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Zusammenfassung

Fiber-based optical communication networks are reaching a point where the capacity required on a single link can significantly exceed the capacity of a single-mode fiber, and at the same time conventional network architectures can no longer be scaled cost-effectively. Space-division multiplexing () addresses the capacity bottleneck imposed by the use of single-mode fibers within a completely new approach that relies on new fiber types, optical amplifiers, and optical switches capable of supporting multiple spatial channels.

The aim of this chapter is, on one hand, to provide an overview of the components that are necessary for the implementation of SDM transmission and, on the other hand, to review the modeling of the main propagation effects that occur in multimode and multicore fibers. The chapter also includes a description of the techniques that are used in SDM transmission experiments and an update on transmission records reported from around the globe. The chapter ends with the description of potential architectures supporting SDM networks.

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References

  • R.-J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, B. Goebel: Capacity limits of optical fiber networks, J. Lightwave Technol. 28(4), 662–701 (2010)

    Article  Google Scholar 

  • P. Winzer: Spatial multiplexing in fiber optics: The 10X scaling of metro/core capacities, Bell Labs Tech. J. 19, 22–30 (2014)

    Article  Google Scholar 

  • D.J. Richardson, J.M. Fini, L.E. Nelson: Space-division multiplexing in optical fibres, Nat. Photonics 7(5), 354–362 (2013)

    Article  Google Scholar 

  • G. Li, N. Bai, N. Zhao, C. Xia: Space-division multiplexing: The next frontier in optical communication, Adv. Opt. Photonics 6(4), 413–487 (2014)

    Article  Google Scholar 

  • R. Ryf, N.K. Fontaine, H. Chen, B. Guan, B. Huang, M. Esmaeelpour, A.H. Gnauck, S. Randel, S. Yoo, A. Koonen, R. Shubochkin, Y. Sun, R. Lingle: Mode-multiplexed transmission over conventional graded-index multimode fibers, Opt. Express 23(1), 235–246 (2015)

    Article  Google Scholar 

  • P. Sillard, D. Molin, M. Bigot-Astruc, A. Amezcua-Correa, K. de Jongh, F. Achten: 50 \(\upmu\)m multimode fibers for mode division multiplexing, J. Lightwave Technol. 34(8), 1672–1677 (2016)

    Article  Google Scholar 

  • P. Sillard, D. Molin, M. Bigot, A. Amezcua-Correa, K. de Jongh, F. Achten: DMGD-compensated links. In: Opt. Fiber Commun. Conf. (2017), https://doi.org/10.1364/OFC.2017.Tu2J.4

    Chapter  Google Scholar 

  • P. Winzer, A. Gnauck, A. Konczykowska, F. Jorge, J.-Y. Dupuy: Penalties from in-band crosstalk for advanced optical modulation formats. In: 37th Eur. Conf. Opt. Commun. (2011), https://doi.org/10.1364/ECOC.2011.Tu.5.B.7

    Chapter  Google Scholar 

  • J. Sakaguchi, W. Klaus, J.M.D. Mendinueta, B.J. Puttnam, R.S. Luís, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, T. Kobayashi: Large spatial channel (36-core \(\times\) 3 mode) heterogeneous few-mode multicore fiber, J. Lightwave Technol. 34(1), 93–103 (2016)

    Article  Google Scholar 

  • S. Matsuo, K. Takenaga, Y. Sasaki, Y. Amma, S. Saito, K. Saitoh, T. Matsui, K. Nakajima, T. Mizuno, H. Takara, Y. Miyamoto, T. Morioka: High-spatial-multiplicity multicore fibers for future dense space-division-multiplexing systems, J. Lightwave Technol. 34(6), 1464–1475 (2016)

    Article  Google Scholar 

  • T. Mizuno, K. Shibahara, H. Ono, Y. Abe, Y. Miyamoto, F. Ye, T. Morioka, Y. Sasaki, Y. Amma, K. Takenaga, S. Matsuo, K. Aikawa, K. Saitoh, Y. Jung, D.J. Richardson, K. Pulverer, M. Bohn, M. Yamada: 32-core dense SDM unidirectional transmission of PDM-16QAM signals over 1600 km using crosstalk-managed single-mode heterogeneous multicore transmission line. In: Opt. Fiber Commun. Conf. (2016), https://doi.org/10.1364/OFC.2016.Th5C.3

    Chapter  Google Scholar 

  • A. Turukhin, H. Batshon, M. Mazurczyk, Y. Sun, C. Davidson, J. Chai, O. Sinkin, W. Patterson, G. Wolter, M. Bolshtyansky: Demonstration of 0.52 Pb/s potential transmission capacity over 8,830 km using multicore fiber. In: 42nd Eur. Conf. Opt. Commun. (2016)

    Google Scholar 

  • P. Pepeljugoski, F.E. Doany, D. Kuchta, B. Lee, C.L. Schow, L. Schares: Connector performance analysis for D-shaped multi-core multi mode fiber. In: Opt. Fiber Commun. Conf. (2014), https://doi.org/10.1364/OFC.2014.Th4J.4

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  • L. Grüner-Nielsen, Y. Sun, J.W. Nicholson, D. Jakobsen, K.G. Jespersen, J.R. Lingle, B. Pálsdóttir: Few mode transmission fiber with low DGD, low mode coupling, and low loss, J. Lightwave Technol. 30(23), 3693–3698 (2012)

    Article  Google Scholar 

  • P. Sillard, D. Molin, M. Bigot-Astruc, K. de Jongh, F. Achten, J.E. Antonio-López, R. Amezcua-Correa: Micro-bend-resistant low-differential-mode-group-delay few-mode fibers, J. Lightwave Technol. 35(4), 734–740 (2017)

    Article  Google Scholar 

  • J. van Weerdenburg, R. Ryf, R. Alvarez-Aguirre, N.K. Fontaine, R.J. Essiambre, H. Chen, J.C. Alvarado-Zacarias, R. Amezcua-Correa, S. Gross, N. Riesen, M. Withford, D.W. Peckham, A. McCurdy, R. Lingle, T. Koonen, C. Okonkwo: Mode-multiplexed 16-QAM transmission over 2400-km large-effective-area depressed-cladding 3-mode fiber. In: Opt. Fiber Commun. Conf. (2018), https://doi.org/10.1364/OFC.2018.W4C.2

    Chapter  Google Scholar 

  • R. Ryf, N.K. Fontaine, H. Chen, S. Wittek, J. Li, J.C. Alvarado-Zacarias, R. Amezcua-Correa, J.E. Antonio-Lopez, M. Capuzzo, R. Kopf, A. Tate, H. Safar, C. Bolle, D.T. Neilson, E. Burrows, K. Kim, M. Bigot-Astruc, F. Achten, P. Sillard, A. Amezcua-Correa, J. Du, Z. He, J. Carpenter: Mode-multiplexed transmission over 36 spatial modes of a graded-index multimode fiber. In: Eur. Conf. Opt. Commun. (2018), https://doi.org/10.1109/ECOC.2018.8535431

    Chapter  Google Scholar 

  • R. Ryf, N.K. Fontaine, S. Wittek, K. Choutagunta, M. Mazur, H. Chen, J.C. Alvarado-Zacarias, R. Amezcua-Correa, M. Capuzzo, R. Kopf, A. Tate, H. Safar, C. Bolle, D.T. Neilson, E. Burrows, K. Kim, M. Bigot-Astruc, F. Achten, P. Sillard, A. Amezcua-Correa, J.M. Kahn, J. Schröder, J. Carpenter: High-spectral-efficiency mode-multiplexed transmission over graded-index multimode fiber. In: Eur. Conf. Opt. Commun. (2018), https://doi.org/10.1109/ECOC.2018.8535536

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  • L. Wang, S. LaRochelle: Design of eight-mode polarization-maintaining few-mode fiber for multiple-input multiple-output-free spatial division multiplexing, Opt. Lett. 40(24), 5846–5849 (2015)

    Article  Google Scholar 

  • W. Wang, J. Zhao, H. Yu, Z. Yang, Y. Zhang, Z. Zhang, C. Guo, G. Li: Demonstration of 6 \(\times\)10 Gb/s MIMO-free polarization- and mode-multiplexed transmission, IEEE Photonics Technol. Lett. 30(15), 1372–1375 (2018)

    Article  Google Scholar 

  • N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A.E. Willner, S. Ramachandran: Terabit-scale orbital angular momentum mode division multiplexing in fibers, Science 340(6140), 1545–1548 (2013)

    Article  Google Scholar 

  • N.K. Fontaine, R. Ryf, J. Bland-Hawthorn, S.G. Leon-Saval: Geometric requirements for photonic lanterns in space division multiplexing, Opt. Express 20(24), 27123–27132 (2012)

    Article  Google Scholar 

  • J. Carpenter, T. Wilkinson: Characterization of multimode fiber by selective mode excitation, J. Lightwave Technol. 30(10), 1386–1392 (2012)

    Article  Google Scholar 

  • M. Salsi, C. Koebele, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Bigot-Astruc, L. Provost, F. Cerou, G. Charlet: Transmission at 2 $$\times$$ 100Gb/s, over two modes of 40km-long prototype few-mode fiber, using LCOS based mode multiplexer and demultiplexer. In: Opt. Fiber Commun. Conf. (2011), https://doi.org/10.1364/NFOEC.2011.PDPB9

    Chapter  Google Scholar 

  • H. Chen, R. van Uden, C. Okonkwo, T. Koonen: Compact spatial multiplexers for mode division multiplexing, Opt. Express 22(26), 31582 (2014)

    Article  Google Scholar 

  • Y. Ding, H. Ou, J. Xu, C. Peucheret: Silicon photonic integrated circuit mode multiplexer, IEEE Photonics Technol. Lett. 25(7), 648–651 (2013)

    Article  Google Scholar 

  • K. Igarashi, D. Souma, K. Takeshima, T. Tsuritani: Selective mode multiplexer based on phase plates and Mach-Zehnder interferometer with image inversion function, Opt. Express 23(1), 183–194 (2015)

    Article  Google Scholar 

  • S.H. Chang, H.S. Chung, N.K. Fontaine, R. Ryf, K.J. Park, K. Kim, J.C. Lee, J.H. Lee, B.Y. Kim, Y.K. Kim: Mode division multiplexed optical transmission enabled by all-fiber mode multiplexer, Opt. Express 22(12), 14229–14236 (2014)

    Article  Google Scholar 

  • S.G. Leon-Saval, N.K. Fontaine, J.R. Salazar-Gil, B. Ercan, R. Ryf, J. Bland-Hawthorn: Mode-selective photonic lanterns for space-division multiplexing, Opt. Express 22(1), 1036–1044 (2014)

    Article  Google Scholar 

  • T.A. Birks, S. Yerolatsitis, I. Gris-Sánchez: Fibre-based mode multiplexers. In: Adv. Photonics (2014), https://doi.org/10.1364/SOF.2014.SoW1B.1

    Chapter  Google Scholar 

  • G. Labroille, B. Denolle, P. Jian, P. Genevaux, N. Treps, J.-F. Morizur: Efficient and mode selective spatial mode multiplexer based on multi-plane light conversion, Opt. Express 22(13), 15599–15607 (2014)

    Article  Google Scholar 

  • S.G. Leon-Saval, T.A. Birks, J. Bland-Hawthorn, M. Englund: Multimode fiber devices with single-mode performance, Opt. Lett. 30(19), 2545–2547 (2005)

    Article  Google Scholar 

  • S. Yerolatsitis, I. Gris-Sánchez, T.A. Birks: Adiabatically-tapered fiber mode multiplexers, Opt. Express 22(1), 608–617 (2014)

    Article  Google Scholar 

  • I. Giles, R. Chen, V. Garcia-Munoz: Fiber based multiplexing and demultiplexing devices for few mode fiber space division multiplexed communications. In: Opt. Fiber Commun. Conf. (2014), https://doi.org/10.1364/OFC.2014.Tu3D.1

    Chapter  Google Scholar 

  • A.M. Velázquez-Benítez, J.E. Antonio-Lopez, J.C. Alvarado-Zacarias, G. Lopez-Galmiche, P. Sillard, D.V. Ras, C. Okonkwo, H. Chen, R. Ryf, N.K. Fontaine, R. Amezcua-Correa: Scaling the fabrication of higher order photonic lanterns using microstructured preforms. In: Eur. Conf. Opt. Commun. (2015), https://doi.org/10.1109/ECOC.2015.7341939

    Chapter  Google Scholar 

  • B. Huang, N.K. Fontaine, R. Ryf, B. Guan, S.G. Leon-Saval, R. Shubochkin, Y. Sun, R. Lingle, G. Li: All-fiber mode-group-selective photonic lantern using graded-index multimode fibers, Opt. Express 23(1), 224–234 (2015)

    Article  Google Scholar 

  • B. Guan, B. Ercan, N.K. Fontaine, R. Ryf, H. Chen, R.P. Scott, Y. Zhang, S.J.B. Yoo: 15-spatial-mode photonic lanterns based on ultrafast laser inscription. In: Eur. Conf. Opt. Commun (2015), https://doi.org/10.1109/ECOC.2015.7341651

    Chapter  Google Scholar 

  • N. Riesen, S. Gross, J.D. Love, Y. Sasaki, M.J. Withford: Femtosecond laser written integrated spatial multiplexers for few-mode multicore fibre. In: 42nd Eur. Conf. Opt. Commun. (2016) pp. 1064–1066

    Google Scholar 

  • N.K. Fontaine, R. Ryf, H. Chen, D. Neilson, J. Carpenter: Design of high order mode-multiplexers using multiplane light conversion. In: 43rd Eur. Conf. Opt. Commun. (2017), https://doi.org/10.1109/ECOC.2017.8346129

    Chapter  Google Scholar 

  • S. Bade, B. Denolle, G. Trunet, N. Riguet, P. Jian, O. Pinel, G. Labroille: Fabrication and characterization of a mode-selective 45-mode spatial multiplexer based on multi-plane light conversion. In: Opt. Fiber Commun. Conf. (2018), https://doi.org/10.1364/OFC.2018.Th4B.3

    Chapter  Google Scholar 

  • N.K. Fontaine, R. Ryf, H. Chen, D.T. Neilson, K. Kim, J. Carpenter: Scalable mode sorter supporting 210 Hermite-Gaussian modes. In: Opt. Fiber Commun. Conf. (2018), https://doi.org/10.1364/OFC.2018.Th4B.4

    Chapter  Google Scholar 

  • E. Ip, M.-J. Li, K. Bennett, Y.-K. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, Y. Yano: 146\(\lambda\) × 6 × 19-Gbaud wavelength-and mode-division multiplexed transmission over 10 × 50-km spans of few-mode fiber with a gain-equalized few-mode EDFA, J. Lightwave Technol. 32(4), 790–797 (2014)

    Article  Google Scholar 

  • M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N.K. Fontaine, M.A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, Y. Quiquempois: A six-mode erbium-doped fiber amplifier. In: Eur. Conf. Exhib. Opt. Commun. (2012), https://doi.org/10.1364/ECEOC.2012.Th.3.A.6

    Chapter  Google Scholar 

  • N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K.M. Chung, A.P.T. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li, T. Wang: Mode-division multiplexed transmission with inline few-mode fiber amplifier, Opt. Express 20(3), 2668–2680 (2012)

    Article  Google Scholar 

  • R. Nasiri Mahalati, D. Askarov, J.M. Kahn: Adaptive modal gain equalization techniques in multi-mode erbium-doped fiber amplifiers, J. Lightwave Technol. 32(11), 2133–2143 (2014)

    Article  Google Scholar 

  • K.S. Abedin, J.M. Fini, T.F. Thierry, B. Zhu, M.F. Yan, L. Bansal, F.V. Dimarcello, E.M. Monberg, D.J. DiGiovanni: Seven-core erbium-doped double-clad fiber amplifier pumped simultaneously by side-coupled multimode fiber, Opt. Lett. 39(4), 993–996 (2014)

    Article  Google Scholar 

  • N. Fontaine, B. Guan, R. Ryf, H. Chen, A. Koonen, S. Ben Yoo, K. Abedin, J. Fini, T. Taunay, D. Neilson: Programmable gain equalizer for multi-core fiber amplifiers. In: Opt. Fiber Commun. Conf. (2014), https://doi.org/10.1109/OFC.2014.6887232

    Chapter  Google Scholar 

  • H. Takeshita, K. Matsumotc, E.L.T. de Gabory: Transmission of 200Gbps PM-16QAM signal through 7-core MCF and MC-EDFA using novel turbo cladding pumping scheme for improved efficiency of the optical amplification. In: Eur. Conf. Opt. Commun. (2018), https://doi.org/10.1109/ECOC.2018.8535546

    Chapter  Google Scholar 

  • Y. Jung, E.L. Lim, Q. Kang, T.C. May-Smith, N.H.L. Wong, R. Standish, F. Poletti, J.K. Sahu, S.U. Alam, D.J. Richardson: Cladding pumped few-mode EDFA for mode division multiplexed transmission, Opt. Express 22(23), 29008–29013 (2014)

    Article  Google Scholar 

  • N.K. Fontaine, B. Huang, Z.S. Eznaveh, H. Chen, C. Jin, B. Ercan, A. Velázquez-Benítez, S.H. Chang, R. Ryf, A. Schülzgen, J.C. Alvarado, P. Sillard, C. Gonnet, E. Antonio-Lopez, R. Amezcua-Correa: Multi-mode optical fiber amplifier supporting over 10 spatial modes. In: Opt. Fiber Commun. Conf. (2016), https://doi.org/10.1364/OFC.2016.Th5A.4

    Chapter  Google Scholar 

  • S. Randel, P.J. Winzer, M. Montoliu, R. Ryf: Complexity analysis of adaptive frequency-domain equalization for MIMO-SDM transmission. In: 39th Eur. Conf. Opt. Commun. (2013), https://doi.org/10.1049/cp.2013.1540

    Chapter  Google Scholar 

  • R. Ryf, S. Chandrasekhar, S. Randel, D.T. Neilson, N.K. Fontaine, M. Feuer: Physical layer transmission and switching solutions in support of spectrally and spatially flexible optical networks, IEEE Commun. Mag. 53(2), 52–59 (2015)

    Article  Google Scholar 

  • P.J. Winzer, G.J. Foschini: MIMO capacities and outage probabilities in spatially multiplexed optical transport systems, Opt. Express 19(17), 16680–16696 (2011)

    Article  Google Scholar 

  • H. Kogelnik: Theory of optical waveguides. In: Guided-Wave Optoelectronics, 2nd edn., ed. by T. Tamir (Springer, Berlin, Heidelberg 1988) pp. 7–88

    Chapter  Google Scholar 

  • D. Marcuse: Theory of Dielectric Optical Waveguides (Academic Press, San Diego 1991)

    Google Scholar 

  • R.M. Nejad, L. Wang, J. Lin, S. Larochelle, L.A. Rusch: Parasitic effect of TE and TM modes in OAM-MDM transmission systems. In: Conf. Lasers Electro-Optics (2017), https://doi.org/10.1364/CLEO_SI.2017.SW4I.2

    Chapter  Google Scholar 

  • P. Gregg, P. Kristensen, A. Rubano, S. Golowich, L. Marrucci, S. Ramachandran: Spin-orbit coupled, non-integer OAM fibers: Unlocking a new Eigenbasis for transmitting 24 uncoupled modes. In: Conf. Lasers Electro-Optics (2016), https://doi.org/10.1364/CLEO_AT.2016.JTh4C.7

    Chapter  Google Scholar 

  • D.L.P. Vitullo, C.C. Leary, P. Gregg, R.A. Smith, D.V. Reddy, S. Ramachandran, M.G. Raymer: Observation of interaction of spin and intrinsic orbital angular momentum of light, Phys. Rev. Lett. 118, 083601 (2017)

    Article  Google Scholar 

  • D. Gloge: Weakly guiding fibers, Appl. Opt. 10(10), 2252–2258 (1971)

    Article  Google Scholar 

  • W.P. Huang, L. Li: Coupled-mode theory for optical waveguides: An overview, J. Opt. Soc. Am. A 11(3), 963–983 (1994)

    Article  Google Scholar 

  • A.W. Snyder: Coupled-mode theory for optical fibers, J. Opt. Soc. Am. 62(11), 1267–1277 (1972)

    Article  Google Scholar 

  • J.M. Fini, B. Zhu, T.F. Taunay, M.F. Yan: Statistics of crosstalk in bent multicore fibers, Opt. Express 18(14), 15122–15129 (2010)

    Article  Google Scholar 

  • T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, E. Sasaoka: Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber, Opt. Express 19(17), 16576–16592 (2011)

    Article  Google Scholar 

  • C. Antonelli, M. Shtaif, A. Mecozzi: Modeling of nonlinear propagation in space-division multiplexed fiber-optic transmission, J. Lightwave Technol. 34(1), 36–54 (2016)

    Article  Google Scholar 

  • F. Poletti, P. Horak: Description of ultrashort pulse propagation in multimode optical fibers, J. Opt. Soc. Am. B 25(10), 1645–1654 (2008)

    Article  Google Scholar 

  • M. Kolesik, J.V. Moloney: Nonlinear optical pulse propagation simulation: From Maxwell's to unidirectional equations, Phys. Rev. E 70, 036604 (2004)

    Article  Google Scholar 

  • A.A. Juarez, E. Krune, S. Warm, C.A. Bunge, K. Petermann: Modeling of mode coupling in multimode fibers with respect to bandwidth and loss, J. Lightwave Technol. 32(8), 1549–1558 (2014)

    Article  Google Scholar 

  • C. Antonelli, A. Mecozzi, M. Shtaif, P.J. Winzer: Nonlinear propagation equations in fibers with multiple modes—transitions between representation bases, APL Photonics 4, 022806 (2019)

    Article  Google Scholar 

  • H. Kogelnik, P.J. Winzer: Modal birefringence in weakly guiding fibers, J. Lightwave Technol. 30(14), 2240–2245 (2012)

    Article  Google Scholar 

  • R.C. Jones: A new calculus for the treatment of optical systems. Description and discussion of the calculus, J. Opt. Soc. Am. 31(7), 488–493 (1941)

    Article  MATH  Google Scholar 

  • J.P. Gordon, H. Kogelnik: PMD fundamentals: Polarization mode dispersion in optical fibers, Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000)

    Article  Google Scholar 

  • N. Frigo: A generalized geometrical representation of coupled mode theory, IEEE J. Quantum Electron. 22(11), 2131–2140 (1986)

    Article  Google Scholar 

  • A. Galtarossa, L. Palmieri, M. Schiano, T. Tambosso: Measurement of birefringence correlation length in long, single-mode fibers, Opt. Lett. 26(13), 962–964 (2001)

    Article  Google Scholar 

  • S. Fan, J.M. Kahn: Principal modes in multimode waveguides, Opt. Lett. 30(2), 135–137 (2005)

    Article  Google Scholar 

  • K.-P. Ho, J.M. Kahn: Statistics of group delays in multimode fiber with strong mode coupling, J. Lightwave Technol. 29(21), 3119–3128 (2011)

    Article  Google Scholar 

  • C. Antonelli, A. Mecozzi, M. Shtaif, P.J. Winzer: Stokes-space analysis of modal dispersion in fibers with multiple mode transmission, Opt. Express 20(11), 11718–11733 (2012)

    Article  Google Scholar 

  • I. Roudas, J. Kwapisz: Stokes space representation of modal dispersion, IEEE Photonics J. 9(5), 1–15 (2017)

    Article  Google Scholar 

  • C. Antonelli, A. Mecozzi, M. Shtaif: The delay spread in fibers for SDM transmission: Dependence on fiber parameters and perturbations, Opt. Express 23(3), 2196–2202 (2015)

    Article  Google Scholar 

  • A. Mecozzi, C. Antonelli, M. Shtaif: Intensity impulse response of SDM links, Opt. Express 23(5), 5738–5743 (2015)

    Article  Google Scholar 

  • L. Palmieri, A. Galtarossa: Coupling effects among degenerate modes in multimode optical fibers, IEEE Photonics J. 6(6), 1–8 (2014)

    Article  Google Scholar 

  • F. Curti, B. Daino, G.D. Marchis, F. Matera: Statistical treatment of the evolution of the principal states of polarization in single-mode fibers, J. Lightwave Technol. 8(8), 1162–1166 (1990)

    Article  Google Scholar 

  • A. Galtarossa, L. Palmieri, A. Pizzinat, M. Schiano, T. Tambosso: Measurement of local beat length and differential group delay in installed single-mode fibers, J. Lightwave Technol. 18(10), 1389 (2000)

    Article  Google Scholar 

  • L. Palmieri, A. Galtarossa: Intramodal dispersion properties of step-index few-mode spun fibers, J. Lightwave Technol. 34(2), 303–313 (2016)

    Article  Google Scholar 

  • M. Karlsson, J. Brentel: Autocorrelation function of the polarization-mode dispersion vector, Opt. Lett. 24(14), 939–941 (1999)

    Article  Google Scholar 

  • M. Shtaif, A. Mecozzi, J.A. Nagel: Mean-square magnitude of all orders of polarization mode dispersion and the relation with the bandwidth of the principal states, IEEE Photonics Technol. Lett. 12(1), 53–55 (2000)

    Article  Google Scholar 

  • M. Shtaif, A. Mecozzi: Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion, Opt. Lett. 25(10), 707–709 (2000)

    Article  Google Scholar 

  • M. Shtaif: Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss, Opt. Express 16(18), 13918–13932 (2008)

    Article  Google Scholar 

  • S.J. Savory: Digital filters for coherent optical receivers, Opt. Express 16(2), 804–817 (2008)

    Article  Google Scholar 

  • M.S. Faruk, K. Kikuchi: Adaptive frequency-domain equalization in digital coherent optical receivers, Opt. Express 19(13), 12789–12798 (2011)

    Article  Google Scholar 

  • S. Arik, D. Askarov, J.M. Kahn: Effect of mode coupling on signal processing complexity in mode-division multiplexing, J. Lightwave Technol. 31(3), 423–431 (2013)

    Article  Google Scholar 

  • S.O. Arik, K.-P. Ho, J.M. Kahn: Group delay management and multiinput multioutput signal processing in mode-division multiplexing systems, J. Lightwave Technol. 34(11), 2867–2880 (2016)

    Article  Google Scholar 

  • S.O. Arik, K.-P. Ho, J.M. Kahn: Delay spread reduction in mode-division multiplexing: Mode coupling versus delay compensation, J. Lightwave Technol. 33(21), 4504–4512 (2015)

    Article  Google Scholar 

  • C. Antonelli, A. Mecozzi, M. Shtaif, P.J. Winzer: Random coupling between groups of degenerate fiber modes in mode multiplexed transmission, Opt. Express 21(8), 9484–9490 (2013)

    Article  Google Scholar 

  • F.M. Ferreira, D. Fonseca, H.J.A. da Silva: Design of few-mode fibers with M-modes and low differential mode delay, J. Lightwave Technol. 32(3), 353–360 (2014)

    Article  Google Scholar 

  • F.M. Ferreira, C.S. Costa, S. Sygletos, A.D. Ellis: Semi-analytical modelling of linear mode coupling in few-mode fibers, J. Lightwave Technol. 35(18), 4011–4022 (2017)

    Article  Google Scholar 

  • R. Ryf, R. Essiambre, A. Gnauck, S. Randel, M.A. Mestre, C. Schmidt, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, T. Sasaki: Space-division multiplexed transmission over 4200 km 3-core microstructured fiber. In: Opt. Fiber Commun. Conf. (2012), https://doi.org/10.1364/OFC.2012.PDP5C.2

    Chapter  Google Scholar 

  • C. Antonelli, A. Mecozzi, M. Shtaif, P.J. Fontaine, H. Chen, R. Ryf: Stokes-space analysis of modal dispersion of sdm fibers with mode-dependent loss: theory and experiments, J. Lightwave Technol. 38(7), 1668–1677 (2020)

    Article  Google Scholar 

  • R. Ryf, J.C. Alvarado, B. Huang, J. Antonio-Lopez, S.H. Chang, N.K. Fontaine, H. Chen, R.J. Essiambre, E. Burrows, R. Amezcua-Correa, T. Hayashi, Y. Tamura, T. Hasegawa, T. Taru: Long-distance transmission over coupled-core multicore fiber. In: 42nd Eur. Conf. Opt. Commun. (2016)

    Google Scholar 

  • K.-P. Ho, J.M. Kahn: Mode-dependent loss and gain: statistics and effect on mode-division multiplexing, Opt. Express 19(17), 16612–16635 (2011)

    Article  Google Scholar 

  • K.P. Ho, J.M. Kahn: Frequency diversity in mode-division multiplexing systems, J. Lightwave Technol. 29(24), 3719–3726 (2011)

    Article  Google Scholar 

  • A. Andrusier, M. Shtaif, C. Antonelli, A. Mecozzi: Assessing the effects of mode-dependent loss in space-division multiplexed systems, J. Lightwave Technol. 32(7), 1317–1322 (2014)

    Article  Google Scholar 

  • C. Antonelli, A. Mecozzi, M. Shtaif, P.J. Winzer: Modeling and performance metrics of MIMO-SDM systems with different amplification schemes in the presence of mode-dependent loss, Opt. Express 23(3), 2203–2219 (2015)

    Article  Google Scholar 

  • R. Ryf, S. Randel, A.H. Gnauck, C. Bolle, R.-J. Essiambre, P.J. Winzer, D.W. Peckham, A. McCurdy, R. Lingle: Space-division multiplexing over 10 km of three-mode fiber using coherent 6 x 6 MIMO processing. In: Opt. Fiber Commun. Conf. (2011), https://doi.org/10.1364/OFC.2011.PDPB10

    Chapter  Google Scholar 

  • E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K.M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li: 88 x 3 x 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier. In: 37th Eur. Conf. Exhib. Opt. Commun. (2011)

    Google Scholar 

  • R. Ryf, N.K. Fontaine, M.A. Mestre, S. Randel, X. Palou, C. Bolle, A.H. Gnauck, S. Chandrasekhar, X. Liu, B. Guan, R.-J. Essiambre, P.J. Winzer, S. Leon-Saval, J. Bland-Hawthorn, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grüner-Nielsen, R.V. Jensen, R. Lingle: 12 $$\times$$ 12 MIMO transmission over 130-km few-mode fiber. In: Front. Opt. (2012), https://doi.org/10.1364/FIO.2012.FW6C.4

    Chapter  Google Scholar 

  • R. Ryf, H. Chen, N.K. Fontaine, A.M. Velazquez-Benitez, J. Antonio-Lopez, C. Jin, B. Huang, M. Bigot-Astruc, D. Molin, F. Achten, P. Sillard, R. Amezcua-Correa: 10-mode mode-multiplexed transmission over 125-km single-span multimode fiber. In: Eur. Conf. Opt. Commun. (2015), https://doi.org/10.1109/ECOC.2015.7341687

    Chapter  Google Scholar 

  • N.K. Fontaine, R. Ryf, H. Chen, A.V. Benitez, B. Guan, R. Scott, B. Ercan, S.J.B. Yoo, L.E. Grüner-Nielsen, Y. Sun, R. Lingle, E. Antonio-Lopez, R. Amezcua-Correa: 30×30 MIMO transmission over 15 spatial modes. In: Opt. Fiber Commun. Conf. (2015), https://doi.org/10.1364/OFC.2015.Th5C.1

    Chapter  Google Scholar 

  • H. Chen, R. Ryf, N.K. Fontaine, A.M. Velázquez-Benítez, J. Antonio-López, C. Jin, B. Huang, M. Bigot-Astruc, D. Molin, F. Achten, P. Sillard, R. Amezcua-Correa: High spectral efficiency mode-multiplexed transmission over 87-km 10-mode fiber. In: Opt. Fiber Commun. Conf. (2016)

    Google Scholar 

  • Y. Wakayama, D. Soma, S. Beppu, S. Sumita, K. Igarashi, T. Tsuritani: 266.1-Tbit/s repeatered transmission over 90.4-km 6-mode fiber using dual C+L-band 6-mode EDFA. In: Opt. Fiber Commun. Conf. (2018), https://doi.org/10.1364/OFC.2018.W4C.1

    Chapter  Google Scholar 

  • J. van Weerdenburg, R. Ryf, J.C. Alvarado-Zacarias, R.A. Alvarez-Aguirre, N.K. Fontaine, H. Chen, R. Amezcua-Correa, Y. Sun, L. Grüner-Nielsen, R.V. Jensen, R. Lingle, T. Koonen, C. Okonkwo: 138-Tb/s mode- and wavelength-multiplexed transmission over six-mode graded-index fiber, J. Lightwave Technol. 36(6), 1369–1374 (2018)

    Article  Google Scholar 

  • R. Ryf, S. Randel, N.K. Fontaine, M. Montoliu, E. Burrows, S. Chandrasekhar, A.H. Gnauck, C. Xie, R.-J. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Gruner-Nielsen, R.V. Jensen, R. Lingle: 32-bit/s/Hz spectral efficiency WDM transmission over 177-km few-mode fiber. In: Opt. Fiber Commun. Conf. (2013), https://doi.org/10.1364/OFC.2013.PDP5A.1

    Chapter  Google Scholar 

  • R. Ryf, N.K. Fontaine, B. Guan, R.-J. Essiambre, S. Randel, A.H. Gnauck, S. Chandrasekhar, A. Adamiecki, G. Raybon, B. Ercan, R.P. Scott, S.J.B. Yoo, T. Hayashi, T. Nagashima, T. Sasaki: 1705-km transmission over coupled-core fibre supporting 6 spatial modes. In: Eur. Conf. Opt. Commun. (2014), https://doi.org/10.1109/ECOC.2014.6964273

    Chapter  Google Scholar 

  • R. Ryf, S. Randel, N. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. Gnauck, C. Xie, R.-J. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Gruner-Nielsen, R. Jensen, R. Lingle: 708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes. In: 39th Eur. Conf. Opt. Commun. (2013), https://doi.org/10.1049/cp.2013.1420

    Chapter  Google Scholar 

  • Y. Chen, A. Lobato, Y. Jung, H. Chen, V. Sleiffer, M. Kuschnerov, N. Fontaine, R. Ryf, D. Richardson, B. Lankl, N. Hanik: 41.6 Tbit/s C-band SDM OFDM transmission through 12 spatial and polarization modes over 74.17 km few mode fiber, J. Lightwave Technol. 33(7), 1440–1444 (2015)

    Article  Google Scholar 

  • R. Ryf, N.K. Fontaine, S.H. Chang, J.C. Alvarado, B. Huang, J. Antonio-Lopez, H. Chen, R.J. Essiambre, E. Burrows, R.W. Tkach, R. Amezcua-Correa, T. Hayashi, Y. Tamura, T. Hasegawa, T. Taru: Long-haul transmission over multi-core fibers with coupled cores. In: Eur. Conf. Opt. Commun. (2017), https://doi.org/10.1109/ECOC.2017.8345874

    Chapter  Google Scholar 

  • G. Rademacher, R.S. Luis, B.J. Puttnam, R. Ryf, H. Furukawa, R. Maruyama, K. Aikawa, A. Maruta, Y. Awaji, N. Wada: 93.34 Tbit/s/mode (280 Tbit/s) transmission in a 3-mode graded-index few-mode fiber. In: Opt. Fiber Commun. Conf. (2018), https://doi.org/10.1364/OFC.2018.W4C.3

    Chapter  Google Scholar 

  • G. Rademacher, R. Ryf, N.K. Fontaine, H. Chen, R.J. Essiambre, B.J. Puttnam, R.S. Luís, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, R. Lingle: Long-haul transmission over few-mode fibers with space-division multiplexing, J. Lightwave Technol. 36(6), 1382–1388 (2018)

    Article  Google Scholar 

  • R. Ryf, N.K. Fontaine, M. Montoliu, S. Randel, B. Ercan, H. Chen, S. Chandrasekhar, A. Gnauck, S.G. Leon-Saval, J. Bland-Hawthorn, J.R.S. Gil, Y. Sun, R. Lingle: Photonic-lantern-based mode multiplexers for few-mode-fiber transmission. In: Opt. Fiber Commun. Conf. (2014), https://doi.org/10.1364/OFC.2014.W4J.2

    Chapter  Google Scholar 

  • A. Sierra, S. Randel, P.J. Winzer, R. Ryf, A.H. Gnauck, R.J. Essiambre: On the use of delay-decorrelated I/Q test sequences for QPSK and QAM signals, IEEE Photonics Technol. Lett. 24(12), 1000–1002 (2012)

    Article  Google Scholar 

  • R.G. Van Uden, C.M. Okonkwo, H. Chen, H. de Waardt, A.M. Koonen: Time domain multiplexed spatial division multiplexing receiver, Opt. Express 22(10), 12668–12677 (2014)

    Article  Google Scholar 

  • D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, M. Yoshida, K. Kasai, M. Nakazawa, H. Takahashi, K. Igarashi, I. Morita, M. Suzuki: 10.16-Peta-B/s dense SDM/WDM transmission over 6-mode 19-core fiber across the C+L band, J. Lightwave Technol. 36(6), 1362–1368 (2018)

    Article  Google Scholar 

  • D. Soma, K. Igarashi, Y. Wakayama, K. Takeshima, Y. Kawaguchi, N. Yoshikane, T. Tsuritani, I. Morita, M. Suzuki: 2.05 Peta-bit/s super-Nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band. In: Eur. Conf. Opt. Commun. (2015), https://doi.org/10.1109/ECOC.2015.7341686

    Chapter  Google Scholar 

  • T. Mizuno, T. Kobayashi, H. Takara, A. Sano, H. Kawakami, T. Nakagawa, Y. Miyamoto, Y. Abe, T. Goh, M. Oguma, T. Sakamoto, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, T. Morioka: 12-core x 3-mode dense space division multiplexed transmission over 40 km employing multi-carrier signals with parallel MIMO equalization. In: Opt. Fiber Commun. Conf. (2014), https://doi.org/10.1364/OFC.2014.Th5B.2

    Chapter  Google Scholar 

  • B.J. Puttnam, R.S. Luís, W. Klaus, J. Sakaguchi, J.M.D. Mendinueta, Y. Awaji, N. Wada, Y. Tamura, T. Hayashi, M. Hirano, J. Marciante: 2.15 Pb/s transmission using a 22 core homogeneous single-mode multi-core fiber and wideband optical comb. In: Eur. Conf. Opt. Commun. (2015), https://doi.org/10.1109/ECOC.2015.7341685

    Chapter  Google Scholar 

  • J. Sakaguchi, B.J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa: 305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber, J. Lightwave Technol. 31(4), 554–562 (2013)

    Article  Google Scholar 

  • D. Qian, E. Ip, M.-F. Huang, M.-J. Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, T. Wang: 1.05Pb/s transmission with 109b/s/Hz spectral efficiency using hybrid single- and few-mode cores. In: Front. Opt. (2012), https://doi.org/10.1364/FIO.2012.FW6C.3

    Chapter  Google Scholar 

  • H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, T. Morioka: 1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency. In: Eur. Conf. Exhib. Opt. Commun. (2012), https://doi.org/10.1364/ECEOC.2012.Th.3.C.1

    Chapter  Google Scholar 

  • T. Kobayashi, H. Takara, A. Sano, T. Mizuno, H. Kawakami, Y. Miyamoto, K. Hiraga, Y. Abe, H. Ono, M. Wada, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Yamada, H. Masuda, T. Morioka: 2 $$\times$$ 344 Tb/s propagation-direction interleaved transmission over 1500-km MCF enhanced by multicarrier full electric-field digital back-propagation. In: 39th Eur. Conf. Exhib. Opt. Commun. (2013), https://doi.org/10.1049/cp.2013.1691

    Chapter  Google Scholar 

  • A. Turukhin, H.G. Batshon, M. Mazurczyk, Y. Sun, C.R. Davidson, J.X. Chai, O.V. Sinkin, W. Patterson, G. Wolter, M.A. Bolshtyansky, D.G. Foursa, A. Pilipetskii: Demonstration of 0.52 Pb/s potential transmission capacity over 8,830 km using multicore fiber. In: 42nd Eur. Conf. Opt. Commun. (2016)

    Google Scholar 

  • K. Igarashi, T. Tsuritani, I. Morita, Y. Tsuchida, K. Maeda, M. Tadakuma, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, M. Suzuki: Super-Nyquist-WDM transmission over 7,326-km seven-core fiber with capacity-distance product of 1.03 Exabit/s/km, Opt. Express 22(2), 1220–1228 (2014)

    Article  Google Scholar 

  • S. Chandrasekhar, A.H. Gnauck, X. Liu, P.J. Winzer, Y. Pan, E.C. Burrows, T. Taunay, B. Zhu, M. Fishteyn, M.F. Yan, J.M. Fini, E. Monberg, F. Dimarcello: WDM/SDM transmission of 10 x 128-Gb/s PDM-QPSK over 2688-km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 40,320 km.b/s/Hz, Opt. Express 20(2), 706–711 (2012)

    Article  Google Scholar 

  • H. Takahashi, T. Tsuritani, E.L.T. de Gabory, T. Ito, W.R. Peng, K. Igarashi, K. Takeshima, Y. Kawaguchi, I. Morita, Y. Tsuchida, Y. Mimura, K. Maeda, T. Saito, K. Watanabe, K. Imamura, R. Sugizaki, M. Suzuki: First demonstration of MC-EDFA-repeatered SDM transmission of 40 x 128-Gbit/s PDM-QPSK signals per core over 6,160-km 7-core MCF, Opt. Express 21(1), 789–795 (2013)

    Article  Google Scholar 

  • J. Sakaguchi, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi, M. Watanabe: Space division multiplexed transmission of 109-Tb/s data signals using homogeneous seven-core fiber, J. Lightwave Technol. 30(4), 658–665 (2012)

    Article  Google Scholar 

  • P.J. Winzer: Energy-efficient optical transport capacity scaling through spatial multiplexing, IEEE Photonics Technol. Lett. 23(13), 851–853 (2011)

    Article  Google Scholar 

  • S. Mumtaz, R.J. Essiambre, G.P. Agrawal: Nonlinear propagation in multimode and multicore fibers: Generalization of the Manakov equations, J. Lightwave Technol. 31(3), 398–406 (2013)

    Article  Google Scholar 

  • G. Agrawal: Pulse propagation in fibers. In: Nonlinear Fiber Optics, 5th edn., ed. by G. Agrawal (Academic Press, Boston 2013) pp. 27–56

    Chapter  Google Scholar 

  • C. Antonelli, A. Mecozzi, M. Shtaif: Scaling of inter-channel nonlinear interference noise and capacity with the number of strongly coupled modes in SDM systems. In: Opt. Fiber Commun. Conf. (2016), https://doi.org/10.1364/OFC.2016.W4I.2

    Chapter  Google Scholar 

  • A. Mecozzi, C. Antonelli, M. Shtaif: Nonlinear propagation in multi-mode fibers in the strong coupling regime, Opt. Express 20(11), 11673–11678 (2012)

    Article  Google Scholar 

  • S.V. Manakov: On the theory of two-dimensional stationary self-focusing of electromagnetic waves, Sov. J. Exp. Theor. Phys. 38, 505–516 (1974)

    Google Scholar 

  • D. Marcuse, C.R. Manyuk, P.K.A. Wai: Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence, J. Lightwave Technol. 15(9), 1735–1746 (1997)

    Article  Google Scholar 

  • C. Antonelli, O. Golani, M. Shtaif, A. Mecozzi: Nonlinear interference noise in space-division multiplexed transmission through optical fibers, Opt. Express 25(12), 13055–13078 (2017)

    Article  Google Scholar 

  • S. Mumtaz, R.J. Essiambre, G.P. Agrawal: Reduction of nonlinear penalties due to linear coupling in multicore optical fibers, IEEE Photonics Technol. Lett. 24(18), 1574–1576 (2012)

    Article  Google Scholar 

  • M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, T. Sasaki: Record low loss, record high FOM optical fiber with manufacturable process. In: Opt. Fiber Commun. Conf. (2013), https://doi.org/10.1364/OFC.2013.PDP5A.7

    Chapter  Google Scholar 

  • T. Hayashi, Y. Tamura, T. Hasegawa, T. Taru: Record-low spatial mode dispersion and ultra-low loss coupled multi-core fiber for ultra-long-haul transmission, J. Lightwave Technol. 35(3), 450–457 (2017)

    Article  Google Scholar 

  • R. Essiambre, M. Mestre, R. Ryf, A. Gnauck, R. Tkach, A. Chraplyvy, Y. Sun, X. Jiang, R. Lingle: Experimental observation of inter-modal cross-phase modulation in few-mode fibers, IEEE Photonics Technol. Lett. 25(6), 535–538 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • A. Mecozzi, C. Antonelli, M. Shtaif: Coupled Manakov equations in multimode fibers with strongly coupled groups of modes, Opt. Express 20(21), 23436–23441 (2012)

    Article  Google Scholar 

  • A. Mecozzi, C. Antonelli, M. Shtaif: Nonlinear equations of propagation in multi-mode fibers with random mode coupling. In: 39th Eur. Conf. Opt. Commun. (2013), https://doi.org/10.1049/cp.2013.1453

    Chapter  Google Scholar 

  • F.M. Ferreira, C.S. Costa, S. Sygletos, A.D. Ellis: Nonlinear performance of few-mode fiber links with intermediate coupling, J. Lightwave Technol. 37(3), 989–999 (2019)

    Article  Google Scholar 

  • S. Buch, S. Mumtaz, R.-J. Essiambre, A.M. Tulino, A.D. Agrawal: Averaged nonlinear equations for multimode fibers valid in all regimes of random linear coupling, Opt. Fiber Technol. 48, 123–127 (2019)

    Article  Google Scholar 

  • C. Nuzman, J. Leuthold, R. Ryf, S. Chandrasekhar, C.R. Giles, D.T. Neilson: Design and implementation of wavelength-flexible network nodes, J. Lightwave Technol. 21(3), 648 (2003)

    Article  Google Scholar 

  • D.M. Marom, P.D. Colbourne, A. D’errico, N.K. Fontaine, Y. Ikuma, R. Proietti, L. Zong, J.M. Rivas-Moscoso, I. Tomkos: Survey of photonic switching architectures and technologies in support of spatially and spectrally flexible optical networking, J. Opt. Commun. Netw. 9(1), 1–26 (2017)

    Article  Google Scholar 

  • L. Nelson, M. Feuer, K. Abedin, X. Zhou, T. Taunay, J. Fini, B. Zhu, R. Isaac, R. Harel, G. Cohen, D. Marom: Spatial superchannel routing in a two-span ROADM system for space division multiplexing, J. Lightwave Technol. 32(4), 783–789 (2014)

    Article  Google Scholar 

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Ryf, R., Antonelli, C. (2020). Space-Division Multiplexing. In: Mukherjee, B., Tomkos, I., Tornatore, M., Winzer, P., Zhao, Y. (eds) Springer Handbook of Optical Networks. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-030-16250-4_10

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