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Orbital angular momentum (OAM), as a novel high-dimensional degree of freedom, shows great potential applications in optical communication in improving system channel capacity and solving the problem of scarce communication resources. However, the effective recognition and detection of OAM modes are the core challenges for achieving efficient communication in such systems. In this work, an OAM decoding system consisting of a designed coordinate transformation device, a phase corrector, and a Fourier transform lens is presented based on log-polar coordinate transformation. The coordinate transformation device fabricated by liquid crystal polymer is utilized to map the incident vortex beam from polar coordinates into Cartesian coordinates, followed by the phase corrector to compensate for phase distortions into a collimated beam. Finally, the Fourier transform lens is used to separate the OAM modes at different space positions in its rear focal plane. The performance of the system is numerically evaluated in several ablation studies, and the influence of various grating parameters on beam separation efficiency is analyzed. Experimentally, the system successfully achieves the decoding of OAM modes ranging from –35 to +31 orders. Furthermore, a free-space optical communication demonstration system is constructed based on this OAM decoding system. By introducing specifically designed decoding rules, the system effectively mitigates the adjacent mode crosstalk inherent in logarithmic polar coordinate transformation and successfully transmitted 748934 symbols without errors. These favorable results highlight the capabilities of the proposed OAM-based optical communication system and provide valuable insights for developing future high-capacity optical communication networks.
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图 1 对数极坐标变换过程示意图 (a) 输入–7阶涡旋光束相位分布; (b)坐标变换调制相位; (c) –7阶涡旋光束对应的矩形光场相位分布; (d)校正相位; (e) –7阶涡旋光束对应的分束面光强分布; (f) 对数极坐标变换过程
Figure 1. Concept of the log-polar transformation: (a) The phase distribution of the incident beam with OAM state $|-7\rangle $; (b) the phase modulation of the coordinate transformation; (c) the phase distribution of the transformed rectangular light field corresponding to OAM state $|-7\rangle $; (d) the phase modulation of the phase correction; (e) the sorting plane intensity of the incident beam corresponding to OAM state $|-7\rangle $; (f) the convert sketch of a vortex beam via the log-polar transformation.
图 2 液晶分子主轴排布仿真效果 (a) 坐标变换器件; (b) 校正器件
Figure 2. Simulated main axis arrangement of the liquid crystal molecules: (a) The arrangement distribution of the coordinate transformation device; (b) the phase corrector.
图 3 OAM译码系统及数据传输演示装置 (a) 实验装置, 波长1645 nm的线偏振连续激光, 通过SLM后携带OAM模式, 经由透镜L1和L2构成的4-f滤波系统后在自由空间传输1 m后通过1/4波片输入OAM译码系统, 系统由坐标变换器件U、校正器件C和傅里叶变换透镜Lf组成, 最后分束面光场(傅里叶变换透镜后焦面处光场)由红外焦平面探测器CCD接收; (b) 坐标变换器件实物图; (c) 校正器件实物图; (d) OAM译码系统样机图
Figure 3. Experimental setup of the OAM decoding system for data transmission demonstration: (a) Experimental setup. The incident gaussian beam is a continuous-wave laser operating at 1645 nm, which is encoded by a SLM to generate the desired OAM mode. After passing through a 4-f system composed of lenses L1 and L2, the OAM mode is transmitted 1 m in free space and then incident the OAM decoding system, which is consist of a coordinate transformation device, a phase corrector and a Fourier transformation lens. Lastly, the sorted light field (Light field at the focal plane of Fourier transformation lens) is captured by a CCD. (b) The physical image of the coordinate transformation device. (c) The physical image of the phase corrector. (d) The physical image of the OAM decoding system prototype.
图 4 坐标变换分束效果 (a) 数值仿真不同OAM态在分束面的位置分布; (b) 数值仿真不同OAM态在分束面的水平方向归一化强度分布; (c) 实验测定不同OAM态在分束面的位置分布; (d) 实验测定不同OAM态在分束面的水平方向归一化强度分布
Figure 4. Sorting performance of the coordinate transformation: (a) The simulated position for sorting different OAM states along x-axis and y-axis in the sorting plane; (b) the overlaid line scans of the simulated intensity distributions of different OAM states along the horizontal direction; (c) the experimental position for sorting different OAM states along x-axis and y-axis in the sorting plane; (d) the overlaid line scans of the experimental intensity distributions of different OAM states along the horizontal direction.
图 5 OAM-SK数据传输译码过程 (a) OAM译码系统分束面; (b)译码软件界面
Figure 5. Data transmission decoding of OAM-shift keying: (a) The sorting plane of the OAM decoding system with OAM states $| l\rangle $, where l = –7–+7; (b) the decoding software interface.
表 1 码元与OAM模式编码对应表
Table 1. Corresponding of symbols and OAM modes.
码元 0 1 2 3 4 5 6 7 OAM模式 — ±2 ±3 ±4 ±5 ±6 –6 –5 码元 8 9 A B C D E F OAM模式 –4 –3 –2 +2 +3 +4 +5 +6 
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[1] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185
Google Scholar
[2] Shen Y J, Wang X J, Xie Z W, Min C J, Fu X, Liu Q, Gong M L, Yuan X C 2019 Light Sci. Appl. 8 90
Google Scholar
[3] Willner A E, Huang H, Yan Y, Ren Y, Ahmed N, Xie G, Bao C, Li L, Cao Y, Zhao Z, Wang J, Lavery M P J, Tur M, Ramachandran S, Molisch A F, Ashrafi N, Ashrafi S 2015 Adv. Opt. Photon. 7 66
Google Scholar
[4] Mair A, Vaziri A, Weihs G, Zeilinger A 2001 Nature 412 313
Google Scholar
[5] Fang X Y, Ren H R, Gu M 2020 Nat. Photonics 14 102
Google Scholar
[6] Erhard M, Fickler R, Krenn M, Zeilinger A 2017 Light Sci. Appl. 7 17146
Google Scholar
[7] Wang J, Liu J, Li S, Zhao Y, Du J, Zhu L 2022 Nanophotonics 11 645
Google Scholar
[8] Trichili A, Park K H, Zghal M, Ooi B S, Alouini M S 2019 IEEE Commun. Surv. Tutorials 21 3175
Google Scholar
[9] Chen Y A, Zhang Q, Chen T Y, Cai W Q, Liao S K, Zhang J, Chen K, Yin J, Ren J G, Chen Z, Han S L, Yu Q, Liang K, Zhou F, Yuan X, Zhao M S, Wang T Y, Jiang X, Zhang L, Liu W Y, Li Y, Shen Q, Cao Y, Lu C Y, Shu R, Wang J Y, Li L, Liu N L, Xu F, Wang X B, Peng C Z, Pan J W 2021 Nature 589 214
Google Scholar
[10] Qiu X, Guo H, Chen L 2023 Nat. Commun. 14 8244
Google Scholar
[11] Vallone G, D’Ambrosio V, Sponselli A, Slussarenko S, Marrucci L, Sciarrino F, Villoresi P 2014 Phys. Rev. Lett. 113 060503
Google Scholar
[12] Wang X L, Cai X D, Su Z E, Chen M C, Wu D, Li L, Liu N L, Lu C Y, Pan J W 2015 Nature 518 516
Google Scholar
[13] Du J, Wang J 2015 Opt. Lett. 40 4827
Google Scholar
[14] Shang Z, Fu S Y, Hai L, Zhang Z, Li L, Gao C Q 2022 Opt. Express 30 34053
Google Scholar
[15] Wen Y, Chremmos I, Chen Y, Zhu G, Zhang J, Zhu J, Zhang Y, Liu J, Yu S 2020 Optica 7 254
Google Scholar
[16] Wang J, Yang J Y, Fazal I M, Ahmed N, Yan Y, Huang H, Ren Y, Yue Y, Dolinar S, Tur M, Willner A E 2012 Nat. Photonics 6 488
Google Scholar
[17] Fu S Y, Zhai Y, Zhang J, Liu X, Song R, Zhou H, Gao C Q 2020 PhotoniX 1 19
Google Scholar
[18] Fu S Y, Wang T W, Yan Gao Y, Gao C Q 2016 Chin. Opt. Lett. 14 080501
Google Scholar
[19] Zhao Q, Dong M, Bai Y H, Yang Y J 2020 Photon. Res. 8 745
Google Scholar
[20] Leach J, Padgett M J, Barnett S M, Franke-Arnold S, Courtial J 2002 Phys. Rev. Lett. 88 257901
Google Scholar
[21] Zhou H L, Fu D Z, Dong J J, Zhang P, Chen D X, Cai X L, Li F L, Zhang X L 2016 Light Sci. Appl. 6 16251
Google Scholar
[22] Lavery M P J, Speirits F C, Barnett S M, Padgett M J 2013 Science 341 537
Google Scholar
[23] Wang H, Zhan Z, Hu F, Meng Y, Liu Z, Fu X, Liu Q 2023 PhotoniX 4 9
Google Scholar
[24] Wang J Q, Fu S Y, Shang Z J, Hai L, Gao C Q 2022 Opt. Lett. 47 1419
Google Scholar
[25] Zhou S Y, Li L, Gao C Q, Fu S Y 2023 Opt. Lett. 49 173
Google Scholar
[26] Berkhout G C G, Lavery M P J, Courtial J, Beijersbergen M W, Padgett M J 2010 Phys. Rev. Lett. 105 153601
Google Scholar
[27] Mirhosseini M, Malik M, Shi Z, Boyd R W 2013 Nat. Commun. 4 2781
Google Scholar
[28] Wen Y, Chremmos I, Chen Y, Zhu J, Zhang Y, Yu S 2018 Phys. Rev. Lett. 120 193904
Google Scholar
[29] Cheng J, Wan C H, Zhan Q W 2022 Opt. Express 30 16330
Google Scholar
[30] Cheng J P, Sha X B, Zhang H, Chen Q M, Qu G Y, Song Q H, Yu S M, Xiao S M 2022 Nano Lett. 22 3993
Google Scholar
[31] Li L, Guo Y C, Zhang Z C, Shang Z J, Li C, Wang J Q, Gao L L, Hai L, Gao C Q, Fu S Y 2023 Adv. Photonics 5 056002
Google Scholar
[32] Lavery M P J, Robertson D J, Berkhout G C G, Love G D, Padgett M J, Courtial J 2012 Opt. Express 20 2110
Google Scholar
[33] Lavery M P J, Robertson D J, Sponselli A, Courtial J, Steinhoff N K, Tyler G A, Wilner A E, Padgett M J 2013 New J. Phys. 15 013024
Google Scholar
[34] Chen P, Wei B Y, Hu W, Lu Y Q 2020 Adv. Mater. 32 1903665
Google Scholar
[35] Saber G, Gutiérrez-Castrejón R, Xing Z, Alam S, El-Fiky E, Ceballos-Herrera D E, Cavaliere F, Vall-Llosera G, Lessard S, Plant D V 2021 IEEE Photonics J. 13 1
Google Scholar
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