深圳大学学报理工版

光学旋涡与轨道角动量光通信

袁小聪¹,贾平², 雷霆¹,张萌², 闵长俊¹, 李玉茹³, 李朝晖³,牛憨笨¹

1)深圳大学光电工程学院,光电子器件与系统教育部/广东省重点实验室,深圳 518060; 2)南开大学现代光学研究所,光电信息技术科学教育部重点实验室,天津300071; 3)暨南大学光子技术研究所,广州510632

关键词：光通信技术; 光学旋涡; 轨道角动量; 自由空间光通信; 复用; 调制; 不确定原理; 通信容量; 误码率

Optical vortices and optical communication with orbital angular momentum

Yuan Xiaocong^1, Jia Ping², Lei Ting¹, Zhang Meng², Min Changjun¹, Li Yuru³, Li Zhaohui³, and Niu Hanben¹

Yuan Xiaocong^1, Jia Ping², Lei Ting¹, Zhang Meng², Min Changjun¹, Li Yuru³, Li Zhaohui³, and Niu Hanben¹1)College of Optoelectronic Engineering, Key Laboratory of Optoelectronic Devices and System of Ministry of Education and Guangdong Province, Shenzhen University, Shenzhen 518060, P.R.China2)Institute of Modern Optics, Key Laboratory of Optical Information Science and Technology of Ministry of Education, Nankai University, Tianjin 300071, P.R.China3)Institute of Photonics Technology, Jinan University, Guangzhou 510632, P.R.China

Keywords： optical communication technology; optical vortices; orbital angular momentum; free-space optical communication; multiplexing; modulation; uncertainty principle; communication capacity; bit error rate

DOI: 10.3724/SP.J.1249.2014.04331

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摘要

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参考文献

光学旋涡(optical vortices, OV)光束包含螺旋型相位因子,具有全新的自由度——轨道角动量(orbital angular momentum, OAM).OAM本征值为l, 且理论上拓扑荷l可取任意整数,这为光学旋涡在光通信系统中的各种应用提供基础.目前有很多方法可用于光学旋涡的产生与检测,而光学旋涡在光通信系统中的应用也正是基于这些方法.OAM在自由空间光通信系统中的应用机制可分为OAM键控(OAM状态作为调制方式)和OAM复用(OAM光束作为复用信道).针对这两种机制已展开大量的理论研究和实验探索,认为光学旋涡可为丰富自由空间光通信系统的调制方式和增加传输容量提供潜在的解决方案.光学旋涡光束的OAM和角向位置的不确定性关系也为之带来了与生俱来的安全优势.光学旋涡的独有特性为光通信系统的性能改善提供了巨大潜力.

An optical vortices(OV)beam with a helical phase term shows a new degree of freedom, namely orbital angular momentum(OAM). The eigenvalue of OAM is l, and the topological charge l can be any integer in principle, which offers the basis for various applications of OV in optical communication system. There are many approaches so far for the generation and detection of OV on which the applications of OV in optical communication are based. The application mechanisms of OAM in free-space optical communication(FSO)system can be classified into two different categories: one is OAM shift keying(OAM-SK)where OAM states play as modulation formats; the other is OAM division multiplexing(OAM-DM)where OAM beams play as multiplexing channels. For these two mechanisms, there has been mass theoretical researches and experimental explorations. OV offer potential solutions for enriching the modulation formats or increasing the transmission capacity of FSO system. Furthermore, the uncertainty relationship between OAM and angular position of OV beams also brings about inherent security advantage. These characteristics of OV can provide great potential to improve the performances of OAM-embedded FSO communication system.

引言
1 光学旋涡的产生与检测
2 OV在FSO系统中的两种应用机制
3 OV的性能
4 展望

图1 高斯光束通过螺旋位相片可以产生具有螺旋位相的光学旋涡<br/>Fig.1 A spiral phase plate can generate a helically phased beam from a Gaussian beam

图1 高斯光束通过螺旋位相片可以产生具有螺旋位相的光学旋涡
Fig.1 A spiral phase plate can generate a helically phased beam from a Gaussian beam

图2 模式间的分解与合成[18]<br/>Fig.2 Decomposition and combination of modes[18][Courtesy of Optical Society of America]

图2 模式间的分解与合成[18]
Fig.2 Decomposition and combination of modes[18][Courtesy of Optical Society of America]

$图3 Gaussian光束通过衍射元件转换成OV的原理[14]<br/>Fig.3 Schematic of converting Gaussian beam to OV by diffractive components[14][Courtesy of Optical Society of America]$

图3 Gaussian光束通过衍射元件转换成OV的原理[14]
Fig.3 Schematic of converting Gaussian beam to OV by diffractive components[14][Courtesy of Optical Society of America]

图4 基于Dove棱镜Mach-Zehnder干涉仪的OAM分类装置[28]<br/>Fig.4 An OAM sorter based on Mach-Zehnder interferometer with a Dove prism placed in each arm[28][Courtesy of the American Physical Society]

图4 基于Dove棱镜Mach-Zehnder干涉仪的OAM分类装置[28]
Fig.4 An OAM sorter based on Mach-Zehnder interferometer with a Dove prism placed in each arm[28][Courtesy of the American Physical Society]

$图5 叉形衍射光栅将OV光束转换为高斯光束耦合到探测器[14]<br/>Fig.5 A forked diffraction grating centered on the beam axis can convert an OV beam into Gaussian beam, which can then be coupled to a detector[14][Courtesy of Optical Society of America]$

图5 叉形衍射光栅将OV光束转换为高斯光束耦合到探测器[14]
Fig.5 A forked diffraction grating centered on the beam axis can convert an OV beam into Gaussian beam, which can then be coupled to a detector[14][Courtesy of Optical Society of America]

图6 螺旋位相光束图像重构为线性位相梯度[31-32]<br/>Fig.6 Image reformatting of beams with a helical phase into a linear phase gradient[31-32][Courtesy of Optical Society of America and the American Physical Society]

图6 螺旋位相光束图像重构为线性位相梯度[31-32]
Fig.6 Image reformatting of beams with a helical phase into a linear phase gradient[31-32][Courtesy of Optical Society of America and the American Physical Society]

图7 基于SMOV的OAM检测[37]<br/>Fig.7 Characterization of OAM based on SMOV[37][Courtesy of Optical Society of America]

图7 基于SMOV的OAM检测[37]
Fig.7 Characterization of OAM based on SMOV[37][Courtesy of Optical Society of America]

图8 时变型复合OV光束的产生<br/>Fig.8 Generation of a time variable composed OV beam

图8 时变型复合OV光束的产生
Fig.8 Generation of a time variable composed OV beam

图9 自由空间光通信实验装置(l=8)[10]<br/>Fig.9 Optical setup of the free-space optical demonstration system(l=8)[10][Courtesy of Optical Society of America]

图9 自由空间光通信实验装置(l=8)[10]
Fig.9 Optical setup of the free-space optical demonstration system(l=8)[10][Courtesy of Optical Society of America]

图10 OAM 传输数据的子集[10]<br/>Fig.10 A subset of results from transmitting a data set using OAM[10][Courtesy of Optical Society of America]

图10 OAM 传输数据的子集[10]
Fig.10 A subset of results from transmitting a data set using OAM[10][Courtesy of Optical Society of America]

图11 编码原理和过程以及实验结果[37]<br/>Fig.11 Principle of the whole encoding and decoding process and some experiment results[37][Courtesy of Optical Society of America]

图11 编码原理和过程以及实验结果[37]
Fig.11 Principle of the whole encoding and decoding process and some experiment results[37][Courtesy of Optical Society of America]

图12 基于OAM的自由空间多路光信号复用[41]<br/>Fig.12 Multiplexing of multiple free space optical channels using OAM[41][Courtesy of Optical Society of America]

图12 基于OAM的自由空间多路光信号复用[41]
Fig.12 Multiplexing of multiple free space optical channels using OAM[41][Courtesy of Optical Society of America]

图13 OV信息通道的光学原理[47]<br/>Fig.13 Optical scheme of the vortex information channel[47][Courtesy of IOP Publishing Ltd. and Deutsche Physikalische Gesellschaft]

图13 OV信息通道的光学原理[47]
Fig.13 Optical scheme of the vortex information channel[47][Courtesy of IOP Publishing Ltd. and Deutsche Physikalische Gesellschaft]

图14 利用位相模板检测和编码OV光束[47]<br/>Fig.14 Detection and decoding a single vortex beam using phase mask[47][Courtesy of IOP Publishing Ltd. and Deutsche Physikalische Gesellschaft]

图14 利用位相模板检测和编码OV光束[47]
Fig.14 Detection and decoding a single vortex beam using phase mask[47][Courtesy of IOP Publishing Ltd. and Deutsche Physikalische Gesellschaft]

图15 合成OV场传输4比特信息的实验结果[47]<br/>Fig.15 Experimental results demonstrating transfer of four bits of information by means of the composed vortex field[47][Courtesy of IOP Publishing Ltd. and Deutsche Physikalische Gesellschaft]

图15 合成OV场传输4比特信息的实验结果[47]
Fig.15 Experimental results demonstrating transfer of four bits of information by means of the composed vortex field[47][Courtesy of IOP Publishing Ltd. and Deutsche Physikalische Gesellschaft]

图16 OV探测使用5 × 5 达曼旋涡光栅的实验结果[43]<br/>Fig.16 OV detection results using the 5×5 Dammann vortex grating[43][Courtesy of Optical Society of America]

图16 OV探测使用5 × 5 达曼旋涡光栅的实验结果[43]
Fig.16 OV detection results using the 5×5 Dammann vortex grating[43][Courtesy of Optical Society of America]

图17 遗传算法产生叠加的OV实现高通量的OV复用[42]<br/>Fig.17 Superimposed OVs generated by a genetic algorithm to achieve high-volume OV multiplexing[42][Courtesy of Optical Society of America]

图17 遗传算法产生叠加的OV实现高通量的OV复用[42]
Fig.17 Superimposed OVs generated by a genetic algorithm to achieve high-volume OV multiplexing[42][Courtesy of Optical Society of America]

图18 多维LDPC编码的 OAM 传输系统原理图[48]<br/>Fig.18 Multidimensional LDPC-coded OAM transmission scheme[48][Courtesy of Optical Society of America]

图18 多维LDPC编码的 OAM 传输系统原理图[48]
Fig.18 Multidimensional LDPC-coded OAM transmission scheme[48][Courtesy of Optical Society of America]

图19 OAM-DM通信系统的概念和原理[52]<br/>Fig.19 Concept and principle of the OAM-DM system[52][Courtesy of Macmillan Publishers Limited]

图19 OAM-DM通信系统的概念和原理[52]
Fig.19 Concept and principle of the OAM-DM system[52][Courtesy of Macmillan Publishers Limited]

图20 四种OAM状态{-14, -8, +10, +12}复用/解复用的实验和模拟结果[52]<br/>Fig.20 The Experimental and simulation results of multiplexing/demultiplexing of four OAM states with topological charges {-14, -8, +10, +12}[52]

图20 四种OAM状态{-14, -8, +10, +12}复用/解复用的实验和模拟结果[52]
Fig.20 The Experimental and simulation results of multiplexing/demultiplexing of four OAM states with topological charges {-14, -8, +10, +12}[52]

图21 两张偏振态拓扑荷{+4, +8, -8, +16}的OAM-DM实验结果[52]<br/>Fig.21 The experimental results of OAM-DM with two polarizations in which l from {+4, +8, -8, +16}[52][Courtesy of Macmillan Publishers Limited]

图21 两张偏振态拓扑荷{+4, +8, -8, +16}的OAM-DM实验结果[52]
Fig.21 The experimental results of OAM-DM with two polarizations in which l from {+4, +8, -8, +16}[52][Courtesy of Macmillan Publishers Limited]

图22 LG01光束(间隔π /4的位相等高线)和同一光束引入Kolmogorov扰动后的强度和位相分布[61]<br/>Fig.22 Example intensity and phase map(π /4-spaced contours)of a LG01 beam(left)and the same beam with aberration caused by propagation through Kolmogorov Turbulence(right)[61][Courtesy of the American Physical Society]

图22 LG01光束(间隔π /4的位相等高线)和同一光束引入Kolmogorov扰动后的强度和位相分布[61]
Fig.22 Example intensity and phase map(π /4-spaced contours)of a LG01 beam(left)and the same beam with aberration caused by propagation through Kolmogorov Turbulence(right)[61][Courtesy of the American Physical Society]

图23 模拟的l=1, p=1的LG光束在不同扰动下的平均拓扑荷[62]<br/>Fig.23 Simulation of the average toplogical charge for a LG beam of order l=1, p=1, for various turbulence strengths[62][Courtesy of Optical Society of America]

图23 模拟的l=1, p=1的LG光束在不同扰动下的平均拓扑荷[62]
Fig.23 Simulation of the average toplogical charge for a LG beam of order l=1, p=1, for various turbulence strengths[62][Courtesy of Optical Society of America]

图24 Kolmogorov湍流对OAM通信容量的影响,OAM通道数为N=3, 5, 7, 9 和 11,使用偏振模式的容量以点划线的方式画出作为比较[65]<br/>Fig.24 Influence of Kolmogorov turbulence on the channel capacity of an OAM communication channel for a system dimensionality of N=3, 5, 7, 9 and 11.

图24 Kolmogorov湍流对OAM通信容量的影响,OAM通道数为N=3, 5, 7, 9 和 11,使用偏振模式的容量以点划线的方式画出作为比较[65]
Fig.24 Influence of Kolmogorov turbulence on the channel capacity of an OAM communication channel for a system dimensionality of N=3, 5, 7, 9 and 11.

图25 弱(σR=0.3), 中(σR=1)和强(σR=2)湍流区域的 FSO系统中LDPC(4 320,3 242)编码OAM 调制的BER[63]<br/>Fig.25 The BER performance of LDPC(4 320, 3 242)-coded OAM modulation based FSO system in weak(σR =0.3), medium(σR =1), and strong (σR =2)turbulence regime[63][Courtesy of Optical Society of America]

图25 弱(σR=0.3), 中(σR=1)和强(σR=2)湍流区域的 FSO系统中LDPC(4 320,3 242)编码OAM 调制的BER[63]
Fig.25 The BER performance of LDPC(4 320, 3 242)-coded OAM modulation based FSO system in weak(σR =0.3), medium(σR =1), and strong (σR =2)turbulence regime[63][Courtesy of Optical Society of America]

图26 两种不确定原理的形式[58]<br/>Fig.26 Two forms of uncertainty principle[58][Courtesy of IOP Publishing Ltd. and Deutsche Physikalische Gesellschaft]

图26 两种不确定原理的形式[58]
Fig.26 Two forms of uncertainty principle[58][Courtesy of IOP Publishing Ltd. and Deutsche Physikalische Gesellschaft]

图27 LG01光束光路中不同遮挡物下P(l)的不确定性[10]<br/>Fig.27 Spread or uncertainty in the measured values P(l) for various apertures inserted into the path of an LG01 beam[10][Courtesy of Optical Society of America]

图27 LG01光束光路中不同遮挡物下P(l)的不确定性[10]
Fig.27 Spread or uncertainty in the measured values P(l) for various apertures inserted into the path of an LG01 beam[10][Courtesy of Optical Society of America]