channel add/drop multiplexing [<a href="#B152-sensors-24-00944" class="html-bibr">152</a>]; (<b>b</b>) the schematic of the modified MZI [<a href="#B154-sensors-24-00944" class="html-bibr">154</a>], BS: beam splitter, M: mirror, and DP: Dove prism; (<b>c</b>) concept of OADM for OAM add-drop multiplexing [<a href="#B155-sensors-24-00944" class="html-bibr">155</a>].</p>
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11 pages, 3420 KiB  
Communication
Performance of Orbital Angular Momentum Communication for a Non-Uniformly Correlated High-Order Bessel–Gaussian Beam in a Turbulent Atmosphere
by Zihan Cong, Hui Zhang, Yaru Gao, Yangjian Cai and Yangsheng Yuan
Photonics 2024, 11(2), 131; https://doi.org/10.3390/photonics11020131 - 30 Jan 2024
Viewed by 1207
Abstract
We derived the formula for the detection probability, signal-to-noise ratio (SNR), and average bit error rate (BER) for the signal orbital angular momentum (OAM) state carried via non-uniformly correlated high-order Bessel–Gaussian beam propagation in a turbulent atmosphere. The wavelength, receiver aperture, beam width, [...] Read more.
We derived the formula for the detection probability, signal-to-noise ratio (SNR), and average bit error rate (BER) for the signal orbital angular momentum (OAM) state carried via non-uniformly correlated high-order Bessel–Gaussian beam propagation in a turbulent atmosphere. The wavelength, receiver aperture, beam width, strength of the turbulent atmosphere, and topological charge effect on detection probability, SNR, and average BER of the signal OAM state were demonstrated numerically. The results show that the signal OAM state with low topological charge, a small receiver aperture, a narrow beam width, and a long wavelength can improve the performance of optical communications systems under conditions of weak atmospheric turbulence. Our results will be useful in long-distance free space optical (FSO) communications. Full article
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<p>Detection probability of the OAM mode for non-uniformly correlated high-order Bessel–Gaussian beams in a turbulent atmosphere with different (<b>a</b>) topological charge differences |Δ<span class="html-italic">l</span>| and (<b>b</b>) propagation distances <span class="html-italic">z</span>.</p>
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<p>Detection probability of the signal OAM state for the non-uniformly correlated high-order Bessel–Gaussian beams at the different receiving aperture diameters (D).</p>
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<p>Detection probability of the different signal OAM states carried by the non-uniformly correlated high-order Bessel–Gaussian beams in a turbulent atmosphere.</p>
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<p>Detection probability of the signal OAM state carried by the non-uniformly correlated high-order Bessel–Gaussian beams in a turbulent atmosphere for the different wavelengths studied.</p>
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<p>Detection probability of the signal OAM state carried by the non-uniformly correlated high-order Bessel–Gaussian beams in the turbulent atmosphere for the different beam widths analyzed.</p>
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<p>SNR of the different signal OAM states carried by the non-uniformly correlated high-order Bessel–Gaussian beams in a turbulent atmosphere against the beam width.</p>
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<p>Average BER of the different signal OAM states carried by the non-uniformly correlated high-order Bessel–Gaussian beams in the turbulent atmosphere against the beam width.</p>
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<p>(<b>a</b>) SNR and (<b>b</b>) average BER of the signal OAM state carried by the non-uniformly correlated high-order Bessel–Gaussian beams with different beam widths against the strength of the turbulent atmosphere.</p>
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15 pages, 5867 KiB  
Article
Parallel Interactive Attention Network for Short-Term Origin–Destination Prediction in Urban Rail Transit
by Wenzhong Zhou, Chunhai Gao and Tao Tang
Appl. Sci. 2024, 14(1), 100; https://doi.org/10.3390/app14010100 - 21 Dec 2023
Viewed by 855
Abstract
Short-term origin–destination (termed as OD) prediction is crucial to improve the operation of urban rail transit (termed as URT). The latest research results show that deep learning can effectively improve the performance of short-term OD prediction and meet the real-time requirements. However, many [...] Read more.
Short-term origin–destination (termed as OD) prediction is crucial to improve the operation of urban rail transit (termed as URT). The latest research results show that deep learning can effectively improve the performance of short-term OD prediction and meet the real-time requirements. However, many advanced neural network design ideas have not been fully applied in the field of short-term OD prediction in URT. In this paper, a novel parallel interactive attention network (termed as PIANet) for short-term OD prediction in URT is proposed to further improve the short-term OD prediction accuracy. In the proposed PIANet, a novel omnidirectional attention module (termed as OAM) is proposed to improve the representational power of the network by calculating the feature weights in the channel–spatial dimension. Moreover, a simple yet effective feature interaction is proposed to improve the feature utilization. Based on the two real-world datasets from the Beijing subway, the comparative experiments demonstrate that the proposed PIANet outperforms the state-of-the-art deep learning methods for short-term OD prediction in URT, and the ablation studies demonstrate that the proposed OAMs and feature interaction play an important role in improving the short-term OD prediction accuracy. Full article
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<p>Temporal relationship between the historical OD data and the predicted OD matrix.</p>
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<p>The architecture of omnidirectional attention module.</p>
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<p>The architecture of the dense compression attention block.</p>
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<p>The overall architecture of the parallel interactive attention network.</p>
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<p>Comparisons of the RMSE, MAE, and SMAPE at each time interval during the morning peak hours (i.e., 7:30–9:10) among the proposed PIANet and the comparison methods in BJSubway2021.</p>
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<p>Comparisons of the RMSE, MAE, and SMAPE at each time interval during the morning peak hours (i.e., 7:30–9:10) among the proposed PIANet and the comparison methods in BJSubway2022.</p>
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<p>Comparisons of convergence curves of best validation RMSE among the proposed PIANet and the comparison methods in BJSubway2021 and BJSubway2022.</p>
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<p>Comparisons of convergence curves of best validation RMSE among the proposed PIANet and its variants in BJSubway2021 and BJSubway2022.</p>
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11 pages, 2176 KiB  
Article
Deep Mutual Learning-Based Mode Recognition of Orbital Angular Momentum
by Tan Qu, Zhiming Zhao, Yan Zhang, Jiaji Wu and Zhensen Wu
Photonics 2023, 10(12), 1357; https://doi.org/10.3390/photonics10121357 - 8 Dec 2023
Viewed by 1115
Abstract
Due to its orbital angular momentum (OAM), optical vortex has been widely used in communications and LIDAR target detection. The OAM mode recognition based on deep learning is mostly based on the basic convolutional neural network. To ensure high-precision OAM state detection, a [...] Read more.
Due to its orbital angular momentum (OAM), optical vortex has been widely used in communications and LIDAR target detection. The OAM mode recognition based on deep learning is mostly based on the basic convolutional neural network. To ensure high-precision OAM state detection, a deeper network structure is required to overcome the problem of similar light intensity distribution of different superimposed vortex beams and the effect of atmospheric turbulence disturbance. However, the large number of parameters and the computation of the OAM state detection network conflict with the requirements of deploying optical communication system equipment. In this paper, an online knowledge distillation scheme is selected to achieve an end-to-end single-stage training and the inter-class dark knowledge of similar modes are fully utilized. An optical vortex OAM state detection technique based on deep mutual learning (DML) is proposed. The simulation results show that after mutual learning training, a small detection network with higher accuracy can be obtained, which is more suitable for terminal deployment. Based on the scalability of the number of networks in the DML queue, it provides a new possibility to further improve the detection accuracy of the optical communication. Full article
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<p>Transfer of dark knowledge between classical knowledge distillation classes when detecting superimposed vortex light.</p>
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<p>Transfer of dark knowledge between deep mutual learning classes when detecting superimposed vortex light.</p>
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<p>Framework of OAM mode recognition technology based on DML.</p>
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<p>Structure of CNN-based OAM mode recognition network.</p>
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<p>Light intensity distribution of similar multi-mode OAM beam.</p>
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<p>Variation in the recognition accuracy with the training process of two networks.</p>
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<p>Variation in the recognition accuracy of small CNN networks with different DML networks queue.</p>
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10 pages, 1824 KiB  
Article
Dense Space-Division Multiplexing Exploiting Multi-Ring Perfect Vortex
by Xing Liu, Duo Deng, Zhenjun Yang and Yan Li
Sensors 2023, 23(23), 9533; https://doi.org/10.3390/s23239533 - 30 Nov 2023
Cited by 1 | Viewed by 997
Abstract
Vortex beams carrying orbital angular momentum (OAM) have gained much interest in optical communications because they can be used to expand the number of multiplexing channels and greatly improve the transmission capacity. However, the number of states used for OAM-based communication is generally [...] Read more.
Vortex beams carrying orbital angular momentum (OAM) have gained much interest in optical communications because they can be used to expand the number of multiplexing channels and greatly improve the transmission capacity. However, the number of states used for OAM-based communication is generally limited by the imperfect OAM generation, transmission, and demultiplexing methods. In this work, we proposed a dense space-division multiplexing (DSDM) scheme to further increase the transmission capacity and transmission capacity density of free space optical communications with a small range of OAM modes exploiting a multi-ring perfect vortex (MRPV). The proposed MRPV is generated using a pixel checkerboard complex amplitude modulation method that simultaneously encodes amplitude and phase information in a phase-only hologram. The four rings of the MRPV are mutually independent channels that transmit OAM beams under the condition of occupying only one spatial position, and the OAM mode transmitted in these spatial channels can be efficiently demodulated using a multilayer annular aperture. The effect of atmospheric turbulence on the MRPV was also analyzed, and the results showed that the four channels of the MRPV can be effectively separated under weak turbulence conditions. Under the condition of limited available space and OAM states, the proposed DSDM strategy exploiting MRPV might inspire wide optical communication applications exploiting the space dimension of light beams. Full article
(This article belongs to the Special Issue Novel Technology in Optical Communications)
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<p>The schematic diagrams of (<b>a</b>) the pixel checkerboard complex amplitude modulation method and (<b>b</b>) the optical field with controllable amplitude and phase.</p>
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<p>The MRPV with TCs <span class="html-italic">l</span><sub>1</sub> = 1, <span class="html-italic">l</span><sub>2</sub> = 2, <span class="html-italic">l</span><sub>3</sub> = 3, and <span class="html-italic">l</span><sub>4</sub> = 4 and its (<b>a</b>) phase mask, (<b>b</b>) transverse intensity profile, (<b>c</b>) interference pattern with a spherical wave, (<b>d</b>) experimental pattern. The MRPV with <span class="html-italic">l</span><sub>1</sub> = −1, <span class="html-italic">l</span><sub>2</sub> = 3, <span class="html-italic">l</span><sub>3</sub> = −5, and <span class="html-italic">l</span><sub>4</sub> = 7, and its (<b>e</b>) phase mask, (<b>f</b>) transverse intensity profile, (<b>g</b>) interference pattern with a spherical wave, (<b>h</b>) experimental pattern.</p>
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<p>(<b>a</b>) Schematic diagram of the experimental setup, (<b>b</b>) multilayer annular aperture, (<b>c</b>) the phase of the demultiplexing array.</p>
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<p>Demultiplexing of MRPVs through simulation and experiment. (<b>a1</b>–<b>d1</b>), (<b>a2</b>–<b>d2</b>) the MRPV with TCs <span class="html-italic">l</span><sub>1</sub> = 1, <span class="html-italic">l</span><sub>2</sub> = 2, <span class="html-italic">l</span><sub>3</sub> = 3, and <span class="html-italic">l</span><sub>4</sub> = 4, (<b>e1</b>–<b>h1</b>), (<b>e2</b>–<b>h2</b>) the MRPV with TCs <span class="html-italic">l</span><sub>1</sub> = −4, <span class="html-italic">l</span><sub>2</sub> = −5, <span class="html-italic">l</span><sub>3</sub> = −6, and <span class="html-italic">l</span><sub>4</sub> = −7. The incident OAM states are marked by the bule circles.</p>
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<p>Demultiplexing of the MRPV (<b>a</b>) before transmission, (<b>b</b>) with weak turbulence, (<b>c</b>) with moderate turbulence, (<b>d</b>) with strong turbulence.</p>
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13 pages, 5267 KiB  
Article
Determining the Orbital Angular Momentum of a Vortex Beam Using Strong Field Ionization
by Harrison Pasquinilli, Alex Schimmoller, Spencer Walker and Alexandra S. Landsman
Photonics 2023, 10(12), 1322; https://doi.org/10.3390/photonics10121322 - 29 Nov 2023
Cited by 2 | Viewed by 1780
Abstract
While interferometric methods exist for classifying vortex states of light, these techniques usually require destroying the beam of interest to determine the light’s OAM. A recent two-color pump-probe experiment employed strong field ionization and beam sculpting to classify vortex beams. Here, we propose [...] Read more.
While interferometric methods exist for classifying vortex states of light, these techniques usually require destroying the beam of interest to determine the light’s OAM. A recent two-color pump-probe experiment employed strong field ionization and beam sculpting to classify vortex beams. Here, we propose an alternative strong-field method for distinguishing OAM states of light which does not require beam sculpting and instead utilizes a noncollinear terahertz standing wave to probe ionized electrons. We then use classical trajectory Monte Carlo (CTMC) methods to simulate strong-field ionization of helium under this configuration with the terahertz field both on and off. We find that the resulting electron momenta distributions can be used to extract the OAM of the beam, as long as the vortex beam spot size does not exceed 1/4 the terahertz pulse’s wavelength. Full article
(This article belongs to the Special Issue Atomic and Molecular Processes in Strong Laser Fields)
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<p>Schematic view of the proposed experimental set-up. The infrared vortex beam of Equation (<a href="#FD2-photonics-10-01322" class="html-disp-formula">2</a>) to be characterized is polarized in the <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="bold">x</mi> <mo stretchy="false">^</mo> </mover> </semantics></math> direction and propagates along the <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="bold">z</mi> <mo stretchy="false">^</mo> </mover> </semantics></math> axis. The pulse strikes a helium gas sample at its focus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>z</mi> <mo>=</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math> and triggers ionization. An additional terahertz standing wave (Equation (<a href="#FD4-photonics-10-01322" class="html-disp-formula">4</a>)) propagating along the <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="bold">x</mi> <mo stretchy="false">^</mo> </mover> </mrow> </semantics></math>-axis irradiates the sample and imprints extra momentum onto ionized electrons along its polarization axis <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="bold">y</mi> <mo stretchy="false">^</mo> </mover> </semantics></math>. The value of this additional momentum changes depending on the location of the atom to be ionized relative to the vortex center and allows for the determination of OAM.</p>
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<p>Intensity profiles for non-vortex (<b>a</b>) and vortex (<b>b</b>) beams. (<b>a</b>) Gaussian beam with beam waist <math display="inline"><semantics> <mrow> <msub> <mi>w</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>30</mn> </mrow> </semantics></math> microns. (<b>b</b>) Laguerre–Gaussian beam with the same beam waist and <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. Insets show the accompanying phase profiles for each beam. Red dots (i–iv) indicate points of interest for simulations. The intensity color mapping is normalized to the peak of the electric field.</p>
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<p>A combined field profile of the two beams in the <span class="html-italic">x</span>-<span class="html-italic">y</span> plane at <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (<b>left</b>), and <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math> (<b>right</b>). The color plot depicts the field intensity profile normalized to the peak of the LG beam. Overlaid on both beams is the field profile in <span class="html-italic">x</span> of the THz beam. The spatial profile is properly depicted, and the amplitude is displayed in arbitrary units.</p>
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<p>Photo-electron momentum distributions (PMDs) resulting from strong field ionization by circularly polarized laser pulses. Figure indexing (<b>i</b>–<b>iv</b>) corresponds to the ionization locations and beam profiles depicted in <a href="#photonics-10-01322-f002" class="html-fig">Figure 2</a>.</p>
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<p>Photo-electron momentum distributions (PMDs) resulting from strong field ionization by linearly polarized laser pulses. Figure indexing (<b>i</b>–<b>iv</b>) corresponds to the ionization locations and beam profiles depicted in <a href="#photonics-10-01322-f002" class="html-fig">Figure 2</a>.</p>
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<p>Photo-electron momentum distributions (PMDs) resulting from strong field ionization by (<b>a</b>) Gaussian and (<b>b</b>,<b>c</b>) Laguerre–Gaussian circularly polarized laser pulses. Here, electrons may be ionized from anywhere within the <math display="inline"><semantics> <mover accent="true"> <mi>x</mi> <mo stretchy="false">^</mo> </mover> </semantics></math>-<math display="inline"><semantics> <mover accent="true"> <mi>y</mi> <mo stretchy="false">^</mo> </mover> </semantics></math> plane.</p>
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<p>Results of CTMC calculations with the terahertz field included. (<b>a</b>) Distribution of ionized photo-electrons in the <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="bold">y</mi> <mo stretchy="false">^</mo> </mover> </mrow> </semantics></math>-direction parallel to the THz field polarization determined using Equation (<a href="#FD12-photonics-10-01322" class="html-disp-formula">12</a>) for pumping LG beams containing OAM <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mn>8</mn> </mrow> </semantics></math>. (<b>b</b>) Standard deviation values corresponding to the momentum distribution from panel (<b>a</b>). Blue points correspond to the data shown in panel (<b>a</b>). Red points correspond to an additional approximation valid for short electron excursion. Fields are held constant (in space) at the coordinate of parent ions and momenta are determined from Equation (<a href="#FD6-photonics-10-01322" class="html-disp-formula">6</a>). <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math> trajectories are sampled for each value of <span class="html-italic">ℓ</span>.</p>
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12 pages, 5137 KiB  
Article
Influence of High-Order Twisting Phases on Polarization States and Optical Angular Momentum of a Vector Light Field
by Baoyin Liu, Yingqi Huang, Caixia Liu, Shu-Dan Wu, Khian-Hooi Chew and Rui-Pin Chen
Photonics 2023, 10(10), 1099; https://doi.org/10.3390/photonics10101099 - 29 Sep 2023
Cited by 1 | Viewed by 998
Abstract
This study investigates the influence of high-order twisting phases on polarization states and optical angular momentum of a vector light field with locally linear polarization and a hybrid state of polarization (SoP). The twisted vector optical field (TVOF) is experimentally generated based on [...] Read more.
This study investigates the influence of high-order twisting phases on polarization states and optical angular momentum of a vector light field with locally linear polarization and a hybrid state of polarization (SoP). The twisted vector optical field (TVOF) is experimentally generated based on the orthogonal polarization bases with high-order twisting phases. The initial SoP of a TVOF modulated by the high-order twisting phase possesses various symmetric distributions. The propagation properties of a high-order TVOF with locally linear polarization and hybrid SoP are explored, including the intensity compression, expansion, and conversion between the linear and circular polarization components. In particular, orbital angular momentum (OAM) appears in a high-order TVOF during propagation where no OAM exists in the initial field. The variation of OAM distribution in cross-section becomes more frequent with the increase of the twisting phase order. In addition, a non-symmetric OAM distribution appears in a non-isotropic TVOF, leading to the rotation of the beam around the propagation axis during propagation. The optical energy flow distribution of a high-order TVOF provides a more profound understanding of the propagation dynamics of high-order TVOF. These results provide a new approach for optical field manipulation in a high-order TVOF. Full article
(This article belongs to the Special Issue Recent Advances in Diffractive Optics)
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<p>Phase distributions of the twisting phase: (<b>a</b>) Low-order twisting phase. (<b>b</b>) High-order twisting phase with <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 2. (<b>c</b>) High-order twisting phase with <span class="html-italic">p</span> = 2, <span class="html-italic">q</span> = 2. (<b>d</b>) High-order twisting phase with <span class="html-italic">p</span> = 2, <span class="html-italic">q</span> = 4.</p>
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<p>Schematic of the experimental setup. L1–L5: lenses; SLM: spatial light modulator; AP: aperture; WP: (λ/4 or λ/2) wave plate; RG: Ronchi grating; P: polarizer; CCD: charged-coupled device camera.</p>
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<p>The Stokes parameters of the wisted vector optical field (TVOF) obtained in the experiment, <span class="html-italic">σ<sub>x</sub></span> = <span class="html-italic">σ<sub>y</sub></span> = 0.9 mm. (<b>a</b>) <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 1, <span class="html-italic">u</span> = 12 × 10<sup>6</sup>, Δ<span class="html-italic">θ</span> = π/2; (<b>b</b>) <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 2, <span class="html-italic">u</span> = 12 × 10<sup>9</sup>, Δ<span class="html-italic">θ</span> = 0.</p>
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<p>The Stokes parameters of twisted vector beams under different modulation parameters. The parameters in the figure from columns 1 to 4 are, sequentially: <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 1, <span class="html-italic">u</span> = 12 × 10<sup>6</sup>; <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 2, <span class="html-italic">u</span> = 12 × 10<sup>9</sup>; <span class="html-italic">p</span> = 2, <span class="html-italic">q</span> = 4, <span class="html-italic">u</span> = 12 × 10<sup>18</sup>; <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 2, <span class="html-italic">u</span> = 12 × 10<sup>9</sup>. Plots in columns 1–3 represent isotropic beams with <span class="html-italic">σ<sub>x</sub></span> = <span class="html-italic">σ<sub>y</sub></span> = 0.9 mm, while column 4 represents a non-isotropic beam with 2<span class="html-italic">σ<sub>x</sub></span> = <span class="html-italic">σ<sub>y</sub></span> = 1.8 mm. (<b>a</b>) Locally linear polarized light field; (<b>b</b>) hybrid polarized light field. The state of polarization (SoP) distributions are also represented by the arrows in <span class="html-italic">S</span><sub>0</sub> plots (black lines denote linear polarizations). The green and red ellipses denote left- and right-circular polarization, respectively.</p>
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<p>The Stokes parameters of various TVOF during transmission: (<b>a</b>) isotropic (<span class="html-italic">σ<sub>x</sub></span> = <span class="html-italic">σ<sub>y</sub></span> = 0.9 mm) locally linearly polarized twisted vector optical beam, <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 1, <span class="html-italic">u</span> = 12 × 10<sup>6</sup>; (<b>b</b>) isotropic (<span class="html-italic">σ<sub>x</sub></span> = <span class="html-italic">σ<sub>y</sub></span> = 0.9 mm) hybrid-polarized twisted vector optical beam, <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 2, <span class="html-italic">u</span> = 12 × 10<sup>9</sup>; (<b>c</b>) non-isotropic (2<span class="html-italic">σ<sub>x</sub></span> = <span class="html-italic">σ<sub>y</sub></span> = 1.8 mm) locally linearly polarized twisted vector optical beam, <span class="html-italic">p</span> = 2, q = 2, <span class="html-italic">u</span> = 12 × 10<sup>12</sup>. The SoP distributions are also presented by the arrows in <span class="html-italic">S</span><sub>0</sub> plots (black lines denote linear polarizations). The green and red ellipses denote left- and right-circular polarization, respectively.</p>
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<p>The OAM evolution of TVOF under different parameters: (<b>a</b>) isotropic (<span class="html-italic">σ<sub>x</sub></span> = <span class="html-italic">σ<sub>y</sub></span> = 0.9 mm), locally linearly polarized; (<b>b</b>) isotropic (<span class="html-italic">σ<sub>x</sub></span> = <span class="html-italic">σ<sub>y</sub></span> = 0.9 mm), hybrid-polarized; (<b>c</b>) non-isotropic (2<span class="html-italic">σ<sub>x</sub></span> = <span class="html-italic">σ<sub>y</sub></span> = 1.8 mm), locally linearly polarized. The first row: <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 1; second row: <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 2; third row: <span class="html-italic">p</span> =2, <span class="html-italic">q</span> = 2.</p>
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<p>The optical energy flows of TVOF with various order twisting phases in different propagation distances. The parameters are similar to those in <a href="#photonics-10-01099-f006" class="html-fig">Figure 6</a>, the white arrows indicate the directions of optical energy flow.</p>
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<p>Evolution of the field and SoP of high-order twisted vector beams with <span class="html-italic">m</span> = 2 and different orders of twisting phases: (<b>a</b>) <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 1, <span class="html-italic">u</span> = 12 × 10<sup>6</sup>; (<b>b</b>) <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 2, <span class="html-italic">u</span> = 12 × 10<sup>9</sup>; (<b>c</b>) <span class="html-italic">p</span> = 1, <span class="html-italic">q</span> = 3, <span class="html-italic">u</span> = 12 × 10<sup>12</sup>; (<b>d</b>) <span class="html-italic">p</span> = 2, <span class="html-italic">q</span> = 2, <span class="html-italic">u</span> = 12 × 10<sup>12</sup>. The SoP distributions are also presented by the arrows in plots (black lines denote linear polarizations). The green and red ellipses denote left- and right-circular polarization, respectively.</p>
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12 pages, 2413 KiB  
Article
Controlling the Spin Hall Effect in the Sharp Focus of an Axial Superposition of Two Optical Vortices with Left- and Right-Handed Circular Polarization
by Victor V. Kotlyar, Anton G. Nalimov and Alexey A. Kovalev
Appl. Sci. 2023, 13(14), 8466; https://doi.org/10.3390/app13148466 - 21 Jul 2023
Viewed by 990
Abstract
We consider sharp focusing of an axial superposition of two optical vortices with identical topological charges, but different amplitudes and circular polarizations of different signs. The ratio of the amplitudes of the two beams is a parameter. When this parameter changes, the polarization [...] Read more.
We consider sharp focusing of an axial superposition of two optical vortices with identical topological charges, but different amplitudes and circular polarizations of different signs. The ratio of the amplitudes of the two beams is a parameter. When this parameter changes, the polarization state of the superposition changes from linear polarization to right-hand circular polarization. Based on the Richards–Wolf theory, exact expressions are obtained for the longitudinal components of the spin angular momentum (SAM) density and orbital angular momentum (OAM) density at the focus of the considered superposition. It follows from these expressions that the sum of the total longitudinal components of the SAM and OAM is conserved upon focusing, and also that, due to the spin-orbit conversion, the total longitudinal component of the SAM decreases during focusing, while the total longitudinal component of the OAM increases by the same amount. By changing the ratio of the amplitudes of the constituent beams from 1 to 0, one can change the value of the spin-orbit conversion from zero (for linear polarization) to a maximum (for circular polarization). Also, by changing this parameter, one can control the spin Hall effect at the focus, which takes place at the focus of the considered beam. This study can be applied for controlling the rotation velocity of microparticles trapped in the focus. Full article
(This article belongs to the Special Issue Advances in Optical and Optoelectronic Devices and Systems)
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Figure 1
<p>Dependences of <math display="inline"><semantics><mrow><msub><mover accent="true"><mi>S</mi><mo>^</mo></mover><mi>z</mi></msub><mo>/</mo><mi>W</mi></mrow></semantics></math> (curve 1) and <math display="inline"><semantics><mrow><msub><mover accent="true"><mi>L</mi><mo>^</mo></mover><mi>z</mi></msub><mo>/</mo><mi>W</mi></mrow></semantics></math> (curve 2) on the distance <span class="html-italic">z</span> for a non-vortex field (1) with <span class="html-italic">n</span> = 0 (<b>a</b>) and for an optical vortex with a topological charge <span class="html-italic">n</span> = 1 (<b>b</b>) and at <span class="html-italic">α</span> = 0.</p>
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<p>The dependence of <math display="inline"><semantics><mrow><msub><mover accent="true"><mi>S</mi><mo>^</mo></mover><mi>z</mi></msub><mo>/</mo><mi>W</mi></mrow></semantics></math> (curve 1) and <math display="inline"><semantics><mrow><msub><mover accent="true"><mi>L</mi><mo>^</mo></mover><mi>z</mi></msub><mo>/</mo><mi>W</mi></mrow></semantics></math> (curve 2) on <span class="html-italic">α</span> after the spherical lens (or zone plate) for the initial field (1) at <span class="html-italic">n</span> = 0 (<b>a</b>) and <span class="html-italic">n</span> = 1 (<b>b</b>).</p>
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<p>Dependences of <math display="inline"><semantics><mrow><msub><mover accent="true"><mi>S</mi><mo>^</mo></mover><mi>z</mi></msub><mo>/</mo><mi>W</mi></mrow></semantics></math> (curve 1), <math display="inline"><semantics><mrow><msub><mover accent="true"><mi>L</mi><mo>^</mo></mover><mi>z</mi></msub><mo>/</mo><mi>W</mi></mrow></semantics></math> (curve 2) and their sum (curve 3) on the focal length <span class="html-italic">f</span> of a spherical lens or on the numerical aperture <span class="html-italic">NA</span> (<span class="html-italic">n</span> = 1, <span class="html-italic">α</span> = 0.5).</p>
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<p>Intensity distributions <span class="html-italic">I</span> (<b>a</b>–<b>e</b>,<b>k</b>–<b>o</b>) and longitudinal SAM <span class="html-italic">S<sub>z</sub></span> (<b>f</b>–<b>j</b>,<b>p</b>–<b>t</b>) calculated at the beam focus (1) for different <span class="html-italic">α</span>: 0 (<b>a</b>,<b>f</b>,<b>k</b>,<b>p</b>), 0.5 (<b>b</b>,<b>g</b>,<b>l</b>,<b>q</b>), 0.75 (<b>c</b>,<b>h</b>,<b>m</b>,<b>r</b>), 0.9 (<b>d</b>,<b>i</b>,<b>n</b>,<b>s</b>), and 1 (<b>e</b>,<b>j</b>,<b>o</b>,<b>t</b>). The topological charges are <span class="html-italic">n</span> = 3 (<b>a</b>–<b>j</b>), <span class="html-italic">n</span> = 5 (<b>k</b>–<b>t</b>).</p>
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17 pages, 1941 KiB  
Article
Free-Space Quantum Teleportation with Orbital Angular Momentum Multiplexed Continuous Variable Entanglement
by Xinchao Ruan, Hang Zhang, Wenqi Peng, Hui Xian, Yiwu Zhu, Wei Zhao and Sha Xiong
Mathematics 2023, 11(14), 3209; https://doi.org/10.3390/math11143209 - 21 Jul 2023
Cited by 2 | Viewed by 1310
Abstract
Quantum teleportation is one of the fundamental primitives of quantum cryptography. In order to achieve a wider range of high-capacity information transfer, we propose a free-space quantum teleportation (QT) protocol with orbital angular momentum (OAM) multiplexed continuous variable (CV) entangled states. The preparation [...] Read more.
Quantum teleportation is one of the fundamental primitives of quantum cryptography. In order to achieve a wider range of high-capacity information transfer, we propose a free-space quantum teleportation (QT) protocol with orbital angular momentum (OAM) multiplexed continuous variable (CV) entangled states. The preparation of the entangled states is accomplished by the spontaneous four-wave mixing (SFWM) process occurring in a hot 85Rb vapor cell, and the mode selection for the Bell-state measurement is achieved by employing the balanced homodyne detection technique. The fidelity of teleporting EPR entangled states carrying different topological charges via a Kolmogorov-type atmospheric turbulence channel is derived, and the superiority of enhancing the system channel capacity via OAM multiplexing is demonstrated. Our work provides a feasible scheme to implement high-capacity quantum communication in atmospheric environments. Full article
(This article belongs to the Special Issue Quantum Cryptography and Applications)
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<p>Schematic diagrams of the free-space QT with OAM multiplexed CV entangled states. BS, beam splitter; M, mirror; DP, Dove prism; Sub., subtractor; PD, photo detector; Tel., telescope; SLM, spatial light modulator; Att., attenuator; AM, amplitude modulator; PM, phase modulator; SA, spectrum analyser.</p>
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<p>The properties of the atmospheric turbulence channel in terms of different OAM modes. (<b>a</b>) Transmittance and excess noise versus the propagation distance with <math display="inline"><semantics><mrow><msubsup><mi>C</mi><mi>n</mi><mn>2</mn></msubsup><mo>=</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>16</mn></mrow></msup></mrow></semantics></math> m<math display="inline"><semantics><msup><mrow/><mrow><mo>−</mo><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></semantics></math>; (<b>b</b>) transmittance and excess noise versus the atmospheric turbulence intensity with <math display="inline"><semantics><mrow><mi>z</mi><mo>=</mo><mn>1</mn></mrow></semantics></math> km.</p>
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<p>Dependence of quantum coherence of the OAM multiplexed EPR entangled states on the transmittance for <math display="inline"><semantics><mrow><mi>l</mi><mo>=</mo><mn>0</mn></mrow></semantics></math>, <math display="inline"><semantics><mrow><mi>l</mi><mo>=</mo><mn>1</mn></mrow></semantics></math>, and <math display="inline"><semantics><mrow><mi>l</mi><mo>=</mo><mn>2</mn></mrow></semantics></math>. The error bars represent the difference between the coherence of the entangled state with topological charge <span class="html-italic">l</span> and that of the Gaussian state.</p>
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<p>The effect of transmission distance and atmospheric turbulence intensity on the coherence between the probe and conjugate modes: (<b>a</b>) on the condition of <math display="inline"><semantics><mrow><msubsup><mi>C</mi><mi>n</mi><mn>2</mn></msubsup><mo>=</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>16</mn></mrow></msup></mrow></semantics></math> m<math display="inline"><semantics><msup><mrow/><mrow><mo>−</mo><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></semantics></math>; (<b>b</b>) on the condition of <math display="inline"><semantics><mrow><mi>z</mi><mo>=</mo><mn>1</mn></mrow></semantics></math> km. The excess noise <math display="inline"><semantics><mi>ε</mi></semantics></math> varies dynamically with the two variables in the subfigures.</p>
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<p>(<b>a</b>) The crosstalk matrix of the transmitted OAM states. (<b>b</b>) The density matrix of the detected OAM states.</p>
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<p>Fidelity of the proposed CV-QT protocol versus the topological charge number carried by the unknown input state and (<b>a</b>) the propagation distance; (<b>b</b>) the atmospheric turbulence intensity.</p>
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<p>Channel capacity of the system with different numbers of OAM modes multiplexed versus the transmission distance and the atmospheric turbulence intensity. The purple plane represents the limit for the polarized codes.</p>
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<p>The generation of the OAM multiplexed CV EPR states. (<b>a</b>) The SFWM process occurs in a hot <math display="inline"><semantics><msup><mrow/><mn>85</mn></msup></semantics></math>Rb vapor cell for generating multiple pairs of OAM modes. (<b>b</b>) Double-<math display="inline"><semantics><mi>Λ</mi></semantics></math> energy level diagram of <math display="inline"><semantics><msup><mrow/><mn>85</mn></msup></semantics></math>Rb D1 line in the SFWM process. (<b>c</b>) OAM spectrum from the SFWM process. pr, probe beam; conj, conjugate beam.</p>
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<p>The schematic of BHD for OAM modes: <span class="html-italic">l</span> is the topological charge carried by the OAM modes, <math display="inline"><semantics><mi>θ</mi></semantics></math> is the azimuthal angle.</p>
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15 pages, 5222 KiB  
Article
Atmospheric Turbulence Effects on the Performance of Orbital Angular Momentum Multiplexed Free-Space Optical Links Using Coherent Beam Combining
by Pei Ju, Wenhui Fan, Wei Gao, Zhe Li, Qi Gao, Xiaoqiang Jiang and Tongyi Zhang
Photonics 2023, 10(6), 634; https://doi.org/10.3390/photonics10060634 - 31 May 2023
Cited by 7 | Viewed by 2062
Abstract
Atmospheric effects including absorption and scattering, and turbulence could introduce signal power loss and severe mode crosstalk for the orbital angular momentum (OAM)-based free-space optical communication (FSOC). Therefore, it is of great significance to simultaneously increase signal power and mitigate mode crosstalk. In [...] Read more.
Atmospheric effects including absorption and scattering, and turbulence could introduce signal power loss and severe mode crosstalk for the orbital angular momentum (OAM)-based free-space optical communication (FSOC). Therefore, it is of great significance to simultaneously increase signal power and mitigate mode crosstalk. In this paper, for the OAM beam from a coherent laser array with a discrete vortex (CLA-DV) based on coherent beam combining, we investigate its propagation characteristics by employing theoretical derivation and the random phase screens simulation in atmospheric propagation, respectively. The probability density and OAM spectrum are given and compared for CLA-DV and Gaussian vortex beam. The results demonstrate that the Gaussian vortex beam exhibits smaller mode crosstalk under weak atmospheric turbulence conditions, while CLA-DV shows a good performance on crosstalk mitigation for strong atmospheric turbulence conditions in long-distance links. Furthermore, with a specially designed radial phase-locked Gaussian laser array composed of two orthogonal polarized coherent laser arrays carrying different OAM states, a scheme of optical communication system possessing simultaneously polarization-division multiplexing and OAM multiplexing is proposed. The normalized energy weight matrices of all 16 non-zeroth-order OAM modes are numerically calculated. To verify the feasibility of the proposed scheme, the performance of an eight-bit grayscale Lena image facing various atmosphere turbulences is evaluated. The quality of transmitted images becomes worse with the turbulence strength and transmission distance increase, which is confirmed by the trend of average optical signal error rates. This work will provide theoretical insight for improving the performance of OAM-based FSOC under scattering conditions. Full article
(This article belongs to the Special Issue Advances and Application of Structured Light)
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<p>Schematic illustration of beam propagating in atmospheric turbulence with random phase screens method.</p>
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<p>The received OAM spectrum <span class="html-italic">P<sub>l</sub></span> for Gaussian vortex beam for different waist width <span class="html-italic">w</span><sub>0</sub>.</p>
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<p>The received OAM spectra <span class="html-italic">P<sub>l</sub></span> for (<b>a</b>–<b>c</b>) Gaussian vortex beam (<b>d</b>–<b>f</b>) and CLA-DV with propagation distance of 500 m, 1000 m, and 2000 m in the atmospheric turbulence.</p>
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<p>The normalized energy weight of central OAM mode for Gaussian vortex beam and CLA-DV propagating in the atmospheric turbulence with different values of refraction structure constant <span class="html-italic">C<sub>n</sub></span><sup>2</sup>. (<b>a</b>) <span class="html-italic">C<sub>n</sub></span><sup>2</sup> = 10<sup>−16</sup> m<sup>−2/3</sup>, (<b>b</b>) <span class="html-italic">C<sub>n</sub></span><sup>2</sup> = 10<sup>−15</sup> m<sup>−2/3</sup>, (<b>c</b>) <span class="html-italic">C<sub>n</sub></span><sup>2</sup> = 10<sup>−14</sup> m<sup>−2/3</sup>.</p>
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<p>The received OAM spectra <span class="html-italic">P<sub>l</sub></span> for (<b>a</b>–<b>c</b>) Gaussian vortex beam (<b>d</b>–<b>f</b>) and CLA-DV with propagation distances of 500 m, 1000 m and 2000 m in the atmospheric turbulence.</p>
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<p>The normalized energy weight of central OAM mode for Gaussian vortex beam and CLA-DV propagating in the atmospheric turbulence with different values of refraction structure constant <span class="html-italic">C<sub>n</sub></span><sup>2</sup>. (<b>a</b>) <span class="html-italic">C<sub>n</sub></span><sup>2</sup> = 10<sup>−16</sup> m<sup>−2/3</sup>, (<b>b</b>) <span class="html-italic">C<sub>n</sub></span><sup>2</sup> = 10<sup>−15</sup> m<sup>−2/3</sup>, (<b>c</b>) <span class="html-italic">C<sub>n</sub></span><sup>2</sup> = 10<sup>−14</sup> m<sup>−2/3</sup>.</p>
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<p>Schematic illustration for optical communication link (<b>a</b>), and the principle of data encoding, transmission, and decoding (<b>b</b>) by employing the CLA-DV. HWP, quarter wave plate; PBS, polarization beam splitter; SLM, spatial light modulator; CCD, and charge coupled device.</p>
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<p>The normalized energy weight matrices between OAM modes with their topological charges from <span class="html-italic">l</span><sub>0</sub> = −8 to <span class="html-italic">l</span><sub>0</sub> = 8 at an interval of 1 after transmission of 500 m and 1000 m at different turbulence strengths. (<b>a</b>,<b>d</b>), (<b>b</b>,<b>e</b>) and (<b>c</b>,<b>f</b>) correspond to <span class="html-italic">C<sub>n</sub></span><sup>2</sup> = 10<sup>−16</sup> m<sup>−2/3</sup>, 10<sup>−15</sup> m<sup>−2/3</sup>, and 10<sup>−14</sup> m<sup>−2/3</sup>, respectively.</p>
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<p>The numerical transmitted image data after transmission of 500 m and 1000 m with various turbulence strengths. (<b>a</b>,<b>d</b>), (<b>b</b>,<b>e</b>) and (<b>c</b>,<b>f</b>) correspond to <span class="html-italic">C<sub>n</sub></span><sup>2</sup> = 10<sup>−16</sup> m<sup>−2/3</sup>, 10<sup>−15</sup> m<sup>−2/3</sup>, 10<sup>−14</sup> m<sup>−2/3</sup>, respectively.</p>
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16 pages, 5071 KiB  
Article
Capacity Enhancement Analysis of an OAM-OFDM-SMM Multiplexed Free Space Communication System in Atmospheric Turbulence
by Shivaji Sinha, Chakresh Kumar, Ammar Armghan, Mehtab Singh, Meshari Alsharari and Khaled Aliqab
Appl. Sci. 2023, 13(6), 3897; https://doi.org/10.3390/app13063897 - 19 Mar 2023
Cited by 10 | Viewed by 2135
Abstract
To overcome atmospheric turbulence (AT) distortion during signal propagation through the optical link, orbital angular momentum (OAM) mode states employing multiple inputs and multiple outputs (MIMO) techniques have recently gained prominence in free space optical communication (FSO). As the various OAM modes propagate [...] Read more.
To overcome atmospheric turbulence (AT) distortion during signal propagation through the optical link, orbital angular momentum (OAM) mode states employing multiple inputs and multiple outputs (MIMO) techniques have recently gained prominence in free space optical communication (FSO). As the various OAM modes propagate through the free space optical link, signal attenuation and crosstalk may occur, reducing system capacity and increasing the likelihood of bit errors. In this work, our objective is to propose a spectrally efficient, high-speed and channel capacity efficient crosstalk FSO communication system by combining the features of orthogonal frequency division multiplexing (OFDM), spatial mode multiplexing (SMM), and a mode diversity scheme into an existing OAM-FSO communication system. The incorporation of the OFDM-MIMO concept and spatial mode diversity into the existing OAM-MIMO-FSO system is extremely beneficial in enhancing the transmission capacity, mitigating multipath fading and atmospheric turbulence distortions. The Gamma–Gamma (GG) model is used to assess the performance of the proposed system under various atmospheric turbulence conditions in terms of the performance metrics such as BER vs. number of OAM states for different refractive index structure and Rytov constants, link distance, and an optical signal to noise ratio (OSNR). A FEC limit of 3.8 × 10−3 and a maximum link distance of 2 km are set to evaluate these performance parameters. Finally, the transmission capacity of the proposed system is compared to that of the existing MIMO and OAM-SMM-MIMO systems for different OSNR values under atmospheric turbulence conditions for the OAM state of l = +1, yielding an overall improvement of 3.3 bits/s/Hz compared to conventional MIMO systems and 1.6 bits/s/Hz for the OAM-SMM-MIMO system. Full article
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<p>Schematic concept of OAM based spatial multiplexing in the FSO system.</p>
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<p>Schematic of the OAM-OFDM-SMM-MIMO spatially multiplexed FSO system.</p>
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<p>Intensity and phase profiles of OAM state in different turbulence regions.</p>
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<p>BER vs. OAM states under different refractive index structure parameters.</p>
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<p>BER vs. OAM state for the OAM-SMM-MIMO and the OAM-OFDM-SMM-MIMO FSO systems.</p>
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<p>BER vs. OAM states for different optical link distances.</p>
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<p>BER vs. OSNR for <span class="html-italic">l</span> = +1 OAM mode and OFDM SMM FSO system.</p>
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<p>BER vs. OSNR for different Rytov constants under GG turbulence.</p>
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<p>Channel capacity vs. OSNR for the conventional OAM and the proposed system.</p>
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