Abstract

We demonstrate experimentally a simultaneous threefold modal and wavelength conversion process of a 10-Gbit/s On/Off keying signal in a 1.8-km long graded-index 6-LP-mode fiber. The principle of operation is based on a phase-matched inter-modal four-wave mixing phenomenon occurring between the fundamental mode and 3 higher-order modes of the fiber. The converted signals show well-opened eye-diagrams and error-free processing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  25. M. Guasoni, F. Parmigiani, P. Horak, and D. J. Richardson, “Novel Fiber Design for Wideband Conversion and Amplification in Multimode Fibers,” in 2017 European Conference on Optical Communication (ECOC, 2017), pp. 1–3.
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2019 (2)

O. F. Anjum, P. Horak, Y. Jung, M. Suzuki, Y. Yamamoto, T. Hasegawa, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Bandwidth enhancement of inter-modal four wave mixing Bragg scattering by means of dispersion engineering,” APL Photonics 4(2), 022902 (2019).
[Crossref]

C. Guo, J. Su, Z. Zhang, L. Cui, and X. Li, “Generation of telecom-band correlated photon pairs in different spatial modes using few-mode fibers,” Opt. Lett. 44(2), 235–238 (2019).
[Crossref] [PubMed]

2018 (2)

2017 (5)

2016 (1)

2015 (1)

M. Guasoni, “Generalized modulational instability in multimode fibers: Wideband multimode parametric amplification,” Phys. Rev. A 92(3), 033849 (2015).
[Crossref]

2014 (1)

2013 (2)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photonics Technol. Lett. 25(6), 539–542 (2013).
[Crossref]

2012 (1)

2010 (3)

R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

D. J. Richardson, “Applied physics. Filling the light pipe,” Science 330(6002), 327–328 (2010).
[Crossref] [PubMed]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

2002 (1)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

1998 (1)

1975 (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” Quantum Electron. 11(3), 100–103 (1975).
[Crossref]

Achten, F.

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 (Optical Society of America, 2016), paper Th1J5.

Agrawal, G. P.

Akahashi, H.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Andrekson, P. A.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Anjum, O. F.

O. F. Anjum, P. Horak, Y. Jung, M. Suzuki, Y. Yamamoto, T. Hasegawa, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Bandwidth enhancement of inter-modal four wave mixing Bragg scattering by means of dispersion engineering,” APL Photonics 4(2), 022902 (2019).
[Crossref]

O. F. Anjum, M. Guasoni, P. Horak, Y. Jung, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Polarization insensitive four wave mixing based wavelength conversion in few-mode optical fibers,” J. Lightwave Technol. 36(17), 3678–3683 (2018).
[Crossref]

Ashkin, A.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” Quantum Electron. 11(3), 100–103 (1975).
[Crossref]

Awaji, Y.

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Barré, N.

G. Labroille, P. Jian, N. Barré, B. Denolle, and J. Morizur, “Mode Selective 10-Mode Multiplexer based on Multi-Plane Light Conversion,” in Optical Fiber Communication Conference (Optical Society of America, 2016), paper Th3E5.

Begleris, I.

Bendahmane, A.

Beppu, S.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Bigot-Astruc, M.

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 (Optical Society of America, 2016), paper Th1J5.

Bjorkholm, J. E.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” Quantum Electron. 11(3), 100–103 (1975).
[Crossref]

Bogris, A.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Chen, H.

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Chraplyvy, A. R.

P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, “Fiber-optic transmission and networking: the previous 20 and the next 20 years [Invited],” Opt. Express 26(18), 24190–24239 (2018).
[Crossref] [PubMed]

R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photonics Technol. Lett. 25(6), 539–542 (2013).
[Crossref]

Christensen, J. B.

Couderc, V.

Cui, L.

Dasgupta, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

de Jongh, K.

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 (Optical Society of America, 2016), paper Th1J5.

Denolle, B.

G. Labroille, P. Jian, N. Barré, B. Denolle, and J. Morizur, “Mode Selective 10-Mode Multiplexer based on Multi-Plane Light Conversion,” in Optical Fiber Communication Conference (Optical Society of America, 2016), paper Th3E5.

Desgroseilliers, M.

Dupiol, R.

Ellis, A. D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Esmaeelpour, M.

Essiambre, R.

Essiambre, R. J.

Y. Xiao, R. J. Essiambre, M. Desgroseilliers, A. M. Tulino, R. Ryf, S. Mumtaz, and G. P. Agrawal, “Theory of intermodal four-wave mixing with random linear mode coupling in few-mode fibers,” Opt. Express 22(26), 32039–32059 (2014).
[Crossref] [PubMed]

R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photonics Technol. Lett. 25(6), 539–542 (2013).
[Crossref]

R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Fabert, M.

Fatome, J.

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Fontaine, N. K.

M. Esmaeelpour, R. Essiambre, N. K. Fontaine, R. Ryf, J. Toulouse, Y. Sun, and R. Lingle, “Power Fluctuations of Intermodal Four-Wave Mixing in Few-Mode Fibers,” J. Lightwave Technol. 35(12), 2429–2435 (2017).
[Crossref]

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Foschini, G. J.

Friis, S. M. M.

Geisler, T.

Gnauck, A. H.

R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photonics Technol. Lett. 25(6), 539–542 (2013).
[Crossref]

Goebel, B.

Gross, S.

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Grüner-Nielsen, L.

F. Parmigiani, P. Horak, Y. Jung, L. Grüner-Nielsen, T. Geisler, P. Petropoulos, and D. J. Richardson, “All-optical mode and wavelength converter based on parametric processes in a three-mode fiber,” Opt. Express 25(26), 33602–33609 (2017).
[Crossref]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Guasoni, M.

O. F. Anjum, M. Guasoni, P. Horak, Y. Jung, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Polarization insensitive four wave mixing based wavelength conversion in few-mode optical fibers,” J. Lightwave Technol. 36(17), 3678–3683 (2018).
[Crossref]

M. Guasoni, F. Parmigiani, P. Horak, J. Fatome, and D. J. Richardson, “Intermodal four-wave-mixing and parametric amplification in km-long multi-mode fibers,” J. Lightwave Technol. 35(24), 5296–5305 (2017).
[Crossref]

M. Guasoni, “Generalized modulational instability in multimode fibers: Wideband multimode parametric amplification,” Phys. Rev. A 92(3), 033849 (2015).
[Crossref]

M. Guasoni, F. Parmigiani, P. Horak, and D. J. Richardson, “Novel Fiber Design for Wideband Conversion and Amplification in Multimode Fibers,” in 2017 European Conference on Optical Communication (ECOC, 2017), pp. 1–3.

Guo, C.

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Hasegawa, T.

O. F. Anjum, P. Horak, Y. Jung, M. Suzuki, Y. Yamamoto, T. Hasegawa, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Bandwidth enhancement of inter-modal four wave mixing Bragg scattering by means of dispersion engineering,” APL Photonics 4(2), 022902 (2019).
[Crossref]

Hayashi, T.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Hedekvist, P. O.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Herstrøm, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Horak, P.

Igarashi, K.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Jakobsen, D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Jian, P.

G. Labroille, P. Jian, N. Barré, B. Denolle, and J. Morizur, “Mode Selective 10-Mode Multiplexer based on Multi-Plane Light Conversion,” in Optical Fiber Communication Conference (Optical Society of America, 2016), paper Th3E5.

Jiang, X.

R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photonics Technol. Lett. 25(6), 539–542 (2013).
[Crossref]

Jopson, R. M.

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Jung, Y.

Kakande, J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Karlsson, M.

Koefoed, J. G.

Kramer, G.

Krupa, K.

Labroille, G.

G. Labroille, P. Jian, N. Barré, B. Denolle, and J. Morizur, “Mode Selective 10-Mode Multiplexer based on Multi-Plane Light Conversion,” in Optical Fiber Communication Conference (Optical Society of America, 2016), paper Th3E5.

Li, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Li, X.

Lingle, R.

M. Esmaeelpour, R. Essiambre, N. K. Fontaine, R. Ryf, J. Toulouse, Y. Sun, and R. Lingle, “Power Fluctuations of Intermodal Four-Wave Mixing in Few-Mode Fibers,” J. Lightwave Technol. 35(12), 2429–2435 (2017).
[Crossref]

R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photonics Technol. Lett. 25(6), 539–542 (2013).
[Crossref]

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Luis, R. S.

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Lundström, C.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Mafi, A.

Mestre, M. A.

R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photonics Technol. Lett. 25(6), 539–542 (2013).
[Crossref]

Millot, G.

Molin, D.

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 (Optical Society of America, 2016), paper Th1J5.

Morita, I.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Morizur, J.

G. Labroille, P. Jian, N. Barré, B. Denolle, and J. Morizur, “Mode Selective 10-Mode Multiplexer based on Multi-Plane Light Conversion,” in Optical Fiber Communication Conference (Optical Society of America, 2016), paper Th3E5.

Mumtaz, S.

Nagashima, T.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Neilson, D. T.

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

O’Gorman, J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Parmigiani, F.

O. F. Anjum, P. Horak, Y. Jung, M. Suzuki, Y. Yamamoto, T. Hasegawa, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Bandwidth enhancement of inter-modal four wave mixing Bragg scattering by means of dispersion engineering,” APL Photonics 4(2), 022902 (2019).
[Crossref]

O. F. Anjum, M. Guasoni, P. Horak, Y. Jung, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Polarization insensitive four wave mixing based wavelength conversion in few-mode optical fibers,” J. Lightwave Technol. 36(17), 3678–3683 (2018).
[Crossref]

F. Parmigiani, P. Horak, Y. Jung, L. Grüner-Nielsen, T. Geisler, P. Petropoulos, and D. J. Richardson, “All-optical mode and wavelength converter based on parametric processes in a three-mode fiber,” Opt. Express 25(26), 33602–33609 (2017).
[Crossref]

M. Guasoni, F. Parmigiani, P. Horak, J. Fatome, and D. J. Richardson, “Intermodal four-wave-mixing and parametric amplification in km-long multi-mode fibers,” J. Lightwave Technol. 35(24), 5296–5305 (2017).
[Crossref]

S. M. M. Friis, I. Begleris, Y. Jung, K. Rottwitt, P. Petropoulos, D. J. Richardson, P. Horak, and F. Parmigiani, “Inter-modal four-wave mixing study in a two-mode fiber,” Opt. Express 24(26), 30338–30349 (2016).
[Crossref] [PubMed]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

M. Guasoni, F. Parmigiani, P. Horak, and D. J. Richardson, “Novel Fiber Design for Wideband Conversion and Amplification in Multimode Fibers,” in 2017 European Conference on Optical Communication (ECOC, 2017), pp. 1–3.

Petropoulos, P.

O. F. Anjum, P. Horak, Y. Jung, M. Suzuki, Y. Yamamoto, T. Hasegawa, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Bandwidth enhancement of inter-modal four wave mixing Bragg scattering by means of dispersion engineering,” APL Photonics 4(2), 022902 (2019).
[Crossref]

O. F. Anjum, M. Guasoni, P. Horak, Y. Jung, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Polarization insensitive four wave mixing based wavelength conversion in few-mode optical fibers,” J. Lightwave Technol. 36(17), 3678–3683 (2018).
[Crossref]

F. Parmigiani, P. Horak, Y. Jung, L. Grüner-Nielsen, T. Geisler, P. Petropoulos, and D. J. Richardson, “All-optical mode and wavelength converter based on parametric processes in a three-mode fiber,” Opt. Express 25(26), 33602–33609 (2017).
[Crossref]

S. M. M. Friis, I. Begleris, Y. Jung, K. Rottwitt, P. Petropoulos, D. J. Richardson, P. Horak, and F. Parmigiani, “Inter-modal four-wave mixing study in a two-mode fiber,” Opt. Express 24(26), 30338–30349 (2016).
[Crossref] [PubMed]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Phelan, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Puttnam, B. J.

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Rademacher, G.

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Richardson, D. J.

O. F. Anjum, P. Horak, Y. Jung, M. Suzuki, Y. Yamamoto, T. Hasegawa, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Bandwidth enhancement of inter-modal four wave mixing Bragg scattering by means of dispersion engineering,” APL Photonics 4(2), 022902 (2019).
[Crossref]

O. F. Anjum, M. Guasoni, P. Horak, Y. Jung, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Polarization insensitive four wave mixing based wavelength conversion in few-mode optical fibers,” J. Lightwave Technol. 36(17), 3678–3683 (2018).
[Crossref]

F. Parmigiani, P. Horak, Y. Jung, L. Grüner-Nielsen, T. Geisler, P. Petropoulos, and D. J. Richardson, “All-optical mode and wavelength converter based on parametric processes in a three-mode fiber,” Opt. Express 25(26), 33602–33609 (2017).
[Crossref]

M. Guasoni, F. Parmigiani, P. Horak, J. Fatome, and D. J. Richardson, “Intermodal four-wave-mixing and parametric amplification in km-long multi-mode fibers,” J. Lightwave Technol. 35(24), 5296–5305 (2017).
[Crossref]

S. M. M. Friis, I. Begleris, Y. Jung, K. Rottwitt, P. Petropoulos, D. J. Richardson, P. Horak, and F. Parmigiani, “Inter-modal four-wave mixing study in a two-mode fiber,” Opt. Express 24(26), 30338–30349 (2016).
[Crossref] [PubMed]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

D. J. Richardson, “Applied physics. Filling the light pipe,” Science 330(6002), 327–328 (2010).
[Crossref] [PubMed]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

M. Guasoni, F. Parmigiani, P. Horak, and D. J. Richardson, “Novel Fiber Design for Wideband Conversion and Amplification in Multimode Fibers,” in 2017 European Conference on Optical Communication (ECOC, 2017), pp. 1–3.

Riesen, N.

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Rottwitt, K.

Ryf, R.

M. Esmaeelpour, R. Essiambre, N. K. Fontaine, R. Ryf, J. Toulouse, Y. Sun, and R. Lingle, “Power Fluctuations of Intermodal Four-Wave Mixing in Few-Mode Fibers,” J. Lightwave Technol. 35(12), 2429–2435 (2017).
[Crossref]

Y. Xiao, R. J. Essiambre, M. Desgroseilliers, A. M. Tulino, R. Ryf, S. Mumtaz, and G. P. Agrawal, “Theory of intermodal four-wave mixing with random linear mode coupling in few-mode fibers,” Opt. Express 22(26), 32039–32059 (2014).
[Crossref] [PubMed]

R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photonics Technol. Lett. 25(6), 539–542 (2013).
[Crossref]

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Sillard, P.

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 (Optical Society of America, 2016), paper Th1J5.

Sjödin, M.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Slavík, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Soma, D.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Stolen, R. H.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” Quantum Electron. 11(3), 100–103 (1975).
[Crossref]

Su, J.

Sumita, S.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Sun, Y.

M. Esmaeelpour, R. Essiambre, N. K. Fontaine, R. Ryf, J. Toulouse, Y. Sun, and R. Lingle, “Power Fluctuations of Intermodal Four-Wave Mixing in Few-Mode Fibers,” J. Lightwave Technol. 35(12), 2429–2435 (2017).
[Crossref]

R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photonics Technol. Lett. 25(6), 539–542 (2013).
[Crossref]

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Suzuki, M.

O. F. Anjum, P. Horak, Y. Jung, M. Suzuki, Y. Yamamoto, T. Hasegawa, P. Petropoulos, D. J. Richardson, and F. Parmigiani, “Bandwidth enhancement of inter-modal four wave mixing Bragg scattering by means of dispersion engineering,” APL Photonics 4(2), 022902 (2019).
[Crossref]

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Sygletos, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Syvridis, D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Tkach, R. W.

R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photonics Technol. Lett. 25(6), 539–542 (2013).
[Crossref]

Tonello, A.

Toulouse, J.

Tsuritani, T.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Tulino, A. M.

Wabnitz, S.

Wada, N.

G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R. M. Jopson, R. J. Essiambre, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, and R. Lingle, “Experimental Investigation of Parametric Mode and Wavelength Conversion in a 4.7 km Few-Mode Fiber,” in 2018 European Conference on Optical Communication (ECOC, 2018), pp. 1–3.
[Crossref]

Wakayama, Y.

D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, H. Akahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16 Peta-bit/s dense SDM/WDM transmission over low-DMD 6-mode 19-core fibre across C+L Band,” in Proceedings of the European Conference on Optical Communication (ECOC, 2017), paper ThPDPA1.

Weerasuriya, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[Crossref]

Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 The input configuration. Four high power CW pump waves P1-4 are injected into the LP01, LP11, LP02, LP31 modes respectively, together with a weak signal wave injected into the LP01 mode. The generated idler waves are labelled by dashed lines.
Fig. 2
Fig. 2 (a) Schematic of the phase-matching conditions of the IFWM between LP01 and higher-order modes. (b) Measurement of the relative inverse group velocity (RIGV) as a function of wavelength for the four modes. The four pump wavelengths λP1-λP4 at the same group velocity in each mode are also shown with dashed lines.
Fig. 3
Fig. 3 Theoretical CE vs signal wavelength (Δλ = λP1-λs) curves for the BS (red) and PC (blue) processes between LP01 and (a) LP11, (b) LP02, and (c) LP31. The pump wavelength and power are 1564.5 nm and 28.5 dBm for LP01. The pump wavelength offset (λP1-λPn) is 16 nm for LP11, 24.8 nm for LP02 as well as 31 nm for LP31. The pump power in higher-order modes is 20.5 dBm.
Fig. 4
Fig. 4 Overview of the experimental setup. PM phase modulator, IM intensity modulator, PC polarization controller, EDFA Erbium-doped fiber amplifier, OSA optical spectrum analyzer, BER bit-error-rate measurement.
Fig. 5
Fig. 5 (a-c) Typical spectrum recorded close to the phase matching condition in each group of modes. (d-f) Conversion efficiency of the Bragg-scattering and phase-conjugation processes observed when scanning the pump wavelengths (Δλ = λP1-λPn) in LP11 (d), LP02 (e) and LP31 (f).
Fig. 6
Fig. 6 (a) Experimental measurement of the total output spectrum with respect to the LP01 signal wavelength when pumping the 4 modes simultaneously. The output spectra from each port of the demultiplexer are added to obtain the total spectrum. The spectra are normalized by the pump power measured in the fundamental mode. (b-d) Conversion efficiency of the Bragg-scattering and phase-conjugation processes measured in each group of modes when scanning the wavelength of the LP01 signal wave. For these data, the output spectra from the same mode-group are summed up to calculate the conversion efficiency.
Fig. 7
Fig. 7 (a) Optical spectrum of the multiple BS conversion process. (b-e) Eye-diagrams of the output signals in LP01, LP11a, LP02 and LP31a. (f) Bit-error-rate as a function of incoming power on the receiver for all the converted signals as well as back-to-back (btb) measurements.

Tables (1)

Tables Icon

Table 1 Effective coupling areas (at 1550nm) between LP01 and higher-order modes in the 6-LP-mode fiber.

Equations (13)

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ω i n bs = ω P n ω P 1 + ω s
ω i n pc = ω P n + ω P 1 ω s
β i ( ω )= β 0 i + β 1 i ( ω ω 0 )+ 1 2 β 2 i ( ω ω 0 ) 2 + 1 6 β 3 i ( ω ω 0 ) 3 +
Δβ= β 11 ( ω P 2 )+ β 01 ( ω s ) β 01 ( ω P 1 ) β 11 ( ω i 2 bs ) [ β 1 01 + β 2 01 ( ω P 1 + ω s 2 ω 0 ) β 1 11 β 2 11 ( ω P 2 + ω i 2 bs 2 ω 0 ) ]( ω s ω P 1 )
E ( p ) z =[ i β 0 p β 1 p t i β 2 p 2 2 t 2 + β 3 p 6 3 t 3 +iγ( f pp | E ( p ) | 2 +2 f pq | E ( q ) | 2 ) ] E ( p )
E ( q ) z =[ i β 0 q β 1 q t i β 2 q 2 2 t 2 + β 3 q 6 3 t 3 +iγ( f qq | E ( q ) | 2 +2 f pq | E ( p ) | 2 ) ] E ( q )
E ( 01 ) ( z,t )={ E P1 ( z )exp[i β 01 ( ω P 1 )zi ω P 1 t]+ E s ( z )exp[i β 01 ( ω s )zi ω s t] }exp( i ω 0 t )
E ( 11 ) ( z,t )={ E P2 ( z )exp[i β 11 ( ω P 2 )zi ω P 2 t]+ E i 2 bs ( z )exp[i β 11 ( ω i 2 bs )zi ω i 2 bs t]+ E i 2 pc ( z )exp[i β 11 ( ω i 2 pc )zi ω i 2 pc t]}exp( i ω 0 t )
E i 2 bs (z) z =2iγ f 01 E P1 * (z) E P2 (z) E s (z)exp( iΔ β bs z )
E i 2 pc (z) z =2iγ f 01 E P1 (z) E P2 (z) E s * (z)exp( iΔ β pc z )
P i bs (z)= | E i 2 bs (z) | 2 =4 γ 2 f 01 2 z 2 | E P1 * (0) E P2 (0) E s (0) | 2 sin c 2 ( Δ β bs z/2 )
P i pc (z)= | E i 2 pc (z) | 2 =4 γ 2 f 01 2 z 2 | E P1 (0) E P2 (0) E s * (0) | 2 sin c 2 ( Δ β pc z/2 )
CE= P i ( z ) P s ( z ) =4 γ 2 f 01 2 z 2 | E P1 | 2 | E P2 | 2 sin c 2 ( Δβz/2 )

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