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With the rapid increase of the capacity of optical fiber transmission system, the mode division multiplexing (MDM) transmission system using few-mode fibers (FMFs) (which provides the multi-channel multiplexing, high efficiency of frequency spectrum, and low nonlinear effects) becomes a research focus to upgrade the capacity of the optical communication. In this paper, an analytical expression of bending loss for each high-order mode of parabolic-index FMFs is deduced based on the perturbation theory and verified by finite element method. Based on this expression, the influence of four key structure parameters of trench-assisted parabolic-index FMFs: i.e. the radius of fiber core, the distance between core and trench, the width of trench, and the refractive index difference of trench, on the bending loss performance are discussed in detail. It is found that, firstly, the sensitivity of the bending loss increases with the increase of mode order of FMFs. Secondly, the smaller the core radius, the smaller the bending loss of each mode-order is, since small core radius leads to a smaller effective mode area, which is beneficial for saving power leakage. Additionally, the effective mode area of LP02 mode is lower than that of LP21 mode, while the bending loss of LP02 mode is higher than that of LP21 mode, this observation is different from other mode-orders. Thirdly, an optimized distance between trench and core for each high-order mode is also investigated for obtaining minimum bending loss, which plays an important role in controlling the bending performance of FMFs. So the higher the mode-order, the smaller the optimized distance between core and trench is, and this observation could be used to optimize the bending loss of the fiber. With the increase of the distance between the core and trench, the effective mode area of high-order mode increases quickly at first, then it is approximately unaltered. The distance between the core and trench is a key factor that influences both the bending loss and the effective mode area of each mode. Finally, the bending loss of each mode decreases with the increase of the width of trench around the fiber core or the refractive index difference of trench. These results are helpful for understanding the mechanism of bending loss for FMFs and are of significance for designing and manufacturing of few-mode bend-insensitive fibers, especially for the optimization of the bending loss of specific high-order mode.
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Keywords:
- few-mode fiber /
- bending loss /
- trench assisted /
- bend-insensitive
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[2] Morioka T 2009 Proceedings of the 14th Opto-Electronics and Communications Conference Hong Kong, China, July 13-17, 2009 p1
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[19] Wang Q, Farrell G, Feir T 2005 Opt. Express 13 4476
[20] Vassallo C 1985 Opt. Quantum. Electron 17 201
[21] Vassallo C 1985 J. Lightwave Technol. LT-3 416
[22] Li H S, Ren G B, Yin B, Lian Y D, Bai Y L, Jian W, Jian S S 2015 Opt. Common. 352 84
[23] Hagen R 1992 J. Lightwave Technol. 10 543
[24] Ren G B, Lin Z, Zheng SW, Jian S S 2013 Opt. Lett. 38 781
[25] Zhang Z Y, Ren G B, Zhou D A, Wu J L 2014 Laser Opt. Electron. Prog. 51 78 (in Chinese) [张子阳, 任国斌, 周定安, 吴家梁 2014 激光与光电子学进展 51 78]
[26] Schermer R T, Cole J H 2007 IEEE J. Quantum. Electron 43 899
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[1] Desurvire E B 2006 J. Lightwave Technol. 24 4697
[2] Morioka T 2009 Proceedings of the 14th Opto-Electronics and Communications Conference Hong Kong, China, July 13-17, 2009 p1
[3] Yan L S, Liu X, Shieh W 2011 IEEE Photon. J. 3 325
[4] Essiambre R J, Kramer G, Winzer P, Foschini G J, Goebel B 2010 J. Lightwave Technol. 28 662
[5] Xie Y W, Fu S N, Zhang H L, Tang M, Shen P, Liu D M 2013 Acta Opt. Sin. 9 09060101 (in Chinese) [谢意维, 付松年, 张海亮, 唐明, 沈平, 刘德明 2013 光学学报 9 09060101]
[6] Yao S C, Fu S N, Zhang M M, Tang M, Shen P, Liu D M 2013 Acta Phys. Sin. 62 144215 (in Chinese) [姚殊畅, 付松年, 张敏明, 唐明, 沈平, 刘德明 2013 62 144215]
[7] Marcuse D 1976 J. Opt. Soc. Am. 66 311
[8] Watekar P R, Ju S, Yoon Y S, Lee Y S, Han W T 2008 Opt. Express 16 13545
[9] Watekar P R, Ju S, Htein L, Han W T 2010 Opt. Express 18 13761
[10] Goto Y, Nakajima K, Kurashima T 2012 Proceeding of the 17th Opto-electronics and Communications Conference (OECC) BuSan, July 2-6, 2012 p813
[11] Lin Z 2014 Ph. D. Dissertation (Beijing: Beijing Jiaotong University) (in Chinese) [林桢2007博士学位论文 (北京:北京交通大学)]
[12] Li H S, Ren G B, Gao Y X, Lian Y D, Cao M, Jian S S 2015 IEEE Photon. Technol. Lett. 27 1293
[13] Jiang S S, Liu Y, Xing E J 2015 Acta Phys. Sin. 64 064212 (in Chinese) [姜姗姗, 刘艳, 邢尔军 2015 64 064212]
[14] Schulze C, Lorenz A, Flamm D, Hartung A, Schrter S, Bartelt H, Duparr M 2013 Opt. Express 21 3170
[15] Lars G N, Sun Y, Nicholson J W, Jakobsen D, Jespersen K G, Lingle R, Palsdottir B 2012 J. Lightwave Technol. 30 3693
[16] Denis D 2009 Opt. Express 17 22081
[17] Lin Z, Zheng S W, Ren G B, Jian S S 2013 Acta Phys. Sin. 62 064214 (in Chinese) [林桢, 郑斯文, 任国斌, 简水生 2013 62 064214]
[18] Faustini L, Martini G 1997 J. Lightwave Technol. 15 671
[19] Wang Q, Farrell G, Feir T 2005 Opt. Express 13 4476
[20] Vassallo C 1985 Opt. Quantum. Electron 17 201
[21] Vassallo C 1985 J. Lightwave Technol. LT-3 416
[22] Li H S, Ren G B, Yin B, Lian Y D, Bai Y L, Jian W, Jian S S 2015 Opt. Common. 352 84
[23] Hagen R 1992 J. Lightwave Technol. 10 543
[24] Ren G B, Lin Z, Zheng SW, Jian S S 2013 Opt. Lett. 38 781
[25] Zhang Z Y, Ren G B, Zhou D A, Wu J L 2014 Laser Opt. Electron. Prog. 51 78 (in Chinese) [张子阳, 任国斌, 周定安, 吴家梁 2014 激光与光电子学进展 51 78]
[26] Schermer R T, Cole J H 2007 IEEE J. Quantum. Electron 43 899
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