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In recent years, the demand for network bandwidth has increased significantly, and the capacity of wave division multiplexing (WDM) systems has reached the nonlinear Shannon limit. In order to adapt to the development of future networks, space division multiplexing (SDM) technology attracts more and more attention. In this paper, we put forward a novel structure of pulse amplitude modulation(PAM) regenerator based on few-mode nonlinear optical fiber loop mirror (FM-NOLM) for the first time, and theoretically analyze the working principle for few-mode reshaping. It can regenerate degraded PAM signals and improve transmission performance in SDM system. The detailed design steps of the regenerator are given, in which the sulfide highly nonlinear fiber and multimode coupler are used to build up the FM-NOLM and their mode characteristics are simulated by COMSOL software. The parameters of the regenerator are determined by taking the few-mode optical fiber supporting LP01, LP11, and LP21 modes as an example, and then the power transfer function (PTF) curve of each mode for PAM signals is calculated. We simulate and analyze the noise reduction ratio (NRR) performance of the few-mode regenerator for PAM-4 signals, and compare with the case of single mode fiber. Our simulation shows that: (1) for each spatial mode of PAM signal, all regenerative levels have the same consistent power transfer performance; (2) for the input signal-to-noise ratio (SNR) greater than 20 dB, the NRR for each mode can exceed 3 dB, and increase with the input SNR at the slope of about 1.2; (3) the NRR difference between the three modes is less than 1.1 dB for the same input SNR. In order to illustrate the reshaping function of the regenerator, we also present the power distribution histograms for PAM-4 signals before and after regeneration when the input SNR is 25 dB. This scheme proposed here has some advantages over the existing regenerators in the applicability for the long-haul SDM system with high spectral efficiency and regeneration of any level number of PAM signals in theory due to its uniform multi-level regeneration function, but also is capable of being extended to the wavelength domain for higher transmission capacity.
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Keywords:
- few-mode fiber /
- all-optical regeneration /
- nonlinear fiber loop mirror /
- noise reduction radio
[1] Berdague S, Facq P 1982 Appl. Opt. 21 1950
Google Scholar
[2] Ryf R, Randel S, Fontaine N K, Palou X 2013 39th European Conference and Exhibition on Optical Communication London, UK, September 22–26, 2013 We2 D.1
[3] Sakamoto T, Saitoh K, Saitoh S, Abe Y, Takenaga K, Urushibara A, Wada M, Matsui T, Aikawa K, Nakajima K 2018 44th European Conference and Exhibition on Optical Communication Roma, Italy, September 23–27, 2018 p1
[4] Filipe M F, Costa S C, Sygletos S, Ellis A D 2019 J. Lightwave Technol. 37 989
Google Scholar
[5] Rademacher G, Luis R S, Puttnam B J, Maruyama R, Aikawa K, Awaji Y, Furukawa H, Petermann K, Wada N 2019 J. Lightwave Technol. 37 1273
Google Scholar
[6] Ryf R, Randel S, Gnauck A H, Bolle C, Sierra A, Mumtaz S, Esmaeelpour M, Burrows E C, Essiambre R, Winzer P J, Peckham D W, Mccurdy A H, Lingle R 2012 J. Lightwave Technol. 30 521
[7] Sidelnikov G, Redyuk A, Ferreira F, Sygletos S 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics ConferenceMunich, Germany, June 25−29, 2017 p1
[8] Tavares J S, Pessoa L M, Salgado H M 2017 J. Lightwave Technol. 35 4072
Google Scholar
[9] Ip E, Li M J, BennettK, Huang Y K, TanakaA, KorolevA, KoreshkovK, Wo od, William, MateoE, Hu J Q, YanoY 2014 J. Lightwave Technol. 32 790
Google Scholar
[10] Mamyshev P V 1998 24th European Conference on Optical Communication Madrid, Spain, September 20−24, 1998 p475
[11] Kakande J, Bogris A, Slavik R, Parmigiani F, Syvridis D, Petropoulos P, Richardson D J 2010 36th European Conference and Exhibition on Optical Communication Torino, Italy, September 19−23, 2010 p1
[12] Stiller B, Onishchukov G, Schmauss B, Leuchs G 2014 Opt. Express 22 1028
Google Scholar
[13] Alan E W, Ahmad F, Fatemeh A, Cao Y W, Amirhossein M A, Ahmed A, Liao P C, Zou K H, Ari N W, Moshe T 2019 J. Lightwave Technol. 37 21
Google Scholar
[14] Wen F, Geng Y, Liao M L, Wu B J, Lu L J, Zhou L J, Zhou X Y, Qiu K, Chen J P 2017 Asia Communications and Photonics Conference Guangdong, China, November 10−13, 2017 p1
[15] Zhou X Y, Wu B J, Wen F, Zhang H C, Zhou H, Qiu K 2014 Opt. Express 22 22937
Google Scholar
[16] Ryf R, Randel S, Gnauck A H, Bolle C, Essiambre R, Winzer P J, Peckham D W, Mccurdy A, Lingle R 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers ConferenceLos Angeles, USA, March 6−10, 2011 p1
[17] Wen F, Wu B J, Qiu K 2019 Opt. Express 27 19940
Google Scholar
[18] 宋阳 2018 硕士学位论文 (成都: 电子科技大学)
Song Y 2018 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China) (in Chinese)
[19] Sygletos S, Weerasuriya R, Ibrahim S K, Gunning F, Phelan R, O'Gorman J, O'Carrol J, Kelly B, Bogris A, Syvridis D, Lundström C, Andrekson P, Parmigiani F, Richardson D J, Ellis A D 2010 12th International Conference on Transparent Optical Networks Munich, Germany, June 27−July 1, 2010 p1
[20] Guo B, Wen F, Wu B J, Sun F, Qiu K 2019 IEEE Access 7 149666
Google Scholar
[21] Wen F, Tsekrekos C P, Geng Y, Zhou X Y, Wu B J, Qiu K, Turitsyn S K, Sygletos S 2018 Opt. Express 26 12698
Google Scholar
[22] 万峰, 武保剑, 曹亚敏, 王瑜浩, 文峰, 邱昆 2019 物理学报 68 20182129
Wan F, Wu B J, Cao Y M, Wang Y H, Wen F, Qiu K 2019 Acta Phys. Sin. 68 20182129
[23] Jiang X R, Wu B J, Guo B, Wen F, Qiu K 2020 Opt. Commun. 458 124840
[24] Li M, Liao Y B 1999 J. Optoelectron. Laser 5 480
[25] 武保剑, 邱昆 2013 光纤信息处理原理及技术 (北京: 科学出版社) 第152−154页
Wu B J, Qiu K 2013 Fiber-optical Information Processing Principles and Technology (Beijing: Science Press) pp152−154 (in Chinese)
[26] 曹亚敏, 武保剑, 万峰, 邱昆 2018 物理学报 6 7094208
Cao Y M, Wu B J, Wan F, Qiu K 2018 Acta Phys. Sin. 6 7094208
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图 1 少模PAM再生器原理图
Figure 1. Schematic diagram of a few-mode PAM regenerator.
图 2 再生器输入输出功率转移曲线
Figure 2. The regenerator’sinput and output power transfer function (PTF) curve.
图 3 LP01, LP11, LP21三个模式的NRR再生性能随(a)归一化输入噪声功率
$\sigma _{{\rm{in}}}^2$ 和(b)输入信噪比${\rm{SN}}{{\rm{R}}_{{\rm{in}}}}$ 的变化曲线Figure 3. The NRR regeneration performance of LP01, LP11, and LP21 with (a) normalized input noise power (b) input signal-to-noise ratio.
图 4 LP01, LP11, LP21再生前后电平功率分布直方图 (a) LP01; (b) LP11; (c) LP21
Figure 4. The each level power histogram before and after regeneration of LP01, LP11 and LP21: (a) LP01; (b) LP11; (c) LP21.
表 1 高非线性硫化物光纤参数
Table 1. The highly nonlinear As-Se chalcogenide glass fiber’s parameters.
模式类型 模场分布 有效折射率 有效模场面积 非线性系数 n Aeff,i/μm2 γi/W–1·km–1 LP01 
1.4444 143.4123 118.72 LP11 
1.4425 206.4894 82.5 LP21 
1.4400 236.8308 71.8 
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表 2 FM-NOLM再生器设计参数
Table 2. The parameters ofFM-NOLM Regenerator
模式
类型多模光纤耦合器 辅助光源功率 少模光放大器增益 模式耦合效率${\rho _i}$ ${P_{y, i}}/{\rm{dBm}}$ ${G_i}/{\rm{dB}}$ LP01 0.84 23.73 1.99 LP11 0.50 22.62 5.83 LP21 0.18 25.50 10.86
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[1] Berdague S, Facq P 1982 Appl. Opt. 21 1950
Google Scholar
[2] Ryf R, Randel S, Fontaine N K, Palou X 2013 39th European Conference and Exhibition on Optical Communication London, UK, September 22–26, 2013 We2 D.1
[3] Sakamoto T, Saitoh K, Saitoh S, Abe Y, Takenaga K, Urushibara A, Wada M, Matsui T, Aikawa K, Nakajima K 2018 44th European Conference and Exhibition on Optical Communication Roma, Italy, September 23–27, 2018 p1
[4] Filipe M F, Costa S C, Sygletos S, Ellis A D 2019 J. Lightwave Technol. 37 989
Google Scholar
[5] Rademacher G, Luis R S, Puttnam B J, Maruyama R, Aikawa K, Awaji Y, Furukawa H, Petermann K, Wada N 2019 J. Lightwave Technol. 37 1273
Google Scholar
[6] Ryf R, Randel S, Gnauck A H, Bolle C, Sierra A, Mumtaz S, Esmaeelpour M, Burrows E C, Essiambre R, Winzer P J, Peckham D W, Mccurdy A H, Lingle R 2012 J. Lightwave Technol. 30 521
[7] Sidelnikov G, Redyuk A, Ferreira F, Sygletos S 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics ConferenceMunich, Germany, June 25−29, 2017 p1
[8] Tavares J S, Pessoa L M, Salgado H M 2017 J. Lightwave Technol. 35 4072
Google Scholar
[9] Ip E, Li M J, BennettK, Huang Y K, TanakaA, KorolevA, KoreshkovK, Wo od, William, MateoE, Hu J Q, YanoY 2014 J. Lightwave Technol. 32 790
Google Scholar
[10] Mamyshev P V 1998 24th European Conference on Optical Communication Madrid, Spain, September 20−24, 1998 p475
[11] Kakande J, Bogris A, Slavik R, Parmigiani F, Syvridis D, Petropoulos P, Richardson D J 2010 36th European Conference and Exhibition on Optical Communication Torino, Italy, September 19−23, 2010 p1
[12] Stiller B, Onishchukov G, Schmauss B, Leuchs G 2014 Opt. Express 22 1028
Google Scholar
[13] Alan E W, Ahmad F, Fatemeh A, Cao Y W, Amirhossein M A, Ahmed A, Liao P C, Zou K H, Ari N W, Moshe T 2019 J. Lightwave Technol. 37 21
Google Scholar
[14] Wen F, Geng Y, Liao M L, Wu B J, Lu L J, Zhou L J, Zhou X Y, Qiu K, Chen J P 2017 Asia Communications and Photonics Conference Guangdong, China, November 10−13, 2017 p1
[15] Zhou X Y, Wu B J, Wen F, Zhang H C, Zhou H, Qiu K 2014 Opt. Express 22 22937
Google Scholar
[16] Ryf R, Randel S, Gnauck A H, Bolle C, Essiambre R, Winzer P J, Peckham D W, Mccurdy A, Lingle R 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers ConferenceLos Angeles, USA, March 6−10, 2011 p1
[17] Wen F, Wu B J, Qiu K 2019 Opt. Express 27 19940
Google Scholar
[18] 宋阳 2018 硕士学位论文 (成都: 电子科技大学)
Song Y 2018 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China) (in Chinese)
[19] Sygletos S, Weerasuriya R, Ibrahim S K, Gunning F, Phelan R, O'Gorman J, O'Carrol J, Kelly B, Bogris A, Syvridis D, Lundström C, Andrekson P, Parmigiani F, Richardson D J, Ellis A D 2010 12th International Conference on Transparent Optical Networks Munich, Germany, June 27−July 1, 2010 p1
[20] Guo B, Wen F, Wu B J, Sun F, Qiu K 2019 IEEE Access 7 149666
Google Scholar
[21] Wen F, Tsekrekos C P, Geng Y, Zhou X Y, Wu B J, Qiu K, Turitsyn S K, Sygletos S 2018 Opt. Express 26 12698
Google Scholar
[22] 万峰, 武保剑, 曹亚敏, 王瑜浩, 文峰, 邱昆 2019 物理学报 68 20182129
Wan F, Wu B J, Cao Y M, Wang Y H, Wen F, Qiu K 2019 Acta Phys. Sin. 68 20182129
[23] Jiang X R, Wu B J, Guo B, Wen F, Qiu K 2020 Opt. Commun. 458 124840
[24] Li M, Liao Y B 1999 J. Optoelectron. Laser 5 480
[25] 武保剑, 邱昆 2013 光纤信息处理原理及技术 (北京: 科学出版社) 第152−154页
Wu B J, Qiu K 2013 Fiber-optical Information Processing Principles and Technology (Beijing: Science Press) pp152−154 (in Chinese)
[26] 曹亚敏, 武保剑, 万峰, 邱昆 2018 物理学报 6 7094208
Cao Y M, Wu B J, Wan F, Qiu K 2018 Acta Phys. Sin. 6 7094208
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