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为了实现高纯度轨道角动量模式的传输和放大, 本文提出了一种可用于轨道角动量的受激布里渊放大的光子晶体光纤放大器并对其结构进行了设计. 利用有限元法在C波段内对该光子晶体光纤放大器的传输性能进行了系统分析, 研究结果表明, 该光子晶体光纤放大器可支持66种轨道角动量模式的高纯度传输和放大, 其传输的轨道角动量模式的纯度均高于99.4%. 通过对不同拓扑荷数的轨道角动量模式的布里渊增益谱进行系统的分析, 发现均具有较高的布里渊增益系数(> 7 × 10–9 m/W), 与现有的性能最优的OAM放大器相比提高了4—5个数量级, 实现了较高的信号增益. 该光子晶体光纤放大器的综合性能显著优于现有基于受激布里渊放大的光纤放大器和掺杂稀土离子的光纤放大器, 这使其能够稳定、准确地对OAM模式进行同步放大和长距离传输, 为轨道角动量模式激光系统的设计提供了一种可能.A probe made of amino acids is arranged in a linear chain and joined together by peptide bonds between the carboxyl and amino groups of adjacent amino acid residues. The sequence of amino acids in a protein is determined by a gene and encoded in the genetic code. This can happen either before the protein is used in the cell, or as part of control mechanisms. In order to transmit and amplify high-purity orbital angular momentum mode, a photonic crystal fiber amplifier based on stimulated Brillouin amplification is proposed and designed in this paper. The transmission properties of the photonic crystal fiber amplifier are systematically analyzed by using the finite element method in the C-band. The results show that this photonic crystal fiber amplifier can support the transmission and amplification of 66 orbital angular momentum modes, and all values of the purity of the orbital angular momentum modes supported by this amplifier are higher than 99.4%. By systematically analyzing the Brillouin gain spectra of orbital angular momentum modes with different topological charges, it is found that they have all high Brillouin gain coefficients (> 7 × 10–9 m/W) which are 4–5 orders of magnitude higher than the existing OAM amplifiers with the best performance, thus higher signal gain can be obtained. The comprehensive performance of the proposed photonic crystal fiber amplifier is superior to that of the existing optical fiber amplifiers based on stimulated Brillouin amplification and the optical fiber amplifiers doped with rare-earth ions. This makes the amplification and long-distance transmission of OAM mode stable and accurate and provides a possibility for designing the orbital angular momentum mode laser system.
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Keywords:
- orbital angular momentum /
- stimulated Brillouin amplification /
- high signal gain /
- photonic crystal fiber
[1] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185
Google Scholar
[2] Fujisawa T, Saitoh K 2020 Photosynth. Res. 2020 1278
[3] Beijersbergen M W, Coerwinkel R P C, Kristensen M, Woerdman J P 1994 Opt. Commun. 112 321
Google Scholar
[4] Heckenberg N R, Mcduff R, Smith C P, White A G 1992 Opt. Lett. 17 221
Google Scholar
[5] Marrucci L, Karimi E, Slussarenko S, Piccirillo B, Santamato E, Nagali E, Sciarrino F 2011 J. Opt. 13 064001
Google Scholar
[6] Bozinovic N, Golowich S, Kristensen P, Ramachandran S 2012 Opt. Lett. 37 2451
Google Scholar
[7] Willner A E, Huang H, Yan Y, Ren Y, Ashrafi S 2015 Adv. Opt. Photonics 7 66
Google Scholar
[8] Heng X B, Gan J L, Zhang Z S, Qian Q, Yang Z M 2019 Opt. Commun. 433 132
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Google Scholar
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Google Scholar
[11] Prabhakar G, Liu X, Demas J, Gregg P, Ramachandran S 2018 Conference on Lasers and Electro-Optics, OSA Technical Digest
[12] Sheng L W, Ba D X, Lu Z W 2019 Appl. Opt. 58 147
Google Scholar
[13] Li H W, Zhao B, Jin L W, Wang D M, Gao W 2019 Photosynth. Res. 7 07000748
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Google Scholar
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[18] 曹介元, 扬开宇 1995 光通信技术 1 30
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 2 PCF放大器支持的OAM模式数量随r的变化
Fig. 2. Number of OAM modes supported by the SBA-PCFA varies with r.
图 3 不同拓扑荷的OAM模式的BGS随纤芯半径变化 (a) l = 1; (b) l = 4; (c) l = 8 (d) l = 12; (e) l = 14; (f) g0随r的变化
Fig. 3. The BGS of OAM modes with different topological charges varies with r: (a) l = 1; (b) l = 4; (c) l = 8; (d) l = 12; (e) l = 14; (f) g0 varies with r.
图 4 (a)支持的OAM模式数量随a的变化; (b) g0随a的变化
Fig. 4. (a) Number of supported OAM modes varies with a; (b) g0 varies with a.
图 5 模场分布 (a) EH2,1; (b) HE5,1; (c) HE10,1; (d) EH14,1
Fig. 5. Intensity of the electric field: (a) EH2,1; (b) HE5,1; (c) HE10,1; (d) EH14,1.
图 6 有效折射率差与波长的关系
Fig. 6. Relationship between the differences in effective refractive index of different modes with wavelength.
图 7 不同模式的纯度与波长的关系
Fig. 7. Relationship between the mode purity and wavelength for different modes.
图 8 (a) 有效模场面积和(b) 非线性系数随波长的变化
Fig. 8. Relationship between wavelength and (a) the effective mode area, (b) nonlinear coefficient for different modes.
图 9 不同模式的色散与波长的关系
Fig. 9. Relationship between dispersion and wavelength for different modes.
图 10 不同模式的限制性损耗与波长的关系
Fig. 10. The relationship between confinement and wavelength for different modes.
图 11 不同拓扑荷数的OAM模式的BGS (a) 1530 nm; (b) 1540 nm; (c) 1550 nm; (d) 1560 nm
Fig. 11. BGS of OAM modes with different topological charge: (a) 1530 nm; (b) 1540 nm; (c) 1550 nm; (d) 1560 nm.
图 12 布里渊增益谱特征参数随拓扑荷数的变化 (a) 最大布里渊增益系数; (b) 布里渊频移; (c) 线宽
Fig. 12. Change of the characteristic parameters of BGS with topological charge: (a) g0; (b) υB; (c) ГB.
图 13 阈值随拓扑荷数的变化 (a) Leff = 0.4 m; (b) Leff = 10 m
Fig. 13. Values of threshold change with topological charge when (a) Leff = 0.4 m, (b) Leff = 10 m.
图 14 光纤有效长度为 (a) 0.4 m和 (b) 10 m时信号增益随泵浦光能量的变化
Fig. 14. Gain changes with the pump energy in the SBA-PCFA with an effective optical fiber length of (a) 0.4 m and (b) 10 m.
图 15 制造误差的影响 (a) 支持的OAM模式数量; (b) 最大布里渊增益系数
Fig. 15. Influence of manufacturing error on (a) the number of supported OAM modes, and (b) the max Brillouin gain.
表 1 Schott SF2的Sellmeier系数
Table 1. Sellmeier coefficients of Schott SF2.
Coefficient B1 C1/µm2 B2 C2/µm2 B3 C3/µm2 Value 1.4734313 0.0109019 0.16368185 0.058568369 1.36920899 127.404933 
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表 2 本文提出的SBA-PCFA的性能
Table 2. Properties of the proposed SBA-PCFA in this work.
Number of supported
OAM modesη/ % γ/ (W–1·km–1) D/(ps·km–1·nm–1) LC/(dB·cm) g0/(m·W–1) Pth/mW υB/GHz ГB/MHz Gain/dB 66 > 99.4 > 25 < 45 < 10–5 > 7 × 10–9 < 14.1 8—8.7 12.6—14.4 < 1697.5
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[1] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185
Google Scholar
[2] Fujisawa T, Saitoh K 2020 Photosynth. Res. 2020 1278
[3] Beijersbergen M W, Coerwinkel R P C, Kristensen M, Woerdman J P 1994 Opt. Commun. 112 321
Google Scholar
[4] Heckenberg N R, Mcduff R, Smith C P, White A G 1992 Opt. Lett. 17 221
Google Scholar
[5] Marrucci L, Karimi E, Slussarenko S, Piccirillo B, Santamato E, Nagali E, Sciarrino F 2011 J. Opt. 13 064001
Google Scholar
[6] Bozinovic N, Golowich S, Kristensen P, Ramachandran S 2012 Opt. Lett. 37 2451
Google Scholar
[7] Willner A E, Huang H, Yan Y, Ren Y, Ashrafi S 2015 Adv. Opt. Photonics 7 66
Google Scholar
[8] Heng X B, Gan J L, Zhang Z S, Qian Q, Yang Z M 2019 Opt. Commun. 433 132
Google Scholar
[9] Gao W, Mu C, Li H, Yang Y, Zhu Z 2015 Appl. Phys. Lett. 107 041119
Google Scholar
[10] Devaux F, Passier R 2007 Eur. Phys. J. D 42 133
Google Scholar
[11] Prabhakar G, Liu X, Demas J, Gregg P, Ramachandran S 2018 Conference on Lasers and Electro-Optics, OSA Technical Digest
[12] Sheng L W, Ba D X, Lu Z W 2019 Appl. Opt. 58 147
Google Scholar
[13] Li H W, Zhao B, Jin L W, Wang D M, Gao W 2019 Photosynth. Res. 7 07000748
[14] Mu C, Wei G, Zhu Z, Zhang H, Pu S 2014 Asia Communications and Photonics Conference
[15] Kabir M A, Ahmed K, Hassan M M, Hossain M M, Paul B K 2020 Opt. Commun. 475 126192
Google Scholar
[16] Kang Q, Gregg P, Jung Y, Lim E, Alam S 2015 Opt. Express 23 28341
Google Scholar
[17] Kumar C, Kumar G 2020 J. Opt. 49 178
Google Scholar
[18] 曹介元, 扬开宇 1995 光通信技术 1 30
Cao J Y, Yang K Y 1995 Optical Communication Technology 1 30
[19] Liu J, Chen S, Wang H Y, Zheng S, Zhu L, Wang A, Wang L L, Du C, Wang J 2020 Research 2020 7623751
[20] Pakarzadeh H, Sharif V 2019 Opt. Commun. 438 18
Google Scholar
[21] Zhao L J, Zhao H Y, Xu Z N, Liang R Y 2021 Commun. Theor. Phys. 73 085501
[22] Chen X, Xia L, Li W, Li C 2017 Chin. Opt. Lett. 15 69
Google Scholar
[23] Israk M F, Razzak M A, Ahmed K, Hassan M M, Kabir M A, Hossain M N, Paula B K, Dhasarathan V 2020 Opt. Commun. 473 126003
Google Scholar
[24] Ghazanfari A, Li W B, Leu M C, Hilmas G E 2017 Addit. Manuf. 15 102
[25] Cubillas A M, Unterkofler S, Euser T G, Etzold B J M, Jones A C, Sadler P J, Wasserscheid P, Russell P St J 2013 Chem. Soc. Rev. 42 8629
Google Scholar
[26] Ebendorff-Heidepriem H, Schuppich J, Dowler A, Lima-Marques L, Monro T M 2014 Opt. Mater. Express 4 1494
Google Scholar
[27] Hicham El H, Youcef O, Laurent B, Géraud B, Bruno C, Aziz B, Sylvain G, Mohamed B 2012 Opt. Express 20 29751
Google Scholar
[28] Vienne G, Xu Y, Jakobsen C, Deyerl H, Jensen J B, Sørensen T, Hansen T P, Huang Y, Terrel M, Lee R K, Mortensen N A, Broeng J, Simonsen H, Bjarklev A, Yariv A 2004 Opt. Express 12 3500
Google Scholar
[29] Issa N A, Eijkelenborg M A V, Fellew M, Cox F, Henry G, Large M C J 2004 Opt. Express 29 1336
[30] Baek J H, Song D S, Hwang I, Lee K H, Lee Y H, Ju Y G, Kondo T, Miyamoto T, Koyama F 2004 Opt. Express 12 859
Google Scholar
[31] Sun C, Wang W, Jia H 2020 Opt. Commun. 458 124757
Google Scholar
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