Abstract

We study the effect of nonlinear coupling in a WDM configuration over a two-mode fiber. A statistical analysis is presented that takes into account the effect of the random phase-sensitive amplification or depletion. Our results show high nonlinear coupling between the modes. We have quantified the channel power fluctuations, due to the wave phase random variations, at the output of the fiber. We also investigate the effect of random linear mode coupling on the nonlinear mode coupling.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. J. Richardson, “Filling the light pipe,” Science 30, 327–328 (2010).
    [Crossref]
  2. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
    [Crossref]
  3. C. Koebele, M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode division multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett. 23, 1316–1318 (2011).
    [Crossref]
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    [Crossref] [PubMed]
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  6. S. Mumtaz, R.-J. Essiambre, and G. P. Agrawal, “Nonlinear propagation in multimode and multicore fibers: generalization of the Manakov equations,” J. Lightwave Technol. 31, 398–406 (2013).
    [Crossref]
  7. C. Antonelli, M. Shtaif, and A. Mecozzi, “Modeling of nonlinear propagation in space-division multiplexed fiber-optic transmission,” J. Lightwave Technol. 34, 36–54 (2016).
    [Crossref]
  8. R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three wave mixing in silica fiber optical waveguides,” App. Phy. Lett. 24, 308–310 (1974).
    [Crossref]
  9. F. Poletti and P. Horak, “Description of ultrashort pulse propagation in multimode optical fibers,” J. Opt. Soc. Am. B 25, 1645–1654 (2008).
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    [Crossref] [PubMed]
  11. A. Ben Salem, A. Trichili, R. Cherif, and M. Zghal, “Rigorous study of supercontinuum generation in few mode fibers,” Appl. Opt. 16, 4317–4322 (2016).
    [Crossref]
  12. R. J. Essiambre, R. Ryf, M. A. Mestre, 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 Photon. Technol. Lett. 25, 539–541 (2013).
    [Crossref]
  13. 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, 32039–32059 (2014).
    [Crossref]
  14. M. Esmaeelpour, R. J. Essiambre, N. Fontaine, R. Ryf, J. Toulouse, Y. Sun, and R. Lingle, “Power fluctuations of inter-modal four-wave mixing in few-mode fibers,” J. Lightwave Technol. 35, 2429–2435 (2017).
    [Crossref]
  15. M. Guasoni, F. Parmigiani, P. Horak, J. Fatome, and D. J. Richardson, “Intermodal four-wave mixing and parametric amplification in kilometer-long multimode fibers,” J. Lightwave Technol. 35, 5296–5305 (2017).
    [Crossref]
  16. W. Pan, Q. Jin, X. Li, and S. Gao, “All-optical wavelength conversion for mode-division multiplexing signals using four-wave mixing in a dual-mode fiber,” J. Opt. Soc. Am. B 32, 2417–2424 (2015).
    [Crossref]
  17. A. Trichili, M. Zghal, L. Palmieri, and M. Santagiustina, “Phase-sensitive mode conversion and equalization in a few mode fiber through parametric interactions,” IEEE Photon. J. 9, 1–10 (2017).
    [Crossref]
  18. I. Neokosmidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, “New techniques for the suppression of the four-wave mixing-induced distortion in nonzero dispersion fiber WDM systems,” J. Lightwave Technol. 23, 1137–1144 (2005).
    [Crossref]
  19. P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightwave Technol. 30, 3857–3879 (2012).
    [Crossref]
  20. V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Express 21, 3308–3317 (2013).
    [Crossref] [PubMed]
  21. R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Express 21, 25685–25699 (2013).
    [Crossref] [PubMed]
  22. O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the bit-error-rate performance of nonlinear fiber-optic systems,” J. Lightwave Technol. 34, 3482–3489 (2016).
    [Crossref]
  23. C. Antonelli, O. Golani, M. Shtaif, and A. Mecozzi, “Nonlinear interference noise in space-division multiplexed transmission through optical fibers,” Opt. Express 25, 13055–13078 (2017).
    [Crossref] [PubMed]
  24. M. Eiselt, “Limits on WDM systems due to four-wave mixing: a statistical approach,” J. Lightwave Technol. 17, 2261–2267 (1999).
    [Crossref]
  25. S. Betti, M. Giaconi, and M. Nardini, “Effect of four-wave mixing on WDM optical systems: a statistical analysis,” IEEE Photon. Technol. Lett. 15, 1079–1081 (2003).
    [Crossref]
  26. 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, 506–520 (2002).
    [Crossref]
  27. Q. Lin and G. P. Agrawal, “Vector theory of four-wave mixing: polarization effects in fiber-optic parametric amplifiers,” J. Opt. Soc. Am. B 21, 1216–1224 (2004).
    [Crossref]
  28. L. Gruner-Nielsen, Y. Sun, J. W. Nicholson, D. Jakobsen, K. G. Jespersen, R. Lingle, and B. Palsdottir, “Few mode transmission fiber with low DGD, low mode coupling, and low loss,” J. Lightwave Technol. 30, 3693–3698 (2012).
    [Crossref]
  29. M. Zelen and N. C. Severo, “Probablity function,” in Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, eds., Vol. 55 of Applied Mathematics Series (National Bureau of Standards, 1964), ch. 26, pp. 926–976.
  30. L. Palmieri, “Coupling mechanism in multimode fibers,” Proc. SPIE 9009, 90090G (2013).
    [Crossref]
  31. L. Palmieri and A. Galtarossa, “Coupling effects among degenerate modes in multimode optical fibers,” IEEE Photon. J. 6, 1–8 (2014).
    [Crossref]
  32. P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
    [Crossref]

2017 (4)

2016 (3)

2015 (1)

2014 (2)

2013 (6)

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Extension and validation of the GN model for non-linear interference to uncompensated links using Raman amplification,” Opt. Express 21, 3308–3317 (2013).
[Crossref] [PubMed]

R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Express 21, 25685–25699 (2013).
[Crossref] [PubMed]

L. Palmieri, “Coupling mechanism in multimode fibers,” Proc. SPIE 9009, 90090G (2013).
[Crossref]

R. J. Essiambre, R. Ryf, M. A. Mestre, 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 Photon. Technol. Lett. 25, 539–541 (2013).
[Crossref]

S. Mumtaz, R.-J. Essiambre, and G. P. Agrawal, “Nonlinear propagation in multimode and multicore fibers: generalization of the Manakov equations,” J. Lightwave Technol. 31, 398–406 (2013).
[Crossref]

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

2012 (4)

2011 (1)

C. Koebele, M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode division multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett. 23, 1316–1318 (2011).
[Crossref]

2010 (1)

D. J. Richardson, “Filling the light pipe,” Science 30, 327–328 (2010).
[Crossref]

2009 (1)

2008 (1)

2005 (1)

2004 (1)

2003 (1)

S. Betti, M. Giaconi, and M. Nardini, “Effect of four-wave mixing on WDM optical systems: a statistical analysis,” IEEE Photon. Technol. Lett. 15, 1079–1081 (2003).
[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, 506–520 (2002).
[Crossref]

1999 (1)

1996 (1)

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[Crossref]

1974 (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three wave mixing in silica fiber optical waveguides,” App. Phy. Lett. 24, 308–310 (1974).
[Crossref]

Agrawal, G. P.

Andrekson, P. A.

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, 506–520 (2002).
[Crossref]

Antonelli, C.

Ashkin, A.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three wave mixing in silica fiber optical waveguides,” App. Phy. Lett. 24, 308–310 (1974).
[Crossref]

Ben Salem, A.

A. Ben Salem, A. Trichili, R. Cherif, and M. Zghal, “Rigorous study of supercontinuum generation in few mode fibers,” Appl. Opt. 16, 4317–4322 (2016).
[Crossref]

Betti, S.

S. Betti, M. Giaconi, and M. Nardini, “Effect of four-wave mixing on WDM optical systems: a statistical analysis,” IEEE Photon. Technol. Lett. 15, 1079–1081 (2003).
[Crossref]

Bigo, S.

C. Koebele, M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode division multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett. 23, 1316–1318 (2011).
[Crossref]

Bjorkholm, J. E.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three wave mixing in silica fiber optical waveguides,” App. Phy. Lett. 24, 308–310 (1974).
[Crossref]

Bosco, G.

Carena, A.

Charlet, G.

C. Koebele, M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode division multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett. 23, 1316–1318 (2011).
[Crossref]

Cherif, R.

A. Ben Salem, A. Trichili, R. Cherif, and M. Zghal, “Rigorous study of supercontinuum generation in few mode fibers,” Appl. Opt. 16, 4317–4322 (2016).
[Crossref]

Chipouras, A.

Chraplyvy, A. R.

R. J. Essiambre, R. Ryf, M. A. Mestre, 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 Photon. Technol. Lett. 25, 539–541 (2013).
[Crossref]

Curri, V.

Dar, R.

Desgroseilliers, M.

Eiselt, M.

Esmaeelpour, M.

Essiambre, R. J.

Essiambre, R.-J.

Fatome, J.

Feder, M.

Fini, J. M.

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

Fontaine, N.

Forghieri, F.

Galtarossa, A.

L. Palmieri and A. Galtarossa, “Coupling effects among degenerate modes in multimode optical fibers,” IEEE Photon. J. 6, 1–8 (2014).
[Crossref]

Gao, S.

Giaconi, M.

S. Betti, M. Giaconi, and M. Nardini, “Effect of four-wave mixing on WDM optical systems: a statistical analysis,” IEEE Photon. Technol. Lett. 15, 1079–1081 (2003).
[Crossref]

Gnauck, A. H.

R. J. Essiambre, R. Ryf, M. A. Mestre, 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 Photon. Technol. Lett. 25, 539–541 (2013).
[Crossref]

Golani, O.

Gruner-Nielsen, L.

Guasoni, M.

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, 506–520 (2002).
[Crossref]

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, 506–520 (2002).
[Crossref]

Horak, P.

Jakobsen, D.

Jespersen, K. G.

Jiang, X.

R. J. Essiambre, R. Ryf, M. A. Mestre, 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 Photon. Technol. Lett. 25, 539–541 (2013).
[Crossref]

Jin, Q.

Kamalakis, T.

Koebele, C.

C. Koebele, M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode division multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett. 23, 1316–1318 (2011).
[Crossref]

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, 506–520 (2002).
[Crossref]

Li, X.

Lin, Q.

Lingle, R.

Mecozzi, A.

Menyuk, C. R.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[Crossref]

Mestre, M. A.

R. J. Essiambre, R. Ryf, M. A. Mestre, 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 Photon. Technol. Lett. 25, 539–541 (2013).
[Crossref]

Mumtaz, S.

Nardini, M.

S. Betti, M. Giaconi, and M. Nardini, “Effect of four-wave mixing on WDM optical systems: a statistical analysis,” IEEE Photon. Technol. Lett. 15, 1079–1081 (2003).
[Crossref]

Nelson, L. E.

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

Neokosmidis, I.

Nicholson, J. W.

Palmieri, L.

A. Trichili, M. Zghal, L. Palmieri, and M. Santagiustina, “Phase-sensitive mode conversion and equalization in a few mode fiber through parametric interactions,” IEEE Photon. J. 9, 1–10 (2017).
[Crossref]

L. Palmieri and A. Galtarossa, “Coupling effects among degenerate modes in multimode optical fibers,” IEEE Photon. J. 6, 1–8 (2014).
[Crossref]

L. Palmieri, “Coupling mechanism in multimode fibers,” Proc. SPIE 9009, 90090G (2013).
[Crossref]

Palsdottir, B.

Pan, W.

Parmigiani, F.

Poggiolini, P.

Poletti, F.

Richardson, D. J.

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

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

D. J. Richardson, “Filling the light pipe,” Science 30, 327–328 (2010).
[Crossref]

Ryf, R.

Salsi, M.

C. Koebele, M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode division multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett. 23, 1316–1318 (2011).
[Crossref]

Santagiustina, M.

A. Trichili, M. Zghal, L. Palmieri, and M. Santagiustina, “Phase-sensitive mode conversion and equalization in a few mode fiber through parametric interactions,” IEEE Photon. J. 9, 1–10 (2017).
[Crossref]

Severo, N. C.

M. Zelen and N. C. Severo, “Probablity function,” in Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, eds., Vol. 55 of Applied Mathematics Series (National Bureau of Standards, 1964), ch. 26, pp. 926–976.

Shtaif, M.

Sphicopoulos, T.

Stolen, R. H.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three wave mixing in silica fiber optical waveguides,” App. Phy. Lett. 24, 308–310 (1974).
[Crossref]

Sun, Y.

Tkach, R. W.

R. J. Essiambre, R. Ryf, M. A. Mestre, 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 Photon. Technol. Lett. 25, 539–541 (2013).
[Crossref]

Toulouse, J.

Trichili, A.

A. Trichili, M. Zghal, L. Palmieri, and M. Santagiustina, “Phase-sensitive mode conversion and equalization in a few mode fiber through parametric interactions,” IEEE Photon. J. 9, 1–10 (2017).
[Crossref]

A. Ben Salem, A. Trichili, R. Cherif, and M. Zghal, “Rigorous study of supercontinuum generation in few mode fibers,” Appl. Opt. 16, 4317–4322 (2016).
[Crossref]

Tulino, A. M.

Wai, P. K. A.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[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, 506–520 (2002).
[Crossref]

Xiao, Y.

Zelen, M.

M. Zelen and N. C. Severo, “Probablity function,” in Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, eds., Vol. 55 of Applied Mathematics Series (National Bureau of Standards, 1964), ch. 26, pp. 926–976.

Zghal, M.

A. Trichili, M. Zghal, L. Palmieri, and M. Santagiustina, “Phase-sensitive mode conversion and equalization in a few mode fiber through parametric interactions,” IEEE Photon. J. 9, 1–10 (2017).
[Crossref]

A. Ben Salem, A. Trichili, R. Cherif, and M. Zghal, “Rigorous study of supercontinuum generation in few mode fibers,” Appl. Opt. 16, 4317–4322 (2016).
[Crossref]

App. Phy. Lett. (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three wave mixing in silica fiber optical waveguides,” App. Phy. Lett. 24, 308–310 (1974).
[Crossref]

Appl. Opt. (1)

A. Ben Salem, A. Trichili, R. Cherif, and M. Zghal, “Rigorous study of supercontinuum generation in few mode fibers,” Appl. Opt. 16, 4317–4322 (2016).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (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, 506–520 (2002).
[Crossref]

IEEE Photon. J. (2)

L. Palmieri and A. Galtarossa, “Coupling effects among degenerate modes in multimode optical fibers,” IEEE Photon. J. 6, 1–8 (2014).
[Crossref]

A. Trichili, M. Zghal, L. Palmieri, and M. Santagiustina, “Phase-sensitive mode conversion and equalization in a few mode fiber through parametric interactions,” IEEE Photon. J. 9, 1–10 (2017).
[Crossref]

IEEE Photon. Technol. Lett. (3)

R. J. Essiambre, R. Ryf, M. A. Mestre, 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 Photon. Technol. Lett. 25, 539–541 (2013).
[Crossref]

C. Koebele, M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode division multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett. 23, 1316–1318 (2011).
[Crossref]

S. Betti, M. Giaconi, and M. Nardini, “Effect of four-wave mixing on WDM optical systems: a statistical analysis,” IEEE Photon. Technol. Lett. 15, 1079–1081 (2003).
[Crossref]

J. Lightwave Technol. (10)

M. Eiselt, “Limits on WDM systems due to four-wave mixing: a statistical approach,” J. Lightwave Technol. 17, 2261–2267 (1999).
[Crossref]

O. Golani, R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, “Modeling the bit-error-rate performance of nonlinear fiber-optic systems,” J. Lightwave Technol. 34, 3482–3489 (2016).
[Crossref]

L. Gruner-Nielsen, Y. Sun, J. W. Nicholson, D. Jakobsen, K. G. Jespersen, R. Lingle, and B. Palsdottir, “Few mode transmission fiber with low DGD, low mode coupling, and low loss,” J. Lightwave Technol. 30, 3693–3698 (2012).
[Crossref]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[Crossref]

S. Mumtaz, R.-J. Essiambre, and G. P. Agrawal, “Nonlinear propagation in multimode and multicore fibers: generalization of the Manakov equations,” J. Lightwave Technol. 31, 398–406 (2013).
[Crossref]

C. Antonelli, M. Shtaif, and A. Mecozzi, “Modeling of nonlinear propagation in space-division multiplexed fiber-optic transmission,” J. Lightwave Technol. 34, 36–54 (2016).
[Crossref]

M. Esmaeelpour, R. J. Essiambre, N. Fontaine, R. Ryf, J. Toulouse, Y. Sun, and R. Lingle, “Power fluctuations of inter-modal four-wave mixing in few-mode fibers,” J. Lightwave Technol. 35, 2429–2435 (2017).
[Crossref]

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

I. Neokosmidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, “New techniques for the suppression of the four-wave mixing-induced distortion in nonzero dispersion fiber WDM systems,” J. Lightwave Technol. 23, 1137–1144 (2005).
[Crossref]

P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightwave Technol. 30, 3857–3879 (2012).
[Crossref]

J. Opt. Soc. Am. B (3)

Nat. Photonics (1)

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

Opt. Express (7)

Proc. SPIE (1)

L. Palmieri, “Coupling mechanism in multimode fibers,” Proc. SPIE 9009, 90090G (2013).
[Crossref]

Science (1)

D. J. Richardson, “Filling the light pipe,” Science 30, 327–328 (2010).
[Crossref]

Other (1)

M. Zelen and N. C. Severo, “Probablity function,” in Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, eds., Vol. 55 of Applied Mathematics Series (National Bureau of Standards, 1964), ch. 26, pp. 926–976.

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Figures (10)

Fig. 1
Fig. 1 System configuration: the WDM channels are spaced by 50 GHz in the C band on both LP01 and LP11 modes.
Fig. 2
Fig. 2 Channel power evolution when mode LP11 at frequency ω2 (channel 3) is not launched.
Fig. 3
Fig. 3 Channel power evolution for equal channel input powers of 10 dBm. Solid lines with marker correspond to the case in which FWM is considered, while dashed lines are obtained without FWM (losses only).
Fig. 4
Fig. 4 Channel output power as a function of input phases for equal channel input powers of 10 dBm.
Fig. 5
Fig. 5 PDF (over 3000 independent realizations) of the four channels for equal input channel powers.
Fig. 6
Fig. 6 PDF (over 3000 independent realizations) of the four channels with −10 dBm for channel 3 as input power while the input power is +10 dBm for the other channels.
Fig. 7
Fig. 7 Conversion efficiency for channel 3 in the case of nonlinear coupling only (black squares) and linear and nonlinear coupling (red dots).
Fig. 8
Fig. 8 Comparison between three cases of channel power evolution. Markers represent the channel powers with nonlinear coupling only, solid lines with marker, correspond to channel powers with linear and nonlinear effects and finally dashed lines are the powers when only linear coupling is included in the modeling.
Fig. 9
Fig. 9 PDF (over 3000 independent realizations) of the four channels for equal input channel powers.
Fig. 10
Fig. 10 PDF (over 3000 independent realizations) of the channels generated by random linear coupling.

Equations (7)

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Δ β ( m n o p ) = β ( m ) ( ω i ) + β ( n ) ( ω j ) β ( o ) ( ω k ) β ( p ) ( ω l )
β ( p ) ( ω l ) β 0 ( p ) + β 1 ( p ) Δ ω l + 1 2 β 2 ( p ) Δ ω l 2 +
i d A 1 d z = i α 1 2 A 1 + γ ( f 1111 | A 1 | 2 A 1 + 2 n , n 1 f 11 n n | A n | 2 A 1 + 2 f 1234 A 2 A 3 A 4 * exp ( i Δ β z ) ) i d A 2 d z = i α 2 2 A 2 + γ ( f 2222 | A 2 | 2 A 2 + 2 n , n 2 f 22 n n | A n | 2 A 2 + 2 f 2143 A 1 A 4 A 3 * exp ( i Δ β z ) ) i d A 3 d z = i α 3 2 A 3 + γ ( f 3333 | A 3 | 2 A 3 + 2 n , n 3 f 33 n n | A n | 2 A 3 + 2 f 3142 A 1 A 4 A 2 * exp ( i Δ β z ) ) i d A 4 d z = i α 4 2 A 4 + γ ( f 4444 | A 4 | 2 A 4 + 2 n , n 4 f 44 n n | A n | 2 A 4 + 2 f 4231 A 2 A 3 A 1 * exp ( i Δ β z ) )
f i j k l = { 1 for 4 wave in LP 01 or LP 11 a or LP 11 b 0.702 for 2 wave in LP 01 and 2 waves in LP 11 a or LP 11 b 0.493 for 2 wave in LP 11 a and 2 waves in LP 11 b 0 for all other cases
d P 1 , 4 d z = d A 1 , 4 d z A 1 , 4 * + d A 1 , 4 * d z A 1 , 4 = α P 1 , 4 4 P 1 P 2 P 3 P 4 sin ( Φ ) d P 2 , 3 d z = d A 2 , 3 d z A 2 , 3 * + d A 2 , 3 * d z A 2 , 3 = α P 2 , 3 + 4 P 1 P 2 P 3 P 4 sin ( Φ )
d Φ d z Δ β + γ ( P 1 + P 4 P 2 P 3 ) 0
f ( x ; a , b ) = 1 B ( a , b ) x a 1 ( 1 x ) b 1 ,

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