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Mode-division multiplexing (MDM) technology based on few-mode fibers (FMFs) is the current research hotspot of optical fiber communication system because of its ability to increase the transmission capacity several times. When the number of multiplexed modes is large, the crosstalk between modes can be removed by multiple input multiple output digital signal processing algorithm at the receiving end. The larger the differential mode group delay (DMGD,
$ \tau_{\rm DMGD} $ ), the more complex the algorithm is. Therefore, in order to reduce the complexity of the receiver, it is necessary to use FMFs with low DMGD. The variational method is proposed to analyze any FMFs with higher refractive index of core than that of cladding. The analytical formula of the fundamental mode size, the normalized propagation constant for each of all guided modes, and DMGD relative to the fundamental mode are derived. Moreover, their relationship with the normalized frequency and other fiber manufacturing parameters are given. On this basis, the graded-index FMFs are studied, and the fiber parameters are optimized. The optimization parameters are the difference between the maximum core refractive index and cladding refractive index n1 – n2 = 0.01, the core radius a = 14 μm, and the paramenter of refractive index distribution α = 1.975. In the optimized FMF, 6 LP modes can be guided and |$ \tau_{\rm DMGD} $ | is less than 15 ps/km within the C band and L band. In the end, the effects of the fiber manufacturing errors on DMGD are discussed.-
Keywords:
- mode-division multiplexing /
- few-mode fibers /
- variational method /
- differential mode group delay
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Wu C Q 2005 Optical Waveguide Theory (2nd Ed. ) (Beijing: Tsinghua University Press) pp100–110 (in Chinese)
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图 1 指数
$\alpha $ 不同时, 梯度折射率光纤模斑尺寸与纤芯半径之比$ s/a $ 随归一化频率V的变化Figure 1. Ratio of the mode size of the graded fiber to the core radius s/a as a function of normalized frequency V when the index α is different.
图 2 指数α不同时, 梯度折射率光纤归一化传播常数blp随归一化频率V的变化 (a) α = 1.5; (b) α = 2.0; (c) α = 2.5
Figure 2. Normalized propagation constant blp of graded index fiber as a function of normalized frequency V when the index α is different: (a) α = 1.5; (b) α = 2.0; (c) α = 2.5.
图 3 LP11模的DMGD随α和a的变化
Figure 3. DMGD of LP11 mode as a function of α and a.
图 4 λ = 1.55 μm, α = 1.975时DMGD随a的变化
Figure 4. DMGD as a function of a when λ = 1.55 μm, α = 1.975.
图 5 DMGD随波长的变化
Figure 5. DMGD as a function of wavelength
图 6 DMGD随折射率、芯区半径和α值制造误差的变化
Figure 6. DMGD as a function of manufacturing errors of refractive index, core radius and α value.
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[1] 涂佳静, 李朝晖 2021 光学学报 41 0106003
Google Scholar
Tu J J, Li Z H 2021 Acta Opt. Sin. 41 0106003
Google Scholar
[2] Ryf R, Randel S, Gnauck A H, Bolle C, Sierra A, Mumtaz S, Esmaeelpour M, Burrows E C, Essiambre René-Jean, Winzer P J, Peckham D W, McCurdy A H, Lingle R 2012 J. Lightwave Technol. 30 521
Google Scholar
[3] Sakamoto T, Mori T, Yamamoto T, Tomita S 2012 J. Lightwave Technol. 30 2783
Google Scholar
[4] [5] Parmigiani F, Jung Y, Grüner-Nielsen L, Geisler T, Petropoulos P, Richardson D J 2017 IEEE Photonic. Tech. L. 29 1764
Google Scholar
[6] Xiao H, Li H, Wu B L, Dong Y, Xiao S Y, Jian S H 2019 Opt. Fiber Technol. 48 7
Google Scholar
[7] Xie Y H, Pei L, Zheng J J, Zhao Q, Ning T G, Li J 2021 Opt. Express 29 15067
Google Scholar
[8] Sillard P, Bigot-Astruc M, Boivin D, Maerten H, Provost L 2011 Proceeding of 37th European Conference and Exposition on Optical Communications Geneva, Switzerland, September 18–22, 2011 pTu.5.LeCervin.7
[9] Sillard P, Molin D 2013 Proceeding of 39th European Conference and Exposition on Optical Communications London, UK, September 22–26, 2013 p1
[10] Ferreira F M, Fonseca D, da Silva H J A 2014 J. Lightwave Technol. 32 353
Google Scholar
[11] Li M J, Hoover B, Li S P, Bickham S, Ten S, Ip E, Huang Y K, Mateo E, Shao Y, Wang T 2012 Proceeding of 17th Opto-Electronics and Communications Conference Busan, Korea (South), July 2–6, 2012 p495
[12] Mori T, Sakamoto T, Wada M, Urushibara A, Yamamoto T, Yamamoto F 2015 Proceeding of European Conference on Optical Communication Valencia, Spain, September 27–October 1, 2015 p1
[13] Sato K, Maruyama R, Kuwaki N, Matsuo S, Ohashi M 2013 Opt. Express 21 16231
Google Scholar
[14] Ryf R, Randel S, Gnauck A H, Bolle C, Essiambre R J, Winzer P J, Peckham D W, McCurdy A, Lingle R 2011 Proceeding of Optical Fiber Communication Conference Los Angeles, United States, March 6–10, 2011 pPDPB10
[15] Randel S, Ryf R, Gnauck A H, Mestre M A, Schmidt C, Essiambre R J, Winzer P J, Delbue R, Pupalaikis P, Sureka A, Sun Y, Jiang X, Lingle R 2012 Proceeding of National Fiber Optic Engineers Conference Los Angeles, United States, March 4–8, 2012 pPDP5C.5
[16] Yang Z Q, Zhao J, Bai N, Ip E, Wang T, Li G F 2015 Proceeding of European Conference on Optical Commu- nication Valencia, Spain, September 27–October 1, 2015 p1
[17] Grüner-Nielsen L, Sun Y, Nicholson J W, Jakobsen D, Jespersen K G, Lingle R, Pálsdóttir B 2012 J. Lightwave Technol. 30 3693
Google Scholar
[18] Jensen R V, GrünerNielsen L, Wong N H L, Sun Y, Jung Y M, Richardson D J 2015 Proceeding of Optical Fiber Communication Conference Los Angeles, United States, March 22–26, 2015 pW2A.34
[19] Maruyama R, Kuwaki N, Matsuo S, Ohashi M 2014 Opt. Express 22 14311
Google Scholar
[20] Mori T, Sakamoto T, Wada M, Yamamoto T, Yamamoto F 2013 Proceeding of Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference Anaheim, United States, March 17–21, 2013 pOTh3K.1
[21] Mori T, Sakamoto T, Wada M, Yamamoto T, Yamamoto F 2014 J. Lightwave Technol. 32 2468
Google Scholar
[22] Sillard P, Bigot-Astruc M, Molin D 2014 2014 J. Lightwave Technol. 32 2824
Google Scholar
[23] Sillard P, Molin D, Bigot-Astruc M, Jongh K D, Achten F, Velazquez-Benitez A M, Amezcua-Correa R, Okonkwo C M 2016 J. Lightwave Technol. 34 425
Google Scholar
[24] 姜珊珊, 刘艳, 邢尔军 2015 64 064212
Google Scholar
Jiang S S, LiuY, Xing E J 2015 Acta Phys. Sin. 64 064212
Google Scholar
[25] 刘畅, 裴丽, 解宇恒, 王建帅, 郑晶晶, 宁提纲, 李晶 2020 中国激光 47 1106004
Google Scholar
Liu C, Pei L, Xie Y H, Wang J S, Zheng J J, Ning T G, Li J 2020 Chin. J. Lasers 47 1106004
Google Scholar
[26] 王彦, 韩颖, 李增辉, 龚琳, 王璐瑶, 李曙光 2022 71 024205
Google Scholar
Wang Y, Han Y, Li Z H, Gong L, Wang L Y, Li S G 2022 Acta Phys. Sin. 71 024205
Google Scholar
[27] 吴重庆 2005 光波导理论 (第二版) (北京: 清华大学出版社) 第100—110页
Wu C Q 2005 Optical Waveguide Theory (2nd Ed. ) (Beijing: Tsinghua University Press) pp100–110 (in Chinese)
[28] 佘守宪 2002 导波光学物理基础 (北京: 北方交通大学出版社) 第327—337页
She S X 2002 Physical Basis of Waveguided Optics (Beijing: North Jiaotong University Press) pp327–337 (in Chinese)
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