Abstract

Few-mode fiber (FMF) supporting many modes with weak-coupling is highly desired in mode division multiplexing (MDM) systems. The multi-parameter design of FMF becomes comparably difficult, inaccurate and time-consuming when it comes for complex fiber structures and many high order modes. In this work, we demonstrate a machine learning method using neural network to inversely design the desired FMF based on multiple-ring structure. By using the minimum index difference between adjacent modes as the weak-coupling optimization aim, we realize the inverse design of 4-ring step-index FMFs for supporting 4, 6 and 10 -mode operation, and 6-ring step-index FMF for supporting 20-mode operation. This method provides high-accuracy, high-efficiency and low-complexity for fast and reusable design of optical fibers, including particularly weak-coupling FMF in this work. It can be widely extended to a lot of fibers and has great potential for instantaneous applications in the optical fiber industry.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (1)

2019 (1)

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

2018 (4)

2017 (1)

2016 (1)

2015 (2)

E. Ip, G. Milione, M. Li, N. Cvijetic, K. Kanonakis, J. Stone, G. Peng, X. Prieto, C. Montero, C. Moreno, and J. Liñares, “SDM transmission of real-time 10GbE traffic using commercial SFP + transceivers over 0.5 km elliptical-core few-mode fiber,” Opt. Express 23(13), 17120–17126 (2015).
[Crossref]

F. Ren, J. Li, T. Hu, R. Tang, J. Yu, M. Qi, Y. He, Z. Chen, and Z. Li, “Cascaded Mode- Division- Multiplexing and Time-Division-Multiplexing Passive Optical Network Based on Low Mode-Crosstalk FMF and Mode MUX/DEMUX,” IEEE Photonics J. 7(5), 1–9 (2015).
[Crossref]

2014 (1)

P. J. Winzer, “Making Spatial Multiplexing a reality,” Nat. Photonics 8(5), 345–348 (2014).
[Crossref]

2012 (3)

H. S. Chen and A. M. J. Koonen, “LP01 and LP11 mode division multiplexing link with mode crossbar switch,” Electron. Lett. 48(19), 1222–1223 (2012).
[Crossref]

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing Over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
[Crossref]

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical core fiber data transmission,” IEEE Photonics Technol. Lett. 24(5), 344–346 (2012).
[Crossref]

2011 (1)

2010 (1)

2009 (1)

Achten, F.

P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, and F. Achten, “Low-differential-mode-group-delay 9-LP-mode fiber,” J. Lightwave Technol. 34(2), 425–430 (2016).
[Crossref]

P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, and F. Achten, “Micro-Bend-Resistant Low-DMGD 6-LP-Mode Fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2016), paper Th1J.5.

M. Bigot, D. Molin, K. de Jongh, D. Van Ras, F. Achten, and P. Sillard, “Next-Generation Multimode Fibers for Space Division Multiplexing,” in Advanced Photonics 2017 (IPR, NOMA, Sensors, Networks, SPPCom, PS), OSA Technical Digest (online) (Optical Society of America, 2017), paper NeM3B.4.

Amezcua-Correa, R.

H. Liu, H. Wen, J. C. A. Zacarias, J. E. Antonio-Lopez, N. Wang, P. Sillard, A. A. Correa, R. Amezcua-Correa, and G. Li, “3×10 Gbit/s mode group multiplexed transmission over a 20 km few-mode fiber using photonic lanterns,” in Optical Fiber Communications Conference & Exhibition, OSA Technical Digest (Optical Society of America, 2017), paper M2D.5.

Antonio-Lopez, J. E.

H. Liu, H. Wen, J. C. A. Zacarias, J. E. Antonio-Lopez, N. Wang, P. Sillard, A. A. Correa, R. Amezcua-Correa, and G. Li, “3×10 Gbit/s mode group multiplexed transmission over a 20 km few-mode fiber using photonic lanterns,” in Optical Fiber Communications Conference & Exhibition, OSA Technical Digest (Optical Society of America, 2017), paper M2D.5.

Arkwright, J. W.

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical core fiber data transmission,” IEEE Photonics Technol. Lett. 24(5), 344–346 (2012).
[Crossref]

Astruc, M.

Bai, N.

Bengio, Y.

X. Glorot and Y. Bengio, “Understanding the difficulty of training deep feedforward neural networks,” http://proceedings.mlr.press/v9/glorot10a.html

Beppu, S.

Bigo, S.

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2 × 100 Gbit/s over 40 km- long prototype few- mode fiber using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express 19(17), 16593–16600 (2011).
[Crossref]

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

Bigot, M.

M. Bigot, D. Molin, K. de Jongh, D. Van Ras, F. Achten, and P. Sillard, “Next-Generation Multimode Fibers for Space Division Multiplexing,” in Advanced Photonics 2017 (IPR, NOMA, Sensors, Networks, SPPCom, PS), OSA Technical Digest (online) (Optical Society of America, 2017), paper NeM3B.4.

Bigot-Astruc, M.

P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, and F. Achten, “Low-differential-mode-group-delay 9-LP-mode fiber,” J. Lightwave Technol. 34(2), 425–430 (2016).
[Crossref]

P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, and F. Achten, “Micro-Bend-Resistant Low-DMGD 6-LP-Mode Fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2016), paper Th1J.5.

M. Bigot-Astruc, D. Boivin, and P. Sillard, “Design and fabrication of weakly-coupled few-modes fibers,” in IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2012), pp. 189–190.

Boivin, D.

M. Bigot-Astruc, D. Boivin, and P. Sillard, “Design and fabrication of weakly-coupled few-modes fibers,” in IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2012), pp. 189–190.

Bolle, C.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing Over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
[Crossref]

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

Boutin, A.

Brindel, P.

Burrows, E. C.

Cai, C.

Cerou, F.

Chang, J. H.

Charlet, G.

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2 × 100 Gbit/s over 40 km- long prototype few- mode fiber using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express 19(17), 16593–16600 (2011).
[Crossref]

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

Chen, H.

Chen, H. S.

H. S. Chen and A. M. J. Koonen, “LP01 and LP11 mode division multiplexing link with mode crossbar switch,” Electron. Lett. 48(19), 1222–1223 (2012).
[Crossref]

Chen, S.

L. Shen, S. Chen, X. Sun, Y. Liu, L. Zhang, T. Hu, and J. Li, “Design, Fabrication, Measurement and MDM Transmission of a Novel Weakly-coupled Ultra Low Loss FMF,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Th2A.24.

Chen, Y.

Y. Chen, J. Du, J. Li, L. Shen, J. Luo, and Z. He, “Time-wavelength-mode equalization by PSO for random fiber laser based FMF Raman amplifier,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W4B. 1.

Y. Chen, J. Du, Y. Huang, K. Xu, and Z. He, “Intelligent gain flattening of FMF Raman amplification by machine learning based inverse design,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper T4B. 1.

Chen, Z.

F. Ren, J. Li, T. Hu, R. Tang, J. Yu, M. Qi, Y. He, Z. Chen, and Z. Li, “Cascaded Mode- Division- Multiplexing and Time-Division-Multiplexing Passive Optical Network Based on Low Mode-Crosstalk FMF and Mode MUX/DEMUX,” IEEE Photonics J. 7(5), 1–9 (2015).
[Crossref]

Correa, A. A.

H. Liu, H. Wen, J. C. A. Zacarias, J. E. Antonio-Lopez, N. Wang, P. Sillard, A. A. Correa, R. Amezcua-Correa, and G. Li, “3×10 Gbit/s mode group multiplexed transmission over a 20 km few-mode fiber using photonic lanterns,” in Optical Fiber Communications Conference & Exhibition, OSA Technical Digest (Optical Society of America, 2017), paper M2D.5.

Corsi, A.

Cvijetic, N.

de Jongh, K.

P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, and F. Achten, “Low-differential-mode-group-delay 9-LP-mode fiber,” J. Lightwave Technol. 34(2), 425–430 (2016).
[Crossref]

P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, and F. Achten, “Micro-Bend-Resistant Low-DMGD 6-LP-Mode Fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2016), paper Th1J.5.

M. Bigot, D. Molin, K. de Jongh, D. Van Ras, F. Achten, and P. Sillard, “Next-Generation Multimode Fibers for Space Division Multiplexing,” in Advanced Photonics 2017 (IPR, NOMA, Sensors, Networks, SPPCom, PS), OSA Technical Digest (online) (Optical Society of America, 2017), paper NeM3B.4.

Diamantopoulos, N. P.

N. P. Diamantopoulos, M. Hayashi, Y. Yoshida, A. Maruta, K. Takenaga, H. Uemura, S. Matsuo, and K. Kitayama, “Mode unbundled ROADM for MDM networks: Characterization of Uni- and Bi- directional mode assignment,” in International Conference on Photonics (IEEE, 2015), pp. 139–141.

Du, J.

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

J. Li, C. Cai, J. Du, S. Jiang, L. Ma, L. Wang, L. Zhu, A. Wang, M. Li, H. Chen, J. Wang, and Z. He, “Ultra-Low-Noise Mode-Division Multiplexed WDM Transmission Over 100-km FMF Based on a Second-Order Few-Mode Raman Amplifier,” J. Lightwave Technol. 36(16), 3254–3260 (2018).
[Crossref]

J. Li, J. Du, L. Wang, S. Jiang, L. Ma, C. Cai, L. Zhu, A. Wang, M. Li, C. Hao, J. Wang, and Z. He, “Experimental demonstration of few-mode Raman amplifier with flat gain covering 1530-1605 nm,” Opt. Lett. 43(18), 4530–4533 (2018).
[Crossref]

S. Jiang, L. Ma, Z. Zhang, X. Xu, S. Wang, J. Du, C. Yang, W. Tong, and Z. He, “Design and Characterization of Ring-Assisted Few-Mode Fibers for Weakly Coupled Mode-Division Multiplexing Transmission,” J. Lightwave Technol. 36(23), 5547–5555 (2018).
[Crossref]

J. Li, J. Du, L. Ma, M.-J. Li, K. Xu, and Z. He, “Second-order few-mode Raman amplifier for mode-division multiplexed optical communication systems,” Opt. Express 25(2), 810–820 (2017).
[Crossref]

Y. Chen, J. Du, J. Li, L. Shen, J. Luo, and Z. He, “Time-wavelength-mode equalization by PSO for random fiber laser based FMF Raman amplifier,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W4B. 1.

Y. Chen, J. Du, Y. Huang, K. Xu, and Z. He, “Intelligent gain flattening of FMF Raman amplification by machine learning based inverse design,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper T4B. 1.

Z. He, J. Du, W. Shen, Y. Huang, C. Wang, K. Xu, and Z. He, “Inverse design of few-mode fiber by Neural Network for weak-coupling optimization,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W2A.15.

Esmaeelpour, M.

Essiambre, R.

Feng, L.

L. Feng, Y. Li, X. Zeng, W. Li, J. Qiu, X. Hong, Y. Zuo, H. Guo, and J. Wu, “An asymmetric fiber for MIMO-free mode division multiplexing transmission,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2017), paper Su2A.95.

Glorot, X.

X. Glorot and Y. Bengio, “Understanding the difficulty of training deep feedforward neural networks,” http://proceedings.mlr.press/v9/glorot10a.html

Gnauck, A. H.

Guo, H.

L. Feng, Y. Li, X. Zeng, W. Li, J. Qiu, X. Hong, Y. Zuo, H. Guo, and J. Wu, “An asymmetric fiber for MIMO-free mode division multiplexing transmission,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2017), paper Su2A.95.

Hao, C.

Hayashi, M.

N. P. Diamantopoulos, M. Hayashi, Y. Yoshida, A. Maruta, K. Takenaga, H. Uemura, S. Matsuo, and K. Kitayama, “Mode unbundled ROADM for MDM networks: Characterization of Uni- and Bi- directional mode assignment,” in International Conference on Photonics (IEEE, 2015), pp. 139–141.

He, Y.

F. Ren, J. Li, T. Hu, R. Tang, J. Yu, M. Qi, Y. He, Z. Chen, and Z. Li, “Cascaded Mode- Division- Multiplexing and Time-Division-Multiplexing Passive Optical Network Based on Low Mode-Crosstalk FMF and Mode MUX/DEMUX,” IEEE Photonics J. 7(5), 1–9 (2015).
[Crossref]

He, Z.

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

J. Li, J. Du, L. Wang, S. Jiang, L. Ma, C. Cai, L. Zhu, A. Wang, M. Li, C. Hao, J. Wang, and Z. He, “Experimental demonstration of few-mode Raman amplifier with flat gain covering 1530-1605 nm,” Opt. Lett. 43(18), 4530–4533 (2018).
[Crossref]

J. Li, C. Cai, J. Du, S. Jiang, L. Ma, L. Wang, L. Zhu, A. Wang, M. Li, H. Chen, J. Wang, and Z. He, “Ultra-Low-Noise Mode-Division Multiplexed WDM Transmission Over 100-km FMF Based on a Second-Order Few-Mode Raman Amplifier,” J. Lightwave Technol. 36(16), 3254–3260 (2018).
[Crossref]

S. Jiang, L. Ma, Z. Zhang, X. Xu, S. Wang, J. Du, C. Yang, W. Tong, and Z. He, “Design and Characterization of Ring-Assisted Few-Mode Fibers for Weakly Coupled Mode-Division Multiplexing Transmission,” J. Lightwave Technol. 36(23), 5547–5555 (2018).
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J. Li, J. Du, L. Ma, M.-J. Li, K. Xu, and Z. He, “Second-order few-mode Raman amplifier for mode-division multiplexed optical communication systems,” Opt. Express 25(2), 810–820 (2017).
[Crossref]

Y. Chen, J. Du, Y. Huang, K. Xu, and Z. He, “Intelligent gain flattening of FMF Raman amplification by machine learning based inverse design,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper T4B. 1.

Y. Chen, J. Du, J. Li, L. Shen, J. Luo, and Z. He, “Time-wavelength-mode equalization by PSO for random fiber laser based FMF Raman amplifier,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W4B. 1.

Z. He, J. Du, W. Shen, Y. Huang, C. Wang, K. Xu, and Z. He, “Inverse design of few-mode fiber by Neural Network for weak-coupling optimization,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W2A.15.

Z. He, J. Du, W. Shen, Y. Huang, C. Wang, K. Xu, and Z. He, “Inverse design of few-mode fiber by Neural Network for weak-coupling optimization,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W2A.15.

Hong, X.

L. Feng, Y. Li, X. Zeng, W. Li, J. Qiu, X. Hong, Y. Zuo, H. Guo, and J. Wu, “An asymmetric fiber for MIMO-free mode division multiplexing transmission,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2017), paper Su2A.95.

Hu, T.

F. Ren, J. Li, T. Hu, R. Tang, J. Yu, M. Qi, Y. He, Z. Chen, and Z. Li, “Cascaded Mode- Division- Multiplexing and Time-Division-Multiplexing Passive Optical Network Based on Low Mode-Crosstalk FMF and Mode MUX/DEMUX,” IEEE Photonics J. 7(5), 1–9 (2015).
[Crossref]

L. Shen, S. Chen, X. Sun, Y. Liu, L. Zhang, T. Hu, and J. Li, “Design, Fabrication, Measurement and MDM Transmission of a Novel Weakly-coupled Ultra Low Loss FMF,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Th2A.24.

Huang, Y.

Z. He, J. Du, W. Shen, Y. Huang, C. Wang, K. Xu, and Z. He, “Inverse design of few-mode fiber by Neural Network for weak-coupling optimization,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W2A.15.

Y. Chen, J. Du, Y. Huang, K. Xu, and Z. He, “Intelligent gain flattening of FMF Raman amplification by machine learning based inverse design,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper T4B. 1.

Igarashi, K.

D. Soma, S. Beppu, Y. Wakayama, K. Igarashi, T. Tsuritani, I. Morita, and M. Suzuki, “257-Tbit/s Weakly Coupled 10-Mode C + L-Band WDM Transmission,” J. Lightwave Technol. 36(6), 1375–1381 (2018).
[Crossref]

Y. Wakayama, D. Soma, K. Igarashi, H. Taga, and T. Tsuritani, “Experimental characterization of step-index few-mode fiber for weakly-coupled 10-mode-multiplexed transmission,” in Opto-Electronics and Communications Conference and Photonics Global Conference (IEEE, 2017), pp. 1–3.

Ip, E.

Jiang, S.

Kakihara, K.

Kanonakis, K.

Kitayama, K.

N. P. Diamantopoulos, M. Hayashi, Y. Yoshida, A. Maruta, K. Takenaga, H. Uemura, S. Matsuo, and K. Kitayama, “Mode unbundled ROADM for MDM networks: Characterization of Uni- and Bi- directional mode assignment,” in International Conference on Photonics (IEEE, 2015), pp. 139–141.

Koebele, C.

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2 × 100 Gbit/s over 40 km- long prototype few- mode fiber using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express 19(17), 16593–16600 (2011).
[Crossref]

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

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H. S. Chen and A. M. J. Koonen, “LP01 and LP11 mode division multiplexing link with mode crossbar switch,” Electron. Lett. 48(19), 1222–1223 (2012).
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H. Liu, H. Wen, J. C. A. Zacarias, J. E. Antonio-Lopez, N. Wang, P. Sillard, A. A. Correa, R. Amezcua-Correa, and G. Li, “3×10 Gbit/s mode group multiplexed transmission over a 20 km few-mode fiber using photonic lanterns,” in Optical Fiber Communications Conference & Exhibition, OSA Technical Digest (Optical Society of America, 2017), paper M2D.5.

Li, J.

J. Li, C. Cai, J. Du, S. Jiang, L. Ma, L. Wang, L. Zhu, A. Wang, M. Li, H. Chen, J. Wang, and Z. He, “Ultra-Low-Noise Mode-Division Multiplexed WDM Transmission Over 100-km FMF Based on a Second-Order Few-Mode Raman Amplifier,” J. Lightwave Technol. 36(16), 3254–3260 (2018).
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J. Li, J. Du, L. Wang, S. Jiang, L. Ma, C. Cai, L. Zhu, A. Wang, M. Li, C. Hao, J. Wang, and Z. He, “Experimental demonstration of few-mode Raman amplifier with flat gain covering 1530-1605 nm,” Opt. Lett. 43(18), 4530–4533 (2018).
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J. Li, J. Du, L. Ma, M.-J. Li, K. Xu, and Z. He, “Second-order few-mode Raman amplifier for mode-division multiplexed optical communication systems,” Opt. Express 25(2), 810–820 (2017).
[Crossref]

F. Ren, J. Li, T. Hu, R. Tang, J. Yu, M. Qi, Y. He, Z. Chen, and Z. Li, “Cascaded Mode- Division- Multiplexing and Time-Division-Multiplexing Passive Optical Network Based on Low Mode-Crosstalk FMF and Mode MUX/DEMUX,” IEEE Photonics J. 7(5), 1–9 (2015).
[Crossref]

L. Shen, S. Chen, X. Sun, Y. Liu, L. Zhang, T. Hu, and J. Li, “Design, Fabrication, Measurement and MDM Transmission of a Novel Weakly-coupled Ultra Low Loss FMF,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Th2A.24.

Y. Chen, J. Du, J. Li, L. Shen, J. Luo, and Z. He, “Time-wavelength-mode equalization by PSO for random fiber laser based FMF Raman amplifier,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W4B. 1.

J. Luo, J. Li, Q. Sui, and Z. Li, “30 Gb/s 2×2 MDM-DD-OFDM Transmission over 200 m Conventional MMF Link without MIMO Compensation,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper AS4D.2.

Li, M.

Li, M.-J.

Li, W.

L. Feng, Y. Li, X. Zeng, W. Li, J. Qiu, X. Hong, Y. Zuo, H. Guo, and J. Wu, “An asymmetric fiber for MIMO-free mode division multiplexing transmission,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2017), paper Su2A.95.

Li, Y.

L. Feng, Y. Li, X. Zeng, W. Li, J. Qiu, X. Hong, Y. Zuo, H. Guo, and J. Wu, “An asymmetric fiber for MIMO-free mode division multiplexing transmission,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2017), paper Su2A.95.

Li, Z.

F. Ren, J. Li, T. Hu, R. Tang, J. Yu, M. Qi, Y. He, Z. Chen, and Z. Li, “Cascaded Mode- Division- Multiplexing and Time-Division-Multiplexing Passive Optical Network Based on Low Mode-Crosstalk FMF and Mode MUX/DEMUX,” IEEE Photonics J. 7(5), 1–9 (2015).
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J. Luo, J. Li, Q. Sui, and Z. Li, “30 Gb/s 2×2 MDM-DD-OFDM Transmission over 200 m Conventional MMF Link without MIMO Compensation,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper AS4D.2.

Liñares, J.

Lingle, R.

Liu, H.

H. Liu, H. Wen, J. C. A. Zacarias, J. E. Antonio-Lopez, N. Wang, P. Sillard, A. A. Correa, R. Amezcua-Correa, and G. Li, “3×10 Gbit/s mode group multiplexed transmission over a 20 km few-mode fiber using photonic lanterns,” in Optical Fiber Communications Conference & Exhibition, OSA Technical Digest (Optical Society of America, 2017), paper M2D.5.

Liu, Y.

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
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L. Shen, S. Chen, X. Sun, Y. Liu, L. Zhang, T. Hu, and J. Li, “Design, Fabrication, Measurement and MDM Transmission of a Novel Weakly-coupled Ultra Low Loss FMF,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Th2A.24.

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N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical core fiber data transmission,” IEEE Photonics Technol. Lett. 24(5), 344–346 (2012).
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Luo, J.

J. Luo, J. Li, Q. Sui, and Z. Li, “30 Gb/s 2×2 MDM-DD-OFDM Transmission over 200 m Conventional MMF Link without MIMO Compensation,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper AS4D.2.

Y. Chen, J. Du, J. Li, L. Shen, J. Luo, and Z. He, “Time-wavelength-mode equalization by PSO for random fiber laser based FMF Raman amplifier,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W4B. 1.

Ma, L.

Mardoyan, H.

Maruta, A.

N. P. Diamantopoulos, M. Hayashi, Y. Yoshida, A. Maruta, K. Takenaga, H. Uemura, S. Matsuo, and K. Kitayama, “Mode unbundled ROADM for MDM networks: Characterization of Uni- and Bi- directional mode assignment,” in International Conference on Photonics (IEEE, 2015), pp. 139–141.

Matsuo, S.

N. P. Diamantopoulos, M. Hayashi, Y. Yoshida, A. Maruta, K. Takenaga, H. Uemura, S. Matsuo, and K. Kitayama, “Mode unbundled ROADM for MDM networks: Characterization of Uni- and Bi- directional mode assignment,” in International Conference on Photonics (IEEE, 2015), pp. 139–141.

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A. R. May and M. N. Zervas, “Few-mode fibers with improved mode spacing,” in European Conference on Optical Communication (IEEE, 2015) pp. 1–3.

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Milord, L.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

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P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, and F. Achten, “Low-differential-mode-group-delay 9-LP-mode fiber,” J. Lightwave Technol. 34(2), 425–430 (2016).
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P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, and F. Achten, “Micro-Bend-Resistant Low-DMGD 6-LP-Mode Fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2016), paper Th1J.5.

M. Bigot, D. Molin, K. de Jongh, D. Van Ras, F. Achten, and P. Sillard, “Next-Generation Multimode Fibers for Space Division Multiplexing,” in Advanced Photonics 2017 (IPR, NOMA, Sensors, Networks, SPPCom, PS), OSA Technical Digest (online) (Optical Society of America, 2017), paper NeM3B.4.

Montero, C.

Moreno, C.

Morita, I.

Mumtaz, S.

Peckham, D. W.

Peng, G.

Prieto, X.

Provost, L.

Qi, M.

F. Ren, J. Li, T. Hu, R. Tang, J. Yu, M. Qi, Y. He, Z. Chen, and Z. Li, “Cascaded Mode- Division- Multiplexing and Time-Division-Multiplexing Passive Optical Network Based on Low Mode-Crosstalk FMF and Mode MUX/DEMUX,” IEEE Photonics J. 7(5), 1–9 (2015).
[Crossref]

Qiu, J.

L. Feng, Y. Li, X. Zeng, W. Li, J. Qiu, X. Hong, Y. Zuo, H. Guo, and J. Wu, “An asymmetric fiber for MIMO-free mode division multiplexing transmission,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2017), paper Su2A.95.

Randel, S.

Ren, F.

F. Ren, J. Li, T. Hu, R. Tang, J. Yu, M. Qi, Y. He, Z. Chen, and Z. Li, “Cascaded Mode- Division- Multiplexing and Time-Division-Multiplexing Passive Optical Network Based on Low Mode-Crosstalk FMF and Mode MUX/DEMUX,” IEEE Photonics J. 7(5), 1–9 (2015).
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N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical core fiber data transmission,” IEEE Photonics Technol. Lett. 24(5), 344–346 (2012).
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L. Rosa, K. Saitoh, K. Kakihara, and M. Koshiba, “Genetic-algorithm assisted design of C-band CROW-miniaturized PCW interleaver,” J. Lightwave Technol. 27(14), 2678–2687 (2009).
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L. Rosa and K. Saitoh, “Optimization of large-mode-area taperedindex multi-core fibers with high differential mode bending loss for ytterbium-doped fiber applications,” in European Conference on Optical Communication (IEEE, 2010), pp. 1–3.

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Ryf, R.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing Over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
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C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

Saitoh, K.

L. Rosa, K. Saitoh, K. Kakihara, and M. Koshiba, “Genetic-algorithm assisted design of C-band CROW-miniaturized PCW interleaver,” J. Lightwave Technol. 27(14), 2678–2687 (2009).
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L. Rosa and K. Saitoh, “Optimization of large-mode-area taperedindex multi-core fibers with high differential mode bending loss for ytterbium-doped fiber applications,” in European Conference on Optical Communication (IEEE, 2010), pp. 1–3.

Salsi, M.

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2 × 100 Gbit/s over 40 km- long prototype few- mode fiber using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express 19(17), 16593–16600 (2011).
[Crossref]

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

Shen, L.

Y. Chen, J. Du, J. Li, L. Shen, J. Luo, and Z. He, “Time-wavelength-mode equalization by PSO for random fiber laser based FMF Raman amplifier,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W4B. 1.

L. Shen, S. Chen, X. Sun, Y. Liu, L. Zhang, T. Hu, and J. Li, “Design, Fabrication, Measurement and MDM Transmission of a Novel Weakly-coupled Ultra Low Loss FMF,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Th2A.24.

Shen, W.

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

Z. He, J. Du, W. Shen, Y. Huang, C. Wang, K. Xu, and Z. He, “Inverse design of few-mode fiber by Neural Network for weak-coupling optimization,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W2A.15.

Sierra, A.

Sillard, P.

P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, and F. Achten, “Low-differential-mode-group-delay 9-LP-mode fiber,” J. Lightwave Technol. 34(2), 425–430 (2016).
[Crossref]

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2 × 100 Gbit/s over 40 km- long prototype few- mode fiber using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express 19(17), 16593–16600 (2011).
[Crossref]

H. Liu, H. Wen, J. C. A. Zacarias, J. E. Antonio-Lopez, N. Wang, P. Sillard, A. A. Correa, R. Amezcua-Correa, and G. Li, “3×10 Gbit/s mode group multiplexed transmission over a 20 km few-mode fiber using photonic lanterns,” in Optical Fiber Communications Conference & Exhibition, OSA Technical Digest (Optical Society of America, 2017), paper M2D.5.

P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, and F. Achten, “Micro-Bend-Resistant Low-DMGD 6-LP-Mode Fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2016), paper Th1J.5.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

M. Bigot-Astruc, D. Boivin, and P. Sillard, “Design and fabrication of weakly-coupled few-modes fibers,” in IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2012), pp. 189–190.

M. Bigot, D. Molin, K. de Jongh, D. Van Ras, F. Achten, and P. Sillard, “Next-Generation Multimode Fibers for Space Division Multiplexing,” in Advanced Photonics 2017 (IPR, NOMA, Sensors, Networks, SPPCom, PS), OSA Technical Digest (online) (Optical Society of America, 2017), paper NeM3B.4.

Soma, D.

D. Soma, S. Beppu, Y. Wakayama, K. Igarashi, T. Tsuritani, I. Morita, and M. Suzuki, “257-Tbit/s Weakly Coupled 10-Mode C + L-Band WDM Transmission,” J. Lightwave Technol. 36(6), 1375–1381 (2018).
[Crossref]

Y. Wakayama, D. Soma, K. Igarashi, H. Taga, and T. Tsuritani, “Experimental characterization of step-index few-mode fiber for weakly-coupled 10-mode-multiplexed transmission,” in Opto-Electronics and Communications Conference and Photonics Global Conference (IEEE, 2017), pp. 1–3.

Song, Q.

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

Sperti, D.

Stone, J.

Sui, Q.

J. Luo, J. Li, Q. Sui, and Z. Li, “30 Gb/s 2×2 MDM-DD-OFDM Transmission over 200 m Conventional MMF Link without MIMO Compensation,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper AS4D.2.

Sun, X.

L. Shen, S. Chen, X. Sun, Y. Liu, L. Zhang, T. Hu, and J. Li, “Design, Fabrication, Measurement and MDM Transmission of a Novel Weakly-coupled Ultra Low Loss FMF,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2018), paper Th2A.24.

Suzuki, M.

Taga, H.

Y. Wakayama, D. Soma, K. Igarashi, H. Taga, and T. Tsuritani, “Experimental characterization of step-index few-mode fiber for weakly-coupled 10-mode-multiplexed transmission,” in Opto-Electronics and Communications Conference and Photonics Global Conference (IEEE, 2017), pp. 1–3.

Takenaga, K.

N. P. Diamantopoulos, M. Hayashi, Y. Yoshida, A. Maruta, K. Takenaga, H. Uemura, S. Matsuo, and K. Kitayama, “Mode unbundled ROADM for MDM networks: Characterization of Uni- and Bi- directional mode assignment,” in International Conference on Photonics (IEEE, 2015), pp. 139–141.

Tang, R.

F. Ren, J. Li, T. Hu, R. Tang, J. Yu, M. Qi, Y. He, Z. Chen, and Z. Li, “Cascaded Mode- Division- Multiplexing and Time-Division-Multiplexing Passive Optical Network Based on Low Mode-Crosstalk FMF and Mode MUX/DEMUX,” IEEE Photonics J. 7(5), 1–9 (2015).
[Crossref]

Tong, W.

Tran, P.

Tsuritani, T.

D. Soma, S. Beppu, Y. Wakayama, K. Igarashi, T. Tsuritani, I. Morita, and M. Suzuki, “257-Tbit/s Weakly Coupled 10-Mode C + L-Band WDM Transmission,” J. Lightwave Technol. 36(6), 1375–1381 (2018).
[Crossref]

Y. Wakayama, D. Soma, K. Igarashi, H. Taga, and T. Tsuritani, “Experimental characterization of step-index few-mode fiber for weakly-coupled 10-mode-multiplexed transmission,” in Opto-Electronics and Communications Conference and Photonics Global Conference (IEEE, 2017), pp. 1–3.

Uemura, H.

N. P. Diamantopoulos, M. Hayashi, Y. Yoshida, A. Maruta, K. Takenaga, H. Uemura, S. Matsuo, and K. Kitayama, “Mode unbundled ROADM for MDM networks: Characterization of Uni- and Bi- directional mode assignment,” in International Conference on Photonics (IEEE, 2015), pp. 139–141.

Van Ras, D.

M. Bigot, D. Molin, K. de Jongh, D. Van Ras, F. Achten, and P. Sillard, “Next-Generation Multimode Fibers for Space Division Multiplexing,” in Advanced Photonics 2017 (IPR, NOMA, Sensors, Networks, SPPCom, PS), OSA Technical Digest (online) (Optical Society of America, 2017), paper NeM3B.4.

Verluise, F.

Wakayama, Y.

D. Soma, S. Beppu, Y. Wakayama, K. Igarashi, T. Tsuritani, I. Morita, and M. Suzuki, “257-Tbit/s Weakly Coupled 10-Mode C + L-Band WDM Transmission,” J. Lightwave Technol. 36(6), 1375–1381 (2018).
[Crossref]

Y. Wakayama, D. Soma, K. Igarashi, H. Taga, and T. Tsuritani, “Experimental characterization of step-index few-mode fiber for weakly-coupled 10-mode-multiplexed transmission,” in Opto-Electronics and Communications Conference and Photonics Global Conference (IEEE, 2017), pp. 1–3.

Wang, A.

Wang, C.

Z. He, J. Du, W. Shen, Y. Huang, C. Wang, K. Xu, and Z. He, “Inverse design of few-mode fiber by Neural Network for weak-coupling optimization,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W2A.15.

Wang, J.

Wang, L.

Wang, N.

H. Liu, H. Wen, J. C. A. Zacarias, J. E. Antonio-Lopez, N. Wang, P. Sillard, A. A. Correa, R. Amezcua-Correa, and G. Li, “3×10 Gbit/s mode group multiplexed transmission over a 20 km few-mode fiber using photonic lanterns,” in Optical Fiber Communications Conference & Exhibition, OSA Technical Digest (Optical Society of America, 2017), paper M2D.5.

Wang, S.

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
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Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
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L. Feng, Y. Li, X. Zeng, W. Li, J. Qiu, X. Hong, Y. Zuo, H. Guo, and J. Wu, “An asymmetric fiber for MIMO-free mode division multiplexing transmission,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2017), paper Su2A.95.

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Z. He, J. Du, W. Shen, Y. Huang, C. Wang, K. Xu, and Z. He, “Inverse design of few-mode fiber by Neural Network for weak-coupling optimization,” in Optical Fiber Communication Conference Postdeadline Papers, OSA Technical Digest (Optical Society of America, 2020), paper W2A.15.

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Figures (14)

Fig. 1.
Fig. 1. Flow chart of the proposed NN assisted inverse design method.
Fig. 2.
Fig. 2. The parameters of ring-assisted FMF. (a) 6-ring-core FMF structure (b) schematic diagram of four LP modes of 4-ring-core FMF; (c) schematic diagram of twenty LP modes of 6-ring-core FMF;
Fig. 3.
Fig. 3. The inverse design frame of NN. (a) The FMF modes; (b) NN structure; (c) 6-ring FMF structure.
Fig. 4.
Fig. 4. Correlation diagrams between actual and predict data to evaluate the design accuracy
Fig. 5.
Fig. 5. Predicted structural parameter of the 6-ring FMF.
Fig. 6.
Fig. 6. Predicted mode dispersion curves for the 6-ring 20-mode FMF.
Fig. 7.
Fig. 7. The effective refractive index difference distribution
Fig. 8.
Fig. 8. The effective refractive index difference distribution of different deviation.
Fig. 9.
Fig. 9. The effective refractive index difference distribution of different deviation of single parameter.
Fig. 10.
Fig. 10. Correlation diagrams and predicted structure parameter of (a) six and (b) ten modes.
Fig. 11.
Fig. 11. The effective refractive index difference distribution and predicted structure parameter of (a) four and (b) ten modes.
Fig. 12.
Fig. 12. Predicted structural parameter of the 6-ring FMF.
Fig. 13.
Fig. 13. The predict and actual effective refractive index difference distribution
Fig. 14.
Fig. 14. The effective refractive index difference distribution of different deviation.

Tables (4)

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Table 1. The structure parameter ranges of 6-ring-core FMF

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Table 2. The relative errors of the predicted value of Δ n e f f

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Table 3. The result of 20-mode FMF based on 6-ring structure

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Table 4. The result of 20-mode FMF based on 6-ring trench structure