四波混频光相位运算器原理及其噪声性能研究

曹亚敏; 武保剑; 万峰; 邱昆

doi:10.7498/aps.67.20172638

摘要

推导了抽运消耗情形下简并和非简并四波混频（FWM）闲频光幅度和相位的统一解析表达式.采用极限方法，计算证明了非相敏放大模式下闲频光相位与输入光初始相位之间的关系，揭示了FWM相位加减混合运算器的工作原理.以四相相移键控信号为例，对基于非简并FWM的相位运算器进行了设计，重点分析了三种基本加减混合运算的噪声转移性能及其对光纤长度、输入光波长和功率的依赖特性.计算表明：该运算器的噪声指数约为1.1 dB；当输入光信号的信噪比大于24 dB时无纠错编码的符号错误率可低于10-3.

关键词:

Abstract

The existing theoretical equations cannot provide an excellent guidance for developing four-wave mixing (FWM)-based optical logic devices, though the experiments have been done in several researches. The optimization of noise figure performances of such devices should be further investigated. In the paper, the universal analytic expressions for the amplitude and phase of the idler in degenerate or non-degenerate FWM process under pump depletion are derived in detail from the nonlinear coupled-mode equations for guiding optical waves propagation in highly nonlinear fiber. The universal analytic expressions are obtained by the first-and the third-kind of elliptic integrals. By using equivalent infinitesimal to calculate the limit of phase sensitive amplification, we find out the initial phase relationship between the idler and the input guided wave for phase-independent amplification, which is crucially important for explaining the operating principles of the FWM-based adder and subtracter. As an example, the configuration of non-degenerate FWM-based hybrid arithmetic device with three logic functions of A+B-C, A+C-B, and B+C-A for QPSK signals is presented, and then the noise transfer characteristics in terms of signal-to-noise ratio (SNR) and error vector magnitude (EVM) are taken into account by adjusting the fiber length, input wavelength, and optical power. The calculation results show as follows. 1) This kind of arithmetic device has a noise figure of about 1.1 dB and an input SNR of more than 24 dB is necessary for the symbol error rate of 10-3 without forward error correction, corresponding to an output EVM of 23.2%. 2) The length of highly nonlinear fiber used in the hybrid arithmetic device may be taken flexibly, provided that the variation of FWM conversion efficiency is controlled in a range of 1 dB relative to the maximum, with an EVM fluctuation of less than for the idlers. 3) The hybrid arithmetic device has an operating optical bandwidth of about 16 nm for the SNR degradation of 1.3 dB. 4) The output EVM increases with the increase of input power, and the allowable input power should be no more than 100 mW for an input SNR of 28 dB, noting that the larger the input SNR, the higher the allowable input power is.

Keywords:

作者及机构信息

1.
电子科技大学通信与信息工程学院, 光纤传感与通信教育部重点实验室, 成都 611731

通信作者: 武保剑, bjwu@uestc.edu.cn

基金项目: 国家自然科学基金（批准号：61671108，61505021）资助的课题.

Authors and contacts

1.
Key Laboratory of Optical Fiber Sensing and Communication, Ministry of Education, School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Corresponding author: Wu Bao-Jian, bjwu@uestc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61671108, 61505021).

参考文献

[1]	Wang J, Yang J Y, Huang H, Willner A E 2013 Opt. Express 21 488
[2]	Azeemuddin S, Chaitanya G V, Sayeh M R 2012 J. Opt. 41 142
[3]	Wang W R, Yu J L, Han B C, Guo J Z, Luo J, Wang J, Liu Y, Yang E Z 2012 Acta Phys. Sin. 8 084214 (in Chinese) [王文睿, 于晋龙, 韩丙辰, 郭精忠, 罗俊, 王菊, 刘毅, 杨恩泽 2012 物理学报 8 084214]
[4]	Wang A D, Hu X, Zhu L, Zeng M Q, Fu L, Wang J 2015 Opt. Express 23 31728
[5]	Yan S L 2013 Acta Phys. Sin. 62 230504 (in Chinese) [颜森林 2013 物理学报 62 230504]
[6]	Chen X, Huo L, Lou C Y, Wang J, Yu W K, Jiang X Y, Zhao Z X, Zhang E Y 2016 Acta Phys. Sin. 65 054208 (in Chinese) [陈新, 霍力, 娄采云, 王强, 余文科, 姜向宇, 赵之玺, 章恩耀 2016 物理学报 65 054208]
[7]	Li M X, Chen H, Zhang Y L, Qi S F, Zhang H J, Deng J, Chen Z J, Zhong S Q, Zhang D J 2011 Des. Tech. Pos. Telecom. 11 18 (in Chinese) [李懋循, 陈皓, 张耀亮, 祁劭峰, 张慧剑, 邓建, 陈志强, 钟胜前, 张德江 2011 邮电设计技术 11 18]
[8]	Zhang J W, Zhao Y L, Ji Y F 2016 Inf. Commun. Tech. 1 10 (in Chinese) [张佳玮, 赵永利, 纪越峰 2016 信息通信技术 1 10]
[9]	Wang F Q 2017 Chin. Phys. B 26 034202
[10]	Wang Z 2016 Sci. Tech. Rev. 34 121 (in Chinese) [王智 2016 科技导报 34 121]
[11]	Su Q Q, Zhang G W, Pu J X 2012 Acta Phys. Sin. 61 144208 (in Chinese) [苏倩倩, 张国文, 蒲继雄 2012 物理学报 61 144208]
[12]	Li Q L, Zhu M Y, Li D Q, Zhang Z, Wei Y Z, Hu M, Zhou X F, Tang X H 2014 Appl. Opt. 53 4708
[13]	Wang P, Chen B X, Wang G D, Sui G R, Zou L E, Bang Z J, Ji S 2011 Opt. Optoe. Tech. 9 48 (in Chinese) [王平, 陈抱雪, 王关德, 隋国荣, 邹林儿, 浜中广见, 矶守 2011 光学与光电技术 9 48]
[14]	Yin Z, Dong J J, Zhang X L 2011 16th OptoElectronics and Communications Conference Kaohsiung, Taiwan, China, July 4-8, 2011 p563
[15]	Karamdeep S, Gurmeet K, Lal S M 2016 Opt. Eng. 55 077104
[16]	Long Y, Gui C, Wang A, Hu X, Zhu L, Zhou L, Wang J 2016 Optical Fiber Communications Conference and Exhibition Anaheim, USA, March 20-24, 2016 Th2A.6
[17]	Hu X, Wang A D, Zeng M Q, Long Y, Zhu L, Fu L, Wang J 2016 Sci. Rep. 6 32911
[18]	Chen W, Meng Z, Zhou H J, Luo H 2012 Acta Phys. Sin. 18 184210 (in Chinese) [陈伟, 孟洲, 周会娟, 罗洪 2012 物理学报 18 184210]
[19]	Li S B, Wu B J, Wen F, Han R 2013 Acta Phys. Sin. 62 024213 (in Chinese) [李述标, 武保剑, 文峰, 韩瑞 2013 物理学报 62 024213]
[20]	Zhou X Y, Wu B J, Wen F, Yuan H, Qiu K 2013 Opt. Commun. 308 1
[21]	Agrawal G P (translated by Jia D F, Yu Z H, et al) 2010 Nonlinear Fiber Optics, Fourth Edition Application of Nonlinear Fiber Optics (2nd Ed.) (Beijing: Publishing House of Electronics Industry) p274 (in Chinese) [阿戈沃G P 著 (贾东方, 余震虹, 等译) 2010 非线性光纤光学原理及应用(第二版) (北京: 电子工业出版社)第274页]
[22]	Liu Y, Tan Z W, Fu Y J, Ning D G, Jian S S 2003 Semi. Optoelectron. 2 110 (in Chinese) [刘艳, 谭中伟, 傅永军, 宁提纲, 简水生 2003 半导体光电 2 110]
[23]	Marhic M E 2013 J. Opt. Soc. Am. B 30 1462
[24]	Wang J, Sun Q Z, Sun J Q 2009 Opt. Express 17 12555
[25]	Bai J H, Li J J, Wu L A, Fu P M, Wang R Q, Zuo Z C 2017 Chin. Phys. B 26 044204
[26]	Fan C X, Cao L N 2010 Principles of Communications (6th Ed.) (Beijing: National Defense University Press) p13 (in Chinese) [樊昌信, 曹丽娜 2010 通信原理 (第6版) (北京: 国防工业出版社) 第13页]
[27]	Agrawal G P (translated by Jia D F, Yu Z H, et al.) 2010 Nonlinear Fiber Optics, Fourth Edition Application of Nonlinear Fiber Optics (2nd Ed.) (Beijing: Publishing House of Electronics Industry) p25 (in Chinese) [阿戈沃G P 著 (贾东方, 余震虹, 等译) 2010 非线性光纤光学原理及应用(第2版) (北京: 电子工业出版社)第25 页]
[28]	Gui C C, Wang J, Zhang Z L, Du J 2013 Sci. Rep. 4 378
[29]	Gui C C, Wang J 2014 Sci. Rep. 4 7491

施引文献

[1]	Wang J, Yang J Y, Huang H, Willner A E 2013 Opt. Express 21 488
[2]	Azeemuddin S, Chaitanya G V, Sayeh M R 2012 J. Opt. 41 142
[3]	Wang W R, Yu J L, Han B C, Guo J Z, Luo J, Wang J, Liu Y, Yang E Z 2012 Acta Phys. Sin. 8 084214 (in Chinese) [王文睿, 于晋龙, 韩丙辰, 郭精忠, 罗俊, 王菊, 刘毅, 杨恩泽 2012 物理学报 8 084214]
[4]	Wang A D, Hu X, Zhu L, Zeng M Q, Fu L, Wang J 2015 Opt. Express 23 31728
[5]	Yan S L 2013 Acta Phys. Sin. 62 230504 (in Chinese) [颜森林 2013 物理学报 62 230504]
[6]	Chen X, Huo L, Lou C Y, Wang J, Yu W K, Jiang X Y, Zhao Z X, Zhang E Y 2016 Acta Phys. Sin. 65 054208 (in Chinese) [陈新, 霍力, 娄采云, 王强, 余文科, 姜向宇, 赵之玺, 章恩耀 2016 物理学报 65 054208]
[7]	Li M X, Chen H, Zhang Y L, Qi S F, Zhang H J, Deng J, Chen Z J, Zhong S Q, Zhang D J 2011 Des. Tech. Pos. Telecom. 11 18 (in Chinese) [李懋循, 陈皓, 张耀亮, 祁劭峰, 张慧剑, 邓建, 陈志强, 钟胜前, 张德江 2011 邮电设计技术 11 18]
[8]	Zhang J W, Zhao Y L, Ji Y F 2016 Inf. Commun. Tech. 1 10 (in Chinese) [张佳玮, 赵永利, 纪越峰 2016 信息通信技术 1 10]
[9]	Wang F Q 2017 Chin. Phys. B 26 034202
[10]	Wang Z 2016 Sci. Tech. Rev. 34 121 (in Chinese) [王智 2016 科技导报 34 121]
[11]	Su Q Q, Zhang G W, Pu J X 2012 Acta Phys. Sin. 61 144208 (in Chinese) [苏倩倩, 张国文, 蒲继雄 2012 物理学报 61 144208]
[12]	Li Q L, Zhu M Y, Li D Q, Zhang Z, Wei Y Z, Hu M, Zhou X F, Tang X H 2014 Appl. Opt. 53 4708
[13]	Wang P, Chen B X, Wang G D, Sui G R, Zou L E, Bang Z J, Ji S 2011 Opt. Optoe. Tech. 9 48 (in Chinese) [王平, 陈抱雪, 王关德, 隋国荣, 邹林儿, 浜中广见, 矶守 2011 光学与光电技术 9 48]
[14]	Yin Z, Dong J J, Zhang X L 2011 16th OptoElectronics and Communications Conference Kaohsiung, Taiwan, China, July 4-8, 2011 p563
[15]	Karamdeep S, Gurmeet K, Lal S M 2016 Opt. Eng. 55 077104
[16]	Long Y, Gui C, Wang A, Hu X, Zhu L, Zhou L, Wang J 2016 Optical Fiber Communications Conference and Exhibition Anaheim, USA, March 20-24, 2016 Th2A.6
[17]	Hu X, Wang A D, Zeng M Q, Long Y, Zhu L, Fu L, Wang J 2016 Sci. Rep. 6 32911
[18]	Chen W, Meng Z, Zhou H J, Luo H 2012 Acta Phys. Sin. 18 184210 (in Chinese) [陈伟, 孟洲, 周会娟, 罗洪 2012 物理学报 18 184210]
[19]	Li S B, Wu B J, Wen F, Han R 2013 Acta Phys. Sin. 62 024213 (in Chinese) [李述标, 武保剑, 文峰, 韩瑞 2013 物理学报 62 024213]
[20]	Zhou X Y, Wu B J, Wen F, Yuan H, Qiu K 2013 Opt. Commun. 308 1
[21]	Agrawal G P (translated by Jia D F, Yu Z H, et al) 2010 Nonlinear Fiber Optics, Fourth Edition Application of Nonlinear Fiber Optics (2nd Ed.) (Beijing: Publishing House of Electronics Industry) p274 (in Chinese) [阿戈沃G P 著 (贾东方, 余震虹, 等译) 2010 非线性光纤光学原理及应用(第二版) (北京: 电子工业出版社)第274页]
[22]	Liu Y, Tan Z W, Fu Y J, Ning D G, Jian S S 2003 Semi. Optoelectron. 2 110 (in Chinese) [刘艳, 谭中伟, 傅永军, 宁提纲, 简水生 2003 半导体光电 2 110]
[23]	Marhic M E 2013 J. Opt. Soc. Am. B 30 1462
[24]	Wang J, Sun Q Z, Sun J Q 2009 Opt. Express 17 12555
[25]	Bai J H, Li J J, Wu L A, Fu P M, Wang R Q, Zuo Z C 2017 Chin. Phys. B 26 044204
[26]	Fan C X, Cao L N 2010 Principles of Communications (6th Ed.) (Beijing: National Defense University Press) p13 (in Chinese) [樊昌信, 曹丽娜 2010 通信原理 (第6版) (北京: 国防工业出版社) 第13页]
[27]	Agrawal G P (translated by Jia D F, Yu Z H, et al.) 2010 Nonlinear Fiber Optics, Fourth Edition Application of Nonlinear Fiber Optics (2nd Ed.) (Beijing: Publishing House of Electronics Industry) p25 (in Chinese) [阿戈沃G P 著 (贾东方, 余震虹, 等译) 2010 非线性光纤光学原理及应用(第2版) (北京: 电子工业出版社)第25 页]
[28]	Gui C C, Wang J, Zhang Z L, Du J 2013 Sci. Rep. 4 378
[29]	Gui C C, Wang J 2014 Sci. Rep. 4 7491

[1]	盖云冉, 郑康, 丁春玲, 郝向英, 金锐博. 基于半导体量子阱中四波混频效应的高效光学非互易. 物理学报, 2024, 73(1): 014201. doi: 10.7498/aps.73.20231212
[2]	孙凡, 文峰, 武保剑, Tan Ming-Ming, 凌云, 邱昆. 基于双向正交泵浦半导体光放大器结构的全光相位保持幅度再生技术. 物理学报, 2022, 71(20): 204204. doi: 10.7498/aps.71.20220703
[3]	徐笑吟, 刘胜帅, 荆杰泰. 基于四波混频过程的纠缠光放大. 物理学报, 2022, 71(5): 050301. doi: 10.7498/aps.71.20211324
[4]	翟淑琴, 康晓兰, 刘奎. 基于级联四波混频过程的量子导引. 物理学报, 2021, 70(16): 160301. doi: 10.7498/aps.70.20201981
[5]	Xiaoyin Xu, shengshuai liu, 荆杰泰. 基于四波混频过程的纠缠光放大. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211324
[6]	余胜, 刘焕章, 刘胜帅, 荆杰泰. 基于四波混频过程和线性分束器产生四组份纠缠. 物理学报, 2020, 69(9): 090303. doi: 10.7498/aps.69.20200040
[7]	杨荣国, 张超霞, 李妮, 张静, 郜江瑞. 级联四波混频系统中纠缠增强的量子操控. 物理学报, 2019, 68(9): 094205. doi: 10.7498/aps.68.20181837
[8]	孙江, 常晓阳, 张素恒, 熊志强. 应用双非简并四波混频理论研究原子的碰撞效应. 物理学报, 2016, 65(15): 154206. doi: 10.7498/aps.65.154206
[9]	惠战强, 张建国. 基于光子晶体光纤中双抽运四波混频效应的非归零到归零码型转换实验研究. 物理学报, 2013, 62(8): 084209. doi: 10.7498/aps.62.084209
[10]	惠战强, 张建国. 基于光子晶体光纤中四波混频效应的单到双非归零到归零码型转换. 物理学报, 2012, 61(1): 014217. doi: 10.7498/aps.61.014217
[11]	孙江, 孙娟, 王颖, 苏红新. 双光子共振非简并四波混频测量Ba原子里德伯态的碰撞展宽和频移. 物理学报, 2012, 61(11): 114214. doi: 10.7498/aps.61.114214
[12]	孙江, 刘鹏, 孙娟, 苏红新, 王颖. 双光子共振非简并四波混频测量钡原子里德伯态碰撞展宽中的伴线研究. 物理学报, 2012, 61(12): 124205. doi: 10.7498/aps.61.124205
[13]	邓莉, 孙真荣, 林位株, 文锦辉. 亚10 fs激光脉冲产生中的受激拉曼散射与四波混频效应. 物理学报, 2008, 57(12): 7668-7673. doi: 10.7498/aps.57.7668
[14]	刘霞, 牛金艳, 孙江, 米辛, 姜谦, 吴令安, 傅盘铭. 布里渊增强非简并四波混频. 物理学报, 2008, 57(8): 4991-4994. doi: 10.7498/aps.57.4991
[15]	朱成禹, 吕志伟, 何伟明, 巴德欣, 王雨雷, 高玮, 董永康. 布里渊增强四波混频时域特性的理论研究. 物理学报, 2007, 56(1): 229-235. doi: 10.7498/aps.56.229
[16]	贾新鸿, 钟东洲, 王飞, 陈海涛. 基于λ/4相移分布反馈半导体激光器四波混频的THz波长转换特性研究. 物理学报, 2007, 56(5): 2637-2646. doi: 10.7498/aps.56.2637
[17]	孙江, 左战春, 郭庆林, 王英龙, 怀素芳, 王颖, 傅盘铭. 应用双光子共振非简并四波混频测量Ba原子里德伯态. 物理学报, 2006, 55(1): 221-225. doi: 10.7498/aps.55.221
[18]	孙江, 左战春, 米辛, 俞祖和, 吴令安, 傅盘铭. 引入量子干涉的双光子共振非简并四波混频. 物理学报, 2005, 54(1): 149-154. doi: 10.7498/aps.54.149
[19]	孙　江, 姜　谦, 米　辛, 俞祖和, 傅盘铭. 利用场关联效应抑制瑞利型非简并四波混频的热背底. 物理学报, 2004, 53(2): 450-455. doi: 10.7498/aps.53.450
[20]	邵钟浩. 具有非均匀零色散波长光纤中的四波混频. 物理学报, 2001, 50(1): 73-78. doi: 10.7498/aps.50.73

计量

文章访问数: 7764
PDF下载量: 133
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板