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本文设计了一种具有对称双环嵌套管结构的新型低损耗少模空芯负曲率光纤, 该光纤支持LP01, LP11, LP21, LP02, LP31a, LP31b共6种纤芯模式. 所设计的光纤以SiO2作为基底材料, 采用特殊的对称双环嵌套结构将包层区域进行划分, 能够有效地减小纤芯模式与包层模式的耦合. 使用有限元法对该少模空芯负曲率光纤的结构参数进行优化, 并分析了纤芯各个模式的限制损耗和弯曲损耗. 仿真结果表明, 所提出的少模空芯负曲率光纤能够同时支持弱耦合的6种纤芯模式独立传输(相邻模式间的有效折射率差均大于10–4, 有效地避免了纤芯内模式间的耦合). 在400 nm带宽(1.23—1.63 μm, 覆盖O, E, S, C, L波段)范围内, 纤芯中的6个模式均保持低损耗稳定传输. 各模式限制损耗在1.4 μm处达到最低, 其中基模LP01模式的限制损耗最低, 为4.3×10–7 dB/m. 此外, 当弯曲半径为7 cm时, 各模式在一定工作波长范围内均保持低弯曲损耗传输. 公差分析表明, 当结构参数偏移±1%时, 该少模空芯负曲率光纤仍然可以保持低损耗弱耦合的传输特性.Few-mode optical fibers have played an increasingly important role in breaking through the transmission capacity limitations of single-mode optical fiber and alleviating the bandwidth crisis in optic fiber communication systems in recent years. Nevertheless, traditional solid core few-mode optical fibers usually suffer optical fiber nonlinearity and mode coupling, leading to mode crosstalk between channels. Hollow core negative curvature fibers (HC-NCF) have attracted widespread attention due to their advantages, such as low latency, low nonlinearity, low dispersion, low transmission loss, and large operating bandwidth. In this work, a novel low-loss few-mode HC-NCF with symmetrically double ring nested tube structure is designed, which supports six core modes including LP01, LP11, LP21, LP02, LP31a, and LP31b. The designed optical fiber is based on silica dioxide substrate and adopts a unique symmetrical double ring nested cladding structure, which can effectively suppress the coupling between the core mode and the cladding mode. The finite element method (FDE) is used to numerically analyze the properties of the proposed few-mode HC-NCF and optimize the structural parameters of the few-mode HC-NCF. Moreover, the confinement loss and bending loss of all core modes are investigated. The simulation results show that the proposed few-mode HC-NCF can support the independent transmission of six weakly coupled core modes (with the effective refractive index difference greater than 1×10–4 between the adjacent core modes, which greatly avoids the coupling between the adjacent modes in the fiber core). In the 400 nm bandwidth (1.23–1.63 μm, covering the O, E, S, C, and L bands), all six modes in the fiber core maintain low loss transmission. Moreover, in the range of 1.3–1.63 μm, the confinement loss (CL) of LP01, LP11 and LP21 mode are all less than 1×10–3 dB/m, and the CL of LP02 and LP31b mode are both less than 3×10–3 dB/m. The CL of each mode reaches the lowest value at 1.4 μm, and the LP01 mode has the lowest CL of 4.3×10–7 dB/m. In addition, for a bending radius of 7 cm, each mode maintains the low bending loss characteristic in a certain operating wavelength range. In the range of 1.23–1.61 μm, the BL of LP01 is less than 4.5×10–4 dB/m, and the BL of LP11 is less than 1.3×10–3 dB/m. The tolerance analysis shows that even with the deviation of structural parameters of ±1%, the few-mode HC-NCF can still maintain the characteristic of low-loss and weak coupling. The designed few-mode HC-NCF has ultra-low CL and bending-insensitive characteristics while supporting independent transmission of six modes, which will find huge potential applications in future high performance mode division multiplexing systems.
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[10] Azendorf F, Schmauss B, Shi B, Fokoua E N, Radan Slavík, Eiselt M 2021 Optical Fiber Communications Conference and Exhibition (OFC) San Francisco, California United States, June 6–10, 2021 p1
[11] Liu W, Zheng Y, Wang Z, Wang Z X, Yang J, Chen M X, Qi M, Rehman S U, Shum P P, Zhu L, Wei L 2021 Adv. Mater. Interfaces 8 2001978Google Scholar
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[13] Urich A, Maier R R, Yu F, Knight J C, Hand D P, Shephard J D 2013 Biomed. Opt. Express 4 193Google Scholar
[14] Couch D E, Hickstein D D, Winters D G, Backus S J, Kirchner M S, Domingue S R, Ramirez J J, Durfee C G, Murnane M M, Kapteyn H C 2020 Optica 7 832Google Scholar
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[17] Roberts P, Couny F, Sabert H, Mangan B, Williams D, Farr L, Mason M, Tomlinson A, Birks T, Knight J, Russell S J P 2005 Opt. Express 13 236Google Scholar
[18] Luan F, George A K, Hedley T D, Pearce G J, Bird D M, Knight J C, Russell P S J 2004 Opt. Lett. 29 2369Google Scholar
[19] Wei C, Weiblen R J, Menyuk C R, Hu J 2017 Adv. Opt. Photonics 9 562Google Scholar
[20] Jasion G T, Bradley T, Harrington K, Sakr H, Poletti F 2020 Optical Fiber Communications Conference and Exhibition (OFC) San Diego, California United States, March 8–12, 2020
[21] Osório J H, Amrani F, Delahaye F, Dhaybi A, Vasko K, Melli F, Giovanardi F, Vandembroucq D, Tessier G, Vincetti L, Debord B, Gérôme F, Benabid F 2023 Nat. Commun. 14 1146Google Scholar
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[33] Zhang H, Chang Y J, Xu Y T, Liu C Z, Xiao X S, Li J S, Ma X X, Wang Y Y, Guo H T 2023 Opt. Express 31 7659Google Scholar
[34] Zhou Y, Cao R, Wang S, Peng J, Li H, Chu Y, Xing Y, Dai N, Li J 2022 IEEE Photonics J. 14 1Google Scholar
[35] Zhu Y, Wang S, Chen M, Zuo X, Wang H, Rao C, Xu Y, Ji D, Liu Y 2022 IEEE Photonics Technol. Lett. 34 283Google Scholar
[36] Nawazuddin M B, Wheeler N V, Hayes J R, Bradley T D, Sandoghchi S R, Gouveia M A, Jasion G T, Richardson D J, Poletti F 2018 J. Lightwave Technol. 36 1213Google Scholar
[37] Yan S, Lou S, Lian Z, Zhang W, Wang X 2019 J. Lightwave Technol. 37 5707Google Scholar
[38] Luo L W, Ophir N, Chen C P, Gabrielli L H, Poitras C B, Bergmen K, Lipson M 2014 Nat. Commun. 5 3069Google Scholar
[39] Chen Y X, Lin Z J, Bélanger-de Villers S, Rusch L A, Shi W 2020 IEEE J. Sel. Top. Quantum Electron. 26 6100107Google Scholar
[40] Naghshvarianjahromi M, Kumar S, Deen M J, Iwaya T, Kimura K, Yoshida M, Hirooka T, Nakazawa M 2022 IEEE J. Sel. Top. Quantum Electron. 28 7500210Google Scholar
[41] Richardson D J, Fini J M, Nelson L E 2013 Nat. Photonics 7 354Google Scholar
[42] Tarighat A, Hsu R C J, Shah A, Sayed A H, Jalali B 2007 IEEE Commun. Mag. 45 57Google Scholar
[43] Berdagué S, Facq P 1982 Appl. Opt. 21 1950Google Scholar
[44] Habib M S, Antonio-Lopez J E, Markos C, Schülzgen A, Amezcua-Correa R 2019 Opt. Express 27 3824Google Scholar
[45] Habib M S, Bang O, Bache M 2016 Opt. Express 24 8429Google Scholar
[46] Wang Z, Tu J, Liu Z, Yu C, Lu C 2020 J. Lightwave Technol. 38 864Google Scholar
[47] Goel C, Yoo S 2021 J. Lightwave Technol. 39 6592Google Scholar
[48] Ou J, Li J P, Zheng W Q, Qin Y W, Xu O, Huang Q D, Peng D, Xiang M, Xu Y, Fu S N 2022 20th International Conference on Optical Communications and Networks (ICOCN) Shenzhen, China, August 12–15, 2022 p1
[49] Liu H, Wang Y, Zhou Y, Guan Z, Yu Z, Ling Q, Luo S, Shao J, Huang D, Chen D 2022 Opt. Express 30 21833Google Scholar
[50] Vincetti L, Setti V 2012 Opt. Express 20 14350Google Scholar
[51] Zhang J, Wang Z, Chen J 2014 Proc. COMSOL Conf. Shanghai, China 2014 p2
[52] Litchinitser N M, Abeeluck A K, Headley C, Eggleton B J 2002 Opt. Lett. 27 1592Google Scholar
[53] Vincetti L 2016 Opt. Express 24 10313Google Scholar
[54] Chen X, Hu X, Yang L, Peng J, Li H, Dai N, Li J 2019 Opt. Express 27 19548Google Scholar
[55] Wang L, LaRochelle S 2015 Opt. Lett. 40 5846Google Scholar
[56] Nagano K, Kawakami S, Nishida S 1978 Appl. Opt. 17 2080Google Scholar
[57] Belardi W, Knight J C 2014 Opt. Express 22 10091Google Scholar
[58] Pryamikov A D, Biriukov A S, Kosolapov A F, Plotnichenko V G, Semjonov S L, Dianov E M 2011 Opt. Express 19 1441Google Scholar
[59] Yu F, Wadsworth W J, Knight J C 2012 Opt. Express 20 11153Google Scholar
[60] Yang S, Sheng X, Zhao G, Lou S, Guo J 2021 IEEE Access 9 29599Google Scholar
[61] Hayashi J G, Ventura A, Cimek J, Slimen F B, White N, Sakr H, Jasion G T, Wheeler N V, Poletti F 2020 22nd International Conference on Transparent Optical Networks (ICTON) Bari, Italy, July 19–23, 2020 p1
[62] Shaha K S R, Khaleque A 2021 Appl. Opt. 60 6243Google Scholar
[63] Wei C, Weiblen R J, Menyuk C R, Hu J 2017 Adv. Opt. Photonics 9 504Google Scholar
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图 4 当纤芯半径R = 16 μm, g = 0.5 μm, 改变k对模式传输特性的影响 (a) 有效折射率; (b) 相邻模式有效折射率差; (c) CL; (d) 相邻模式间DGD
Fig. 4. Impact of changing k on mode transmission characteristics for R = 16 μm and g = 0.5 μm: (a) Effective refractive index; (b) difference of effective refractive index of adjacent modes; (c) CL; (d) DGD between adjacent modes.
图 6 当g = 0.5 μm, k = 0.4时, 改变纤芯半径R对模式传输的影响 (a) 有效折射率; (b) 相邻模式有效折射率差; (c) CL; (d) 相邻模式间的DGD
Fig. 6. Impact of changing R on mode transmission characteristics for g = 0.5 μm and k = 0.4: (a) Effective refractive index; (b) difference of effective refractive index of adjacent modes; (c) CL; (d) DGD between adjacent modes.
图 7 当g = 0.5 μm, k = 0.4, R = 24 μm时, 波长变化对模式传输的影响 (a) 有效折射率; (b) 相邻模式有效折射率差; (c) CL; (d) 相邻模式间的DGD
Fig. 7. Variation of changing wavelength on mode transmission characteristics for g = 0.5 μm, k = 0.4 and R = 16 μm: (a) Effective refractive index; (b) difference of effective refractive index of adjacent modes; (c) CL; (d) DGD between adjacent modes.
图 8 当g = 0.5 μm, k = 0.4, R = 24 μm时, 不同弯曲半径对模式传输的影响 (a) 预期基线; (b) 有效折射率; (c) 相邻模式有效折射率差; (d) BL
Fig. 8. Variation of changing bending radius on mode transmission characteristics for g = 0.5 μm, k = 0.4: (a) Expected baseline; (b) effective refractive index; (c) difference of effective refractive index of adjacent modes; (d) BL.
表 1 少模HC-NCF性能比较
Table 1. Performance comparison of few-mode HC-NCF
结构 中心波长/µm 支持模式数 基模最低限制损耗/(dB·m–1) 工作带宽/nm 弯曲半径/cm 弯曲损耗/(dB·m–1) Wang Z, et al. (2020)[46] 1.55 2 1.7×10–4 @1.53 µm 340 10 6.6×10–4 (200 nm) Goel C, et al. (2021)[47] 1.00 5 1.4×10–5@1 µm — 20 5×10–3 Ou J, et al. (2022)[48] 1.55 2 7.4×10–7@1.06 µm 800 — — Liu H, et al. (2022)[49] 1.55 5 3.4×10–7@1.38 µm 300 6 3×10–4 (210 nm) Our work 1.55 6 4.3×10–7@1.4 µm 330 7 4.5×10–4 (420 nm) -
[1] Benabid F, Knight J C, Antonopoulos G, Russell P S J 2002 Science 298 399Google Scholar
[2] Poletti F, Wheeler N V, Petrovich M N, Baddela N, Fokoua E N, Hayes J R, Gray D R, Li Z, Slavík R, Richardson D J 2013 Nat. Photonics 7 279Google Scholar
[3] Belardi W, Knight J C 2014 Opt. Lett. 39 1853Google Scholar
[4] Yu F, Knight J C 2016 IEEE J. Sel. Top. Quantum Electron. 22 146Google Scholar
[5] Hasan M I, Akhmediev N, Chang W 2017 Opt. Lett. 42 703Google Scholar
[6] Shen W, Du J, Sun L, Wang C, He Z 2020 J. Lightwave Technol. 38 3874Google Scholar
[7] Liu Z, Karanov B, Galdino L, Hayes J R, Lavery D, Clark K, Shi K, Elson D J, Thomsen B C, Petrovich M N, Richardson D J, Poletti F, Slavik R, Bayvel P 2019 J. Lightwave Technol. 37 909Google Scholar
[8] Michaud-Belleau V, Fokoua E R N, Bradley T, Hayes J R, Slavik R 2021 Optica 8 216Google Scholar
[9] Zhu X, Wu D, Wang Y, Yu F, Li Q, Qi Y, Knight J, Chen S, Hu L 2021 Opt. Express 29 1492Google Scholar
[10] Azendorf F, Schmauss B, Shi B, Fokoua E N, Radan Slavík, Eiselt M 2021 Optical Fiber Communications Conference and Exhibition (OFC) San Francisco, California United States, June 6–10, 2021 p1
[11] Liu W, Zheng Y, Wang Z, Wang Z X, Yang J, Chen M X, Qi M, Rehman S U, Shum P P, Zhu L, Wei L 2021 Adv. Mater. Interfaces 8 2001978Google Scholar
[12] Gérôme F, Cook K T, George A K, Wadsworth W J, Knight J C 2007 Opt. Express 15 7126Google Scholar
[13] Urich A, Maier R R, Yu F, Knight J C, Hand D P, Shephard J D 2013 Biomed. Opt. Express 4 193Google Scholar
[14] Couch D E, Hickstein D D, Winters D G, Backus S J, Kirchner M S, Domingue S R, Ramirez J J, Durfee C G, Murnane M M, Kapteyn H C 2020 Optica 7 832Google Scholar
[15] Poletti F 2014 Opt. Express 22 23807Google Scholar
[16] Cregan R F, Mangan B J, Knight J C, Birks T A, Russell P S, Roberts P J, Allan D C 1999 Science 285 1537Google Scholar
[17] Roberts P, Couny F, Sabert H, Mangan B, Williams D, Farr L, Mason M, Tomlinson A, Birks T, Knight J, Russell S J P 2005 Opt. Express 13 236Google Scholar
[18] Luan F, George A K, Hedley T D, Pearce G J, Bird D M, Knight J C, Russell P S J 2004 Opt. Lett. 29 2369Google Scholar
[19] Wei C, Weiblen R J, Menyuk C R, Hu J 2017 Adv. Opt. Photonics 9 562Google Scholar
[20] Jasion G T, Bradley T, Harrington K, Sakr H, Poletti F 2020 Optical Fiber Communications Conference and Exhibition (OFC) San Diego, California United States, March 8–12, 2020
[21] Osório J H, Amrani F, Delahaye F, Dhaybi A, Vasko K, Melli F, Giovanardi F, Vandembroucq D, Tessier G, Vincetti L, Debord B, Gérôme F, Benabid F 2023 Nat. Commun. 14 1146Google Scholar
[22] Mulvad H C H, Abokhamis Mousavi S, Zuba V, Xu L, Sakr H, Bradley T D, Hayes J R, Jasion G T, Numkam Fokoua E R, Taranta A, Alam S, Richardson D J, Poletti F 2022 Nat. Photonics 16 448Google Scholar
[23] Ding W, Wang Y Y, Gao S, Wang M, Wang P 2020 IEEE J. Sel. Top. Quantum Electron. 26 4400312Google Scholar
[24] Gao S F, Wang Y Y, Ding W, Jiang D, Gu S, Zhang X, Wang P 2018 Nat. Commun. 9 2828Google Scholar
[25] Yue B, Feng J, Tao J, Zhou G, Huang X 2021 Opt. Fiber Technol. 67 102734Google Scholar
[26] Xue L, Sheng X, Jia H, Lou S 2023 J. Lightwave Technol. 41 6043Google Scholar
[27] Belardi W 2015 J. Lightwave Technol. 33 4497Google Scholar
[28] Yan S B, Lou S, Wang X, Zhang W, Zhao T 2018 Opt. Fiber Technol. 46 118Google Scholar
[29] Michieletto M, Lyngsø J K, Jakobsen C, Lægsgaard J, Bang O, Alkeskjold T T 2016 Opt. Express 24 7103Google Scholar
[30] Zhang X, Feng Z, Marpaung D A, Fokoua E R, Sakr H, Hayes J R, Poletti F, Richardson D J, Slavík R 2022 Light Sci. Appl 11 213Google Scholar
[31] Yao C Y, Gao S F, Wang Y Y, Wang P, Jin W, Ren W 2020 J. Lightwave Technol. 38 2067Google Scholar
[32] Ma X X, Li J S, Guo H T, Li S G, Zhang H, Xu Y T, Meng X J, Guo Y, Chen Q, Wang C J, Cui X W 2023 Plasmonics 18 899Google Scholar
[33] Zhang H, Chang Y J, Xu Y T, Liu C Z, Xiao X S, Li J S, Ma X X, Wang Y Y, Guo H T 2023 Opt. Express 31 7659Google Scholar
[34] Zhou Y, Cao R, Wang S, Peng J, Li H, Chu Y, Xing Y, Dai N, Li J 2022 IEEE Photonics J. 14 1Google Scholar
[35] Zhu Y, Wang S, Chen M, Zuo X, Wang H, Rao C, Xu Y, Ji D, Liu Y 2022 IEEE Photonics Technol. Lett. 34 283Google Scholar
[36] Nawazuddin M B, Wheeler N V, Hayes J R, Bradley T D, Sandoghchi S R, Gouveia M A, Jasion G T, Richardson D J, Poletti F 2018 J. Lightwave Technol. 36 1213Google Scholar
[37] Yan S, Lou S, Lian Z, Zhang W, Wang X 2019 J. Lightwave Technol. 37 5707Google Scholar
[38] Luo L W, Ophir N, Chen C P, Gabrielli L H, Poitras C B, Bergmen K, Lipson M 2014 Nat. Commun. 5 3069Google Scholar
[39] Chen Y X, Lin Z J, Bélanger-de Villers S, Rusch L A, Shi W 2020 IEEE J. Sel. Top. Quantum Electron. 26 6100107Google Scholar
[40] Naghshvarianjahromi M, Kumar S, Deen M J, Iwaya T, Kimura K, Yoshida M, Hirooka T, Nakazawa M 2022 IEEE J. Sel. Top. Quantum Electron. 28 7500210Google Scholar
[41] Richardson D J, Fini J M, Nelson L E 2013 Nat. Photonics 7 354Google Scholar
[42] Tarighat A, Hsu R C J, Shah A, Sayed A H, Jalali B 2007 IEEE Commun. Mag. 45 57Google Scholar
[43] Berdagué S, Facq P 1982 Appl. Opt. 21 1950Google Scholar
[44] Habib M S, Antonio-Lopez J E, Markos C, Schülzgen A, Amezcua-Correa R 2019 Opt. Express 27 3824Google Scholar
[45] Habib M S, Bang O, Bache M 2016 Opt. Express 24 8429Google Scholar
[46] Wang Z, Tu J, Liu Z, Yu C, Lu C 2020 J. Lightwave Technol. 38 864Google Scholar
[47] Goel C, Yoo S 2021 J. Lightwave Technol. 39 6592Google Scholar
[48] Ou J, Li J P, Zheng W Q, Qin Y W, Xu O, Huang Q D, Peng D, Xiang M, Xu Y, Fu S N 2022 20th International Conference on Optical Communications and Networks (ICOCN) Shenzhen, China, August 12–15, 2022 p1
[49] Liu H, Wang Y, Zhou Y, Guan Z, Yu Z, Ling Q, Luo S, Shao J, Huang D, Chen D 2022 Opt. Express 30 21833Google Scholar
[50] Vincetti L, Setti V 2012 Opt. Express 20 14350Google Scholar
[51] Zhang J, Wang Z, Chen J 2014 Proc. COMSOL Conf. Shanghai, China 2014 p2
[52] Litchinitser N M, Abeeluck A K, Headley C, Eggleton B J 2002 Opt. Lett. 27 1592Google Scholar
[53] Vincetti L 2016 Opt. Express 24 10313Google Scholar
[54] Chen X, Hu X, Yang L, Peng J, Li H, Dai N, Li J 2019 Opt. Express 27 19548Google Scholar
[55] Wang L, LaRochelle S 2015 Opt. Lett. 40 5846Google Scholar
[56] Nagano K, Kawakami S, Nishida S 1978 Appl. Opt. 17 2080Google Scholar
[57] Belardi W, Knight J C 2014 Opt. Express 22 10091Google Scholar
[58] Pryamikov A D, Biriukov A S, Kosolapov A F, Plotnichenko V G, Semjonov S L, Dianov E M 2011 Opt. Express 19 1441Google Scholar
[59] Yu F, Wadsworth W J, Knight J C 2012 Opt. Express 20 11153Google Scholar
[60] Yang S, Sheng X, Zhao G, Lou S, Guo J 2021 IEEE Access 9 29599Google Scholar
[61] Hayashi J G, Ventura A, Cimek J, Slimen F B, White N, Sakr H, Jasion G T, Wheeler N V, Poletti F 2020 22nd International Conference on Transparent Optical Networks (ICTON) Bari, Italy, July 19–23, 2020 p1
[62] Shaha K S R, Khaleque A 2021 Appl. Opt. 60 6243Google Scholar
[63] Wei C, Weiblen R J, Menyuk C R, Hu J 2017 Adv. Opt. Photonics 9 504Google Scholar
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