Principle and noise performance of optical phase arithmetic devices using four wave mixing

Cao Ya-Min; Wu Bao-Jian; Wan Feng; Qiu Kun

doi:10.7498/aps.67.20172638

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:

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).

References

[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

Cited By

[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]	Ge Yun-Ran, Zheng Kang, Ding Chun-Ling, Hao Xiang-Ying, Jin Rui-Bo. Efficient optical nonreciprocity based on four-wave mixing effect in semiconductor quantum well. Acta Physica Sinica, 2024, 73(1): 014201. doi: 10.7498/aps.73.20231212
[2]	Sun Fan, Wen Feng, Wu Bao-Jian, Tan Ming-Ming, Ling Yun, Qiu Kun. All-optical phase-preserving amplitude-regeneration technology based on bidirectional orthogonal-pumped semiconductor optical amplifier configuration. Acta Physica Sinica, 2022, 71(20): 204204. doi: 10.7498/aps.71.20220703
[3]	Xu Xiao-Yin, Liu Sheng-Shuai, Jing Jie-Tai. Amplification of entangled beam based on four-wave mixing process. Acta Physica Sinica, 2022, 71(5): 050301. doi: 10.7498/aps.71.20211324
[4]	Zhai Shu-Qin, Kang Xiao-Lan, Liu Kui. Quantum steering based on cascaded four-wave mixing processes. Acta Physica Sinica, 2021, 70(16): 160301. doi: 10.7498/aps.70.20201981
[5]	. Amplification of entangled beam based on four-wave mixing process. Acta Physica Sinica, 2021, (): . doi: 10.7498/aps.70.20211324
[6]	Yu Sheng, Liu Huan-Zhang, Liu Sheng-Shuai, Jing Jie-Tai. Generation of quadripartite entanglement based on four-wave mixing process and linear beam splitter. Acta Physica Sinica, 2020, 69(9): 090303. doi: 10.7498/aps.69.20200040
[7]	Yang Rong-Guo, Zhang Chao-Xia, Li Ni, Zhang Jing, Gao Jiang-Rui. Quantum manipulation of entanglement enhancement in cascaded four-wave-mixing process. Acta Physica Sinica, 2019, 68(9): 094205. doi: 10.7498/aps.68.20181837
[8]	Sun Jiang, Chang Xiao-Yang, Zhang Su-Heng, Xiong Zhi-Qiang. Theoretical study of atom collision by two-nondegenerate four-wave mixing. Acta Physica Sinica, 2016, 65(15): 154206. doi: 10.7498/aps.65.154206
[9]	Hui Zhan-Qiang, Zhang Jian-Guo. All-optical format conversion from non-return-to-zero to return-to-zero based on dual-pump four-wave mixing in photonic crystal fiber. Acta Physica Sinica, 2013, 62(8): 084209. doi: 10.7498/aps.62.084209
[10]	Hui Zhan-Qiang, Zhang Jian-Guo. All-optical format conversion from non-return-to-zero to return-to-zero based on four-wave mixing in photonic crystal fiber. Acta Physica Sinica, 2012, 61(1): 014217. doi: 10.7498/aps.61.014217
[11]	Sun Jiang, Sun Juan, Wang Ying, Su Hong-Xin. Measurement of the argon-gas-induced broadening and shifting of the barium Rydberg levels by two-photon resonant nondegenerate four-wave mixing. Acta Physica Sinica, 2012, 61(11): 114214. doi: 10.7498/aps.61.114214
[12]	Sun Jiang, Liu Peng, Sun Juan, Su Hong-Xin, Wang Ying. Study of the satellite line in measurement of the argon -gas-induced broadening of the barium Rydberg levels by two-photon resonant nondegenerate four-wave mixing. Acta Physica Sinica, 2012, 61(12): 124205. doi: 10.7498/aps.61.124205
[13]	Deng Li, Sun Zhen-Rong, Lin Wei-Zhu, Wen Jin-Hui. The stimulated Raman scattering and the four wave mixing in the generation of sub-10 fs pulses. Acta Physica Sinica, 2008, 57(12): 7668-7673. doi: 10.7498/aps.57.7668
[14]	Liu Xia, Niu Jin-Yan, Sun Jiang, Mi Xin, Jiang Qian, Wu Ling-An, Fu Pan-Ming. Brillouin-enhanced nondegenerate four-wave mixing. Acta Physica Sinica, 2008, 57(8): 4991-4994. doi: 10.7498/aps.57.4991
[15]	Zhu Cheng-Yu, Lü Zhi-Wei, He Wei-Ming, Ba De-Xin, Wang Yu-Lei, Gao Wei, Dong Yong-Kang. Theoretical study on temporal behavior of Brillouin-enhanced four-wave mixing. Acta Physica Sinica, 2007, 56(1): 229-235. doi: 10.7498/aps.56.229
[16]	Jia Xin-Hong, Zhong Dong-Zhou, Wang Fei, Chen Hai-Tao. Theoretical investigation on THz wavelength conversion based on four-wave mixing in QWS-DFB-LD. Acta Physica Sinica, 2007, 56(5): 2637-2646. doi: 10.7498/aps.56.2637
[17]	Sun Jiang, Zuo Zhan-Chun, Guo Qing-Lin, Wang Ying-Long, Huai Su-Fang, Wang Ying, Fu Pan-Ming. Observation of Rydberg series of neutral barium by two-photon resonent nondegenerate four-wave mixing. Acta Physica Sinica, 2006, 55(1): 221-225. doi: 10.7498/aps.55.221
[18]	Sun Jiang, Zuo Zhan-Chun, Mi Xin, Yu Zu-He, Wu Ling-An, Fu Pan-Ming. Two-photon resonant nondegenerate four-wave mixing via quantum interference. Acta Physica Sinica, 2005, 54(1): 149-154. doi: 10.7498/aps.54.149
[19]	Sun Jiang, Jiang Qian, Mi Xin, Yu Zu-He, Fu Pan-Ming. Thermal background suppression in Rayleigh-type nondegenerate four-wave mixing based on field-correlation effects. Acta Physica Sinica, 2004, 53(2): 450-455. doi: 10.7498/aps.53.450
[20]	Shao Zhong-Hao. . Acta Physica Sinica, 2001, 50(1): 73-78. doi: 10.7498/aps.50.73

Catalog

Vol. 67, Issue 9 - 2018-05-05

Metrics

Abstract views: 7951
PDF Downloads: 136
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板