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Aiming at the shortcomings of helically twisted single-cladding-few-core photonic crystal fibers in generating orbital angular momentum (OAM), the double-cladding and three-core structures with non-uniform inner and outer air holes are introduced into a photonic crystal fiber for the first time and the generation of high-order OAM modes through helical twisting is realized. The fiber is expected to reduce the losses of the generated OAM modes by introducing a specially designed double-cladding structure, while the three cores distributed in a regular triangle around the center are expected to increase the number of generated OAM modes. On the basis of optical transformation theory, the optical fiber is systematically analyzed by the finite element method. It is found that with the twist rate α = 7853.98 rad/m, the generated OAM modes include “OAM–4,1, OAM+9,1, OAM+10,1, OAM+11,1, OAM+13,1”, where +13 is the highest order in the OAM modes currently generated by using helically twisted fibers. And the losses of OAM modes are all less than 1.64×10–3 dB/m, which is at least two orders of magnitude lower than the lowest OAM mode loss reported in the existing references (Napiorkowski M, Urbanczyk W S 2018 Opt. Express 26 12131), and their purity is greater than 93%. Further studies show that the generation of orbital angular momentum depends on the resonant coupling between the core supermode and the ring-core mode, and the parity of the order of the generated OAM modes is related to the polarization direction of the fiber core supermode and the ring-core mode.
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Keywords:
- orbital angular momentum /
- helically twisted optical fiber /
- resonance coupling /
- circular birefringence
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[33] Xu M N, Zhou G Y, Chen C, Zhou G, Sheng Z C, Hou Z Y, Xia C M 2018 J. Opt. 47 428
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
Cui C, Wang Z, Li Q, Wu C Q, Wang J 2019 Acta Phys. Sin. 68 064211
Google Scholar
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图 1 光纤结构 (a) 光纤螺旋扭曲示意图; (b) 光纤仿真截面图; (c) 纤芯放大图
Figure 1. Structure of optical fiber: (a) Schematic diagram of the helically twisted optical fiber; (b) simulation cross-sectional view of the optical fiber; (c) enlarged view of fiber core.
图 2 纤芯6个超模的模场分布情况
Figure 2. Mode field distributions of six supermodes in the fiber core.
图 3 环形芯模式在z方向电场分布图 (a)
${\text{HE}}_{9, 1}^{{\text{odd}}}$ 模式; (b)${\text{EH}}_{7, 1}^{{\text{even}}}$ 模式Figure 3. Electric field distributions of ring-core modes in z direction: (a)
${\text{HE}}_{9, 1}^{{\text{odd}}}$ mode; (b)${\text{EH}}_{7, 1}^{{\text{even}}}$ mode.
图 4 螺旋扭曲光纤的玻印亭矢量分布图和相位图 (a) 环形芯模式和泄漏模式的玻印亭矢量分布; (b)
${\text{HE}}_{10, 1}^{{\text{even}}}$ 模式 (等价于弱${\text{OAM}}_{ + 9, 1}^ - $ 模式)的相位图; (c)${\text{HE}}_{5, 1}^{{\text{odd}}}$ 模式 (等价于弱${\text{OAM}}_{ - 4, 1}^ + $ 模式)的相位图Figure 4. Poynting vector distribution and phase diagrams of helically twisted fiber: (a) Poynting vector distribution of ring-core modes and leaky modes; (b) phase diagrams of
${\text{HE}}_{10, 1}^{{\text{even}}}$ mode (equivalent to${\text{OAM}}_{ + 9, 1}^ - $ mode); (c) phase diagrams of${\text{HE}}_{5, 1}^{{\text{odd}}}$ mode (equivalent to${\text{OAM}}_{ - 4, 1}^ + $ mode).
图 5 圆双折射现象 (内部图片为纤芯超模的极化状态)
Figure 5. Diagram of circular birefringence (Internal pictures show the polarization of the core supermodes).
图 6 α = 7853.982 rad/m时, 超模损耗谱中明显的损耗峰(内部图片为发生共振耦合时的模场分布) (a) λ = 1360 nm (峰a); (b) λ = 1820 (峰b和峰c)和1900 nm (峰d和峰e); (c) λ = 1940 nm (峰f); (d) λ = 2000 (峰g和峰h)和2350 nm (峰i)
Figure 6. Loss peaks in loss spectra when α = 7853.982 rad/m (Internal images show the mode field distribution when resonant couplings occur): (a) λ = 1360 nm (peak a); (b) λ = 1820 (peak b and peak c) and 1900 nm (peak d and peak e); (c) λ = 1940 nm (peak f); (d) λ = 2000 (peak g and peak h) and 2350 nm (peak i).
图 7 α = 7853.982 rad/m时, 模式的折射率与波长的变化 (a) λ = 1360, 1820和1940 nm; (b) λ = 1900, 2000和 2350 nm
Figure 7. Relationship between refractive index and wavelength at α = 7853.982 rad/m: (a) λ = 1360, 1820 and 1940 nm; (b) λ = 1900, 2000 and 2350 nm.
图 8 不同扭曲率下超模的损耗谱 (a) α = 7391.983 rad/m; (b) α = 8377.58 rad/m
Figure 8. Loss spectra of supermodes at different twist rates: (a) α = 7391.983 rad/m; (b) α = 8377.58 rad/m.
图 9 不同扭曲率下的OAM模式纯度
Figure 9. Mode purity at different twist rates.
表 1 α = 7853.982 rad/m时, 共振耦合具体情况
Table 1. Specific situation of resonance couplings when α = 7853.982 rad/m.
Peaks LC/μm Peaks LC/μm M1 (RC, s = –1) + $ {\text{OAM}}_{ + 13, 1}^ + $ ($ {\text{EH}}_{12, 1}^{{\text{odd}}} $) = a 36.20 M1 (RC, s = –1) + $ {\text{OAM}}_{ + 10, 1}^ + $ ($ {\text{EH}}_{9, 1}^{{\text{odd}}} $) = h 47.95 M2 (RC, s = –1) + $ {\text{OAM}}_{ + 11, 1}^ + $ ($ {\text{EH}}_{10, 1}^{{\text{odd}}} $) = b 40.81 M2 (RC, s = –1) + $ {\text{OAM}}_{ - 4, 1}^ + $ ($ {\text{HE}}_{5, 1}^{{\text{odd}}} $) = i 125.32 M3 (LC, s = +1) + $ {\text{OAM}}_{ + 10, 1}^ - $ ($ {\text{HE}}_{11, 1}^{{\text{even}}} $) = g 46.44 — — M4 (LC, s = +1) + $ {\text{OAM}}_{ + 11, 1}^ - $ ($ {\text{HE}}_{12, 1}^{{\text{even}}} $) = c 38.68 — — M5 (RC, s = –1) + $ {\text{OAM}}_{ + 9, 1}^ + $ ($ {\text{EH}}_{8, 1}^{{\text{odd}}} $) = d 50.18 M5 (RC, s = –1) + $ {\text{OAM}}_{ + 10, 1}^ - $ ($ {\text{HE}}_{11, 1}^{{\text{even}}} $) = f 36.93 M6 (LC, s = +1) + $ {\text{OAM}}_{ + 9, 1}^ - $ ($ {\text{HE}}_{10, 1}^{{\text{even}}} $) = e 47.47 — — 
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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] Wang J 2019 Sci. China-Phys. Mech. Astron. 62 034201
Google Scholar
[3] Guanghao R, Xiaoyan W, Yiping C 2015 Opt. Express 23 25707
Google Scholar
[4] Qiu X D, Li F S, Zhang W H, Zhu Z H, Chen L X 2018 Optica 5 208
Google Scholar
[5] Vaity P, Rusch L 2015 Opt. Lett. 40 597
Google Scholar
[6] Li D L, Chang C L, Nie S P, Feng S T, Ma J, Yuan C J 2018 Appl. Phys. Lett. 113 121101
Google Scholar
[7] Ji W, Lee C H, Chen P, Hu W, Ming Y, Zhang L J, Lin T H, Chigrinov V, Lu Y Q 2016 Sci. Rep. 6 25528
Google Scholar
[8] Terhalle B, Langner A, Päivänranta B, Guzenko V A, David C, Ekinci Y 2011 Opt. Lett. 36 4143
Google Scholar
[9] Cai X L, Wang J W, Strain M J, Johnson-Morris B, Zhu J B, Sorel M, O’ Brien J L, Thompson M G, Yu S Y 2012 Science 338 363
Google Scholar
[10] Gambini F, Velha P, Oton C J, Faralli S, 2016 IEEE Photonics Technol. Lett. 28 2355
Google Scholar
[11] González N, Molina-Terriza G, Torres J P 2006 Opt. Express 14 9093
Google Scholar
[12] Pidishety S, Khudus M, Gregg P, Ramachandran, S, Srinivasan B, Brambilla G 2016 Conference on Lasers and Electro-Optics (CLEO)-Science and Innovation San Jose, California, United States, June 5–10, 2016 pSTu1 F. 2
[13] Wang T, Wang F, Shi F, Pang F F, Huang, S J, Wang T Y, Zeng X L 2017 J. Lightwave Technol. 35 2161
Google Scholar
[14] Wu S H, Li Y, Feng L P, Zeng X L, Li W, Qiu J F, Zuo Y, Hong X B, Yu H, Chen R, Giles L P, Wu J 2018 Opt. Lett. 43 2130
Google Scholar
[15] Jiang Y C, Ren G B, Lian Y D, Zhu B F, Jin W X, Jian S S 2016 Opt. Lett. 41 3535
Google Scholar
[16] Li S H, Zhe X, Zhao R X, Shen L, Du C, Wang J 2018 IEEE Photonics J. 10 6601607
Google Scholar
[17] Li S H, Mo Q, Hu X, Du C, Wang J 2015 Opt. Lett. 40 4376
Google Scholar
[18] Han Y, Liu Y G, Wang Z, Huang W, Chen L, Zhang H W, Yang K 2017 Nanophotonics 7 287
Google Scholar
[19] Cao X B, Liu Y Q, Zhang L, Zhao Y H, Wang T Y 2017 Appl. Opt. 56 5167
Google Scholar
[20] Fu C L, Liu S, Bai Z Y, He J, Liao C R, Wang Y, Li Z L, Zhang Y, Yang K M, Yu B, Wang Y P 2018 J. Lightwave Technol. 36 1683
Google Scholar
[21] Wang X, Zeng J W, Sun J B, Nezhad V F, Cartwright A N, Litchinitser N M 2014 Conference on Lasers and Electro-Optics (CLEO) - Laser Science to Photonic Applications San Jose, California, United States, June 8–13, 2014 pJTu4 A. 34
[22] Yu J, Fu C L, Bai Z Y, Wang Y P 2021 J. Lightwave Technol. 39 1416
Google Scholar
[23] Wong G K L, Kang M S, Lee H W, Biancalana F, Conti C, Weiss T, Russell P St J 2012 Science 337 446
Google Scholar
[24] Xi X M, Wong G K L, Frosz M H, Babic F, Ahmed G, Jiang X, Euser T G, Russell P St J 2014 Optica 1 165
Google Scholar
[25] Russell P St J, Beravat R, Wong G K L 2017 Phil. Trans. R. Soc. A 375 20150440
Google Scholar
[26] Fu C L, Liu S, Wang Y, Bai Z Y, He J, Liao C R, Zhang F, Zhang F, Yu B, Gao S C, Li Z H, Wang Y P 2018 Opt. Lett. 43 1786
Google Scholar
[27] Zhang Y F, Li B Y, Xia C M, Hou Z Y, Zhou G Y 2020 Opt. Commun. 475 126245
Google Scholar
[28] Ren K L, Ren L Y, Liang J, Yang L, Xu J, Han D D, Wang Y K, Liu J H, Dong J, He H Y, Zhang W F 2021 Opt. Express 29 8441
Google Scholar
[29] Fujisawa T, Sato T, Saitoh K 2017 J. Lightwave Technol. 35 2894
Google Scholar
[30] Nicolet A, F Zolla, Ould Agha F, Guenneau S 2008 Compel 27 806
Google Scholar
[31] Nicolet A, Zolla F, Agha Y O, Guenneau S 2007 Wave. Random. Complex 17 559
Google Scholar
[32] Edavalath N N, Gnendi M C, Beravat R, Wong G K L, Frosz M H, Mnard J M, Russell P St J 2017 Opt. Lett. 42 2074
Google Scholar
[33] Xu M N, Zhou G Y, Chen C, Zhou G, Sheng Z C, Hou Z Y, Xia C M 2018 J. Opt. 47 428
Google Scholar
[34] Zhang L, Zhang K, Peng J, Deng J, Yang Y, Ma J 2018 Opt. Commun. 429 189
Google Scholar
[35] Kabir M A, Hassan M M, Ahmed K, Rajan M S M, Aly A H, Hossain M N, Paul B K 2020 Opt. Quant. Electron. 52 331
Google Scholar
[36] Ye J F, Li Y, Han Y H, Deng D, Guo Z Y, Gao J M, Sun Q Q, Liu Y, Qu S L 2016 Opt. Express 24 8310
Google Scholar
[37] Xi X M, Weiss T, Wong G K L, Biancalana F, Barnett S M, Padgett M J, Russell P St J 2013 Phys. Rev. Lett. 110 143903
Google Scholar
[38] Beravat R, Wong G K L, Xi X M, Frosz M H, Russell P St J 2016 Opt. Lett. 41 1672
Google Scholar
[39] Weiss T, Wong G K L, Biancalana F, Barnett S M, Xi X M, Russell P St J 2013 J. Opt. Soc. Am. B 30 2921
Google Scholar
[40] Liu H, Wang H R, Chen C C, Zhang W, Zhang S, Wang Q, Ding Y 2019 Opt. Fiber Technol. 47 164
Google Scholar
[41] Napiorkowski M, Urbanczyk W S 2018 Opt. Express 26 12131
Google Scholar
[42] Napiorkowski M, Renversez G, Urbanczyk W 2019 Opt. Express 27 5447
Google Scholar
[43] Zhao L J, Zhao H Y, Xu Z N, Liang R Y 2021 Commun. Theor. Phys. 73 085501
Google Scholar
[44] 崔粲, 王智, 李强, 吴重庆, 王健 2019 68 064211
Google Scholar
Cui C, Wang Z, Li Q, Wu C Q, Wang J 2019 Acta Phys. Sin. 68 064211
Google Scholar
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