Abstract

Optical communication links are usually made with erbium-doped fiber amplifiers, which amplify the signal waves in a phase-insensitive (PI) manner. They can also be made with parametric fiber amplifiers, in which the signal waves interact with idler waves. If information is transmitted using only the signals, parametric amplifiers are PI and their noise figures are comparable to those of erbium amplifiers. However, transmitting correlated information in the signals and idlers, or copying the signals prior to transmission, allows parametric amplifiers to be phase-sensitive (PS), which lowers their noise figures. The information capacities of two-mode PS links exceed those of the corresponding PI links by 2 b/s-Hz.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14 (4), 3–10 (2010).
    [CrossRef]
  2. P. J. Winzer, “Modulation and multiplexing in optical communication systems,” IEEE LEOS Newsletter 23 (1), 4–10 (2009).
  3. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic Press, 1999).
  4. M. N. Islam, Raman Amplifiers for Telecommunications (Springer Verlag, 2003).
  5. 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]
  6. S. Radic and C. J. McKinstrie, “Optical amplification and signal processing in highly-nonlinear optical fiber,” IEICE Trans. Electron. E88C, 859–869 (2005).
    [CrossRef]
  7. C. J. McKinstrie and N. Alic, “Information efficiencies of parametric devices,” to appear in IEEE J. Sel. Top. Quantum Electron.
  8. R. Loudon, The Quantum Theory of Light, 3rd Ed. (Oxford University Press, 2000).
  9. J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129, 481–485 (1963).
    [CrossRef]
  10. C. J. McKinstrie and J. P. Gordon, “Field fluctuations produced by parametric processes in fibers,” to appear in IEEE J. Sel. Top. Quantum Electron.
  11. C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
    [CrossRef] [PubMed]
  12. C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13, 4986–5012 (2005).
    [CrossRef] [PubMed]
  13. M. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13, 7563–7571 (2005).
    [CrossRef] [PubMed]
  14. C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express. 18, 19792–19823 (2010).
    [CrossRef] [PubMed]
  15. C. E. Shannon, “A mathematical theory of communication,” Bell Sys. Tech. J. 28, 379–423 and 623–656 (1948).
  16. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd Ed. (Wiley, 2006).
  17. J. Hansryd and P. A. Andrekson, “Broad-band CW-pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency,” IEEE Photon. Technol. Lett. 13, 194–196 (2001).
    [CrossRef]
  18. C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
    [CrossRef] [PubMed]
  19. K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19, 864–866 (2007).
    [CrossRef]
  20. S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
    [CrossRef]
  21. R. Tang, J. Lasri, P. S. Devgan, V. S. Grigoryan, and P. Kumar, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13, 10483–10493 (2005).
    [CrossRef] [PubMed]
  22. J. Kakande, C. Lundström, P. A. Andrekson, Z. Tong, M. Karlsson, P. Petropoulos, F. Parmigiani, and D. J. Richardson, “Detailed characterization of a fiber-optic parametric amplifier in phase-sensitive and phase-insensitive operation,” Opt. Express 18, 4130–4137 (2010).
    [CrossRef] [PubMed]
  23. E. Desurvire, “Fundamental information-density limits in optically amplified transmission: an entropy analysis,” Opt. Lett. 25, 701–703 (2000).
    [CrossRef]
  24. R. Loudon, “Theory of noise accumulation in optical-amplifier chains,” IEEE J. Quantum Electron. 21, 766–773 (1985).
    [CrossRef]
  25. Z. Tong, C. J. McKinstrie, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers,” Opt. Express 18, 15426–15439 (2010).
    [CrossRef] [PubMed]
  26. Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.
  27. J. Tang, “The Shannon capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, 1104–1109 (2001).
    [CrossRef]
  28. K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91, 203901 (2003).
    [CrossRef] [PubMed]
  29. R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
    [CrossRef] [PubMed]
  30. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. 28, 423–433 (2010).
    [CrossRef]

2010 (5)

2009 (1)

P. J. Winzer, “Modulation and multiplexing in optical communication systems,” IEEE LEOS Newsletter 23 (1), 4–10 (2009).

2008 (1)

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

2007 (1)

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19, 864–866 (2007).
[CrossRef]

2005 (4)

R. Tang, J. Lasri, P. S. Devgan, V. S. Grigoryan, and P. Kumar, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13, 10483–10493 (2005).
[CrossRef] [PubMed]

S. Radic and C. J. McKinstrie, “Optical amplification and signal processing in highly-nonlinear optical fiber,” IEICE Trans. Electron. E88C, 859–869 (2005).
[CrossRef]

C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13, 4986–5012 (2005).
[CrossRef] [PubMed]

M. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13, 7563–7571 (2005).
[CrossRef] [PubMed]

2004 (2)

C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
[CrossRef] [PubMed]

2003 (1)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef] [PubMed]

2002 (2)

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[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, 506–520 (2002).
[CrossRef]

2001 (2)

J. Hansryd and P. A. Andrekson, “Broad-band CW-pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency,” IEEE Photon. Technol. Lett. 13, 194–196 (2001).
[CrossRef]

J. Tang, “The Shannon capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, 1104–1109 (2001).
[CrossRef]

2000 (1)

1985 (1)

R. Loudon, “Theory of noise accumulation in optical-amplifier chains,” IEEE J. Quantum Electron. 21, 766–773 (1985).
[CrossRef]

1963 (1)

J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129, 481–485 (1963).
[CrossRef]

1948 (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Sys. Tech. J. 28, 379–423 and 623–656 (1948).

Alic, N.

C. J. McKinstrie and N. Alic, “Information efficiencies of parametric devices,” to appear in IEEE J. Sel. Top. Quantum Electron.

Andrekson, P. A.

J. Kakande, C. Lundström, P. A. Andrekson, Z. Tong, M. Karlsson, P. Petropoulos, F. Parmigiani, and D. J. Richardson, “Detailed characterization of a fiber-optic parametric amplifier in phase-sensitive and phase-insensitive operation,” Opt. Express 18, 4130–4137 (2010).
[CrossRef] [PubMed]

Z. Tong, C. J. McKinstrie, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers,” Opt. Express 18, 15426–15439 (2010).
[CrossRef] [PubMed]

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]

J. Hansryd and P. A. Andrekson, “Broad-band CW-pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency,” IEEE Photon. Technol. Lett. 13, 194–196 (2001).
[CrossRef]

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.

Becker, P. C.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic Press, 1999).

Blessing, D. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.

Brar, K.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Centanni, J. C.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Chraplyvy, A. R.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Cotter, D.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd Ed. (Wiley, 2006).

Croussore, K.

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19, 864–866 (2007).
[CrossRef]

Derevyanko, S. A.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef] [PubMed]

Desurvire, E.

Devgan, P. S.

R. Tang, J. Lasri, P. S. Devgan, V. S. Grigoryan, and P. Kumar, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13, 10483–10493 (2005).
[CrossRef] [PubMed]

Ellis, A. D.

Essiambre, R. J.

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

Foschini, G. J.

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

Gordon, J. P.

J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129, 481–485 (1963).
[CrossRef]

C. J. McKinstrie and J. P. Gordon, “Field fluctuations produced by parametric processes in fibers,” to appear in IEEE J. Sel. Top. Quantum Electron.

Grigoryan, V. S.

R. Tang, J. Lasri, P. S. Devgan, V. S. Grigoryan, and P. Kumar, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13, 10483–10493 (2005).
[CrossRef] [PubMed]

Grüner-Nielsen, L.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.

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]

J. Hansryd and P. A. Andrekson, “Broad-band CW-pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency,” IEEE Photon. Technol. Lett. 13, 194–196 (2001).
[CrossRef]

Headley, C.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (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]

Islam, M. N.

M. N. Islam, Raman Amplifiers for Telecommunications (Springer Verlag, 2003).

Jorgensen, C. G.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Kakande, J.

Karlsson, M.

J. Kakande, C. Lundström, P. A. Andrekson, Z. Tong, M. Karlsson, P. Petropoulos, F. Parmigiani, and D. J. Richardson, “Detailed characterization of a fiber-optic parametric amplifier in phase-sensitive and phase-insensitive operation,” Opt. Express 18, 4130–4137 (2010).
[CrossRef] [PubMed]

Z. Tong, C. J. McKinstrie, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers,” Opt. Express 18, 15426–15439 (2010).
[CrossRef] [PubMed]

C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express. 18, 19792–19823 (2010).
[CrossRef] [PubMed]

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.

Kramer, G.

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

Kumar, P.

R. Tang, J. Lasri, P. S. Devgan, V. S. Grigoryan, and P. Kumar, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13, 10483–10493 (2005).
[CrossRef] [PubMed]

Lasri, J.

R. Tang, J. Lasri, P. S. Devgan, V. S. Grigoryan, and P. Kumar, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13, 10483–10493 (2005).
[CrossRef] [PubMed]

Li, G.

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19, 864–866 (2007).
[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]

Loudon, R.

R. Loudon, “Theory of noise accumulation in optical-amplifier chains,” IEEE J. Quantum Electron. 21, 766–773 (1985).
[CrossRef]

R. Loudon, The Quantum Theory of Light, 3rd Ed. (Oxford University Press, 2000).

Louisell, W. H.

J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129, 481–485 (1963).
[CrossRef]

Lundström, C.

McKinstrie, C. J.

C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express. 18, 19792–19823 (2010).
[CrossRef] [PubMed]

Z. Tong, C. J. McKinstrie, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers,” Opt. Express 18, 15426–15439 (2010).
[CrossRef] [PubMed]

C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13, 4986–5012 (2005).
[CrossRef] [PubMed]

S. Radic and C. J. McKinstrie, “Optical amplification and signal processing in highly-nonlinear optical fiber,” IEICE Trans. Electron. E88C, 859–869 (2005).
[CrossRef]

C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
[CrossRef] [PubMed]

C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
[CrossRef] [PubMed]

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

C. J. McKinstrie and J. P. Gordon, “Field fluctuations produced by parametric processes in fibers,” to appear in IEEE J. Sel. Top. Quantum Electron.

C. J. McKinstrie and N. Alic, “Information efficiencies of parametric devices,” to appear in IEEE J. Sel. Top. Quantum Electron.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.

Olsson, N. A.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic Press, 1999).

Parmigiani, F.

Petropoulos, P.

Puttnam, B. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.

Radic, S.

S. Radic and C. J. McKinstrie, “Optical amplification and signal processing in highly-nonlinear optical fiber,” IEICE Trans. Electron. E88C, 859–869 (2005).
[CrossRef]

C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13, 4986–5012 (2005).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
[CrossRef] [PubMed]

C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
[CrossRef] [PubMed]

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Raybon, G.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Raymer, M. G.

C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13, 4986–5012 (2005).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
[CrossRef] [PubMed]

Richardson, D. J.

Shannon, C. E.

C. E. Shannon, “A mathematical theory of communication,” Bell Sys. Tech. J. 28, 379–423 and 623–656 (1948).

Simpson, J. R.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic Press, 1999).

Tang, J.

J. Tang, “The Shannon capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, 1104–1109 (2001).
[CrossRef]

Tang, R.

R. Tang, J. Lasri, P. S. Devgan, V. S. Grigoryan, and P. Kumar, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13, 10483–10493 (2005).
[CrossRef] [PubMed]

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd Ed. (Wiley, 2006).

Tipsuwannakul, E.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.

Tkach, R. W.

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14 (4), 3–10 (2010).
[CrossRef]

Toda, H.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.

Tong, Z.

C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express. 18, 19792–19823 (2010).
[CrossRef] [PubMed]

Z. Tong, C. J. McKinstrie, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers,” Opt. Express 18, 15426–15439 (2010).
[CrossRef] [PubMed]

J. Kakande, C. Lundström, P. A. Andrekson, Z. Tong, M. Karlsson, P. Petropoulos, F. Parmigiani, and D. J. Richardson, “Detailed characterization of a fiber-optic parametric amplifier in phase-sensitive and phase-insensitive operation,” Opt. Express 18, 4130–4137 (2010).
[CrossRef] [PubMed]

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.

Turitsyn, K. S.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef] [PubMed]

Turitsyn, S. K.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef] [PubMed]

Vasilyev, M.

Walker, L. R.

J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129, 481–485 (1963).
[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]

Winzer, P. J.

P. J. Winzer, “Modulation and multiplexing in optical communication systems,” IEEE LEOS Newsletter 23 (1), 4–10 (2009).

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

Yu, M.

Yurkevich, I. V.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef] [PubMed]

Zhao, J.

Bell Labs Tech. J. (1)

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14 (4), 3–10 (2010).
[CrossRef]

Bell Sys. Tech. J. (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Sys. Tech. J. 28, 379–423 and 623–656 (1948).

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 J. Quantum Electron. (1)

R. Loudon, “Theory of noise accumulation in optical-amplifier chains,” IEEE J. Quantum Electron. 21, 766–773 (1985).
[CrossRef]

IEEE LEOS Newsletter (1)

P. J. Winzer, “Modulation and multiplexing in optical communication systems,” IEEE LEOS Newsletter 23 (1), 4–10 (2009).

IEEE Photon. Technol. Lett. (2)

J. Hansryd and P. A. Andrekson, “Broad-band CW-pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency,” IEEE Photon. Technol. Lett. 13, 194–196 (2001).
[CrossRef]

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19, 864–866 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate-pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

IEICE Trans. Electron. (1)

S. Radic and C. J. McKinstrie, “Optical amplification and signal processing in highly-nonlinear optical fiber,” IEICE Trans. Electron. E88C, 859–869 (2005).
[CrossRef]

J. Lightwave Technol. (1)

J. Tang, “The Shannon capacity of dispersion-free nonlinear optical fiber transmission,” J. Lightwave Technol. 19, 1104–1109 (2001).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (2)

R. Tang, J. Lasri, P. S. Devgan, V. S. Grigoryan, and P. Kumar, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13, 10483–10493 (2005).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Express. (1)

C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express. 18, 19792–19823 (2010).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. (1)

J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129, 481–485 (1963).
[CrossRef]

Phys. Rev. Lett. (1)

R. J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91, 203901 (2003).
[CrossRef] [PubMed]

Other (7)

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Toward ultra-sensitive optical links enabled by low-noise phase-sensitive amplifiers,” to appear in Nat. Photon.

C. J. McKinstrie and J. P. Gordon, “Field fluctuations produced by parametric processes in fibers,” to appear in IEEE J. Sel. Top. Quantum Electron.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd Ed. (Wiley, 2006).

C. J. McKinstrie and N. Alic, “Information efficiencies of parametric devices,” to appear in IEEE J. Sel. Top. Quantum Electron.

R. Loudon, The Quantum Theory of Light, 3rd Ed. (Oxford University Press, 2000).

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic Press, 1999).

M. N. Islam, Raman Amplifiers for Telecommunications (Springer Verlag, 2003).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Frequency diagrams for degenerate four-wave mixing. (a) modulation interaction and (b) inverse modulation interaction. Downward (upward) arrows denote modes that lose (gain) photons.

Fig. 2
Fig. 2

Frequency diagrams for non-degenerate four-wave mixing. (a) outer-band and (b) inner-band phase conjugation. Downward (upward) arrows denote modes that lose (gain) photons.

Fig. 3
Fig. 3

Illustration of attenuation (modeled as two-mode beam splitting), in which a signal mode (s) interacts with a loss mode (l) at a partially-reflecting mirror (M).

Fig. 4
Fig. 4

Architecture of a stage in a two-mode phase-insensitive link. An attenuator (◃) is followed by a two-mode amplifier (▹). Modes 1 and 2 are the signal and idler, respectively, and mode l is a loss mode. After every stage except the last, the output idler is discarded.

Fig. 5
Fig. 5

Architecture of a stage in a one-mode phase-sensitive link. An attenuator (◃) is followed by a one-mode amplifier (▹). The closed loop around the amplifier indicates that the signal interacts with itself.

Fig. 6
Fig. 6

Architecture of a stage in a two-mode phase-sensitive link. Two attenuators (◃) in parallel are followed by a two-mode amplifier (▹). Modes 1 and 2 are the signal and idler, respectively, and modes k and l are loss modes. Both sidebands are transmitted through the link.

Equations (64)

Equations on this page are rendered with MathJax. Learn more.

C t = ln ( Δ y / Δ n ) 1 / 2 .
C = ln ( 1 + σ x / σ v ) 1 / 2 ,
K y = [ σ 11 + σ v σ 12 σ 12 σ 22 + σ v ] , K n = [ σ v 0 0 σ v ] .
C t = ln [ ( 1 + σ 11 / σ v ) ( 1 + σ 22 / σ v ) ( σ 12 / σ v ) 2 ] 1 / 2 ,
y r = ( μ + ν ) y r , y i = ( μ ν ) y i ,
y 1 r = μ y 1 r + ν y 2 r , y 2 r = ν y 1 r + μ y 2 r ,
y ± = ( μ ± ν ) y ± ,
y 1 r = τ y 1 r + ρ y l r , y l r = ρ y 1 r + τ y l r ,
y ± = ( μ ± ν ) τ y ± + ( μ ± ν ) ρ v ± ,
y ± = τ ( μ ± ν ) y ± + ρ v ± .
y 1 ( 1 ) = ( μ τ ) y 1 ( 0 ) + ( μ ρ ) v l ( 1 ) + ν v 2 ( 1 ) ,
y 2 ( 1 ) = ( ν τ ) y 1 ( 0 ) + ( ν ρ ) v l ( 1 ) + μ v 2 ( 1 ) ,
y 1 ( s ) = ( μ τ ) s y 1 ( 0 ) + r = 1 s ( μ τ ) s r [ ( μ ρ ) v l ( r ) + ν v 2 ( r ) ] ,
y 2 ( s ) = ( ν τ ) y 1 ( s 1 ) + ( ν ρ ) v l ( s ) + μ v 2 ( s ) .
σ x ( s ) = ( μ τ ) 2 s σ x ( 0 ) ,
σ n ( s ) = { ( μ τ ) 2 s + [ ( μ ρ ) 2 + ν 2 ] [ 1 ( μ τ ) 2 s ] / [ 1 ( μ τ ) 2 ] } σ v .
σ x ( s ) = σ x ( 0 ) ,
σ n ( s ) = [ 1 + 2 s ( L 1 ) ] σ v ,
C 1 ( s ) = ln [ 1 + σ x ( s ) / σ n ( s ) ] 1 / 2 .
C 1 ( s 1 / 2 ) = ln [ 1 + σ x ( s 1 / 2 ) / σ n ( s 1 / 2 ) ] 1 / 2 .
K y ( s ) = [ μ 2 ( σ x + σ n ) + ν 2 σ v μ ν ( σ x + σ n + σ v ) μ ν ( σ x + σ n + σ v ) ν 2 ( σ x + σ n ) + μ 2 σ v ] ,
K n ( s ) = [ μ 2 σ n + ν 2 σ v μ ν ( σ n + σ v ) μ ν ( σ n + σ v ) ν 2 σ n + μ 2 σ v ] ,
C 2 ( s ) = ln { 1 + σ x ( s 1 / 2 ) / [ σ n ( s 1 / 2 ) + L σ v / ( L 1 ) ] } 1 / 2 = ln { 1 + σ x ( s ) / [ σ n ( s ) + ( 2 L 1 ) σ v / ( L 1 ) ] } 1 / 2 ,
C t ( s ) = ln [ 1 + σ x ( s 1 / 2 ) / σ n ( s 1 / 2 ) ] 1 / 2 .
y ( 1 ) = ( λ τ ) y ( 0 ) + ( λ ρ ) v ( 1 ) ,
y ( s ) = ( λ τ ) s y ( 0 ) + ( λ ρ ) r = 1 s ( λ τ ) s r v ( r ) ,
σ x ( s ) = ( λ τ ) 2 s σ x ( 0 ) ,
σ n ( s ) = { ( λ τ ) 2 s + ( λ ρ ) 2 [ 1 ( λ τ ) 2 s ] / [ 1 ( λ τ ) 2 ] } σ v ,
σ x ( s ) = σ x ( 0 ) ,
σ n ( s ) = [ 1 + s ( L 1 ) ] σ v .
C r ( s ) ln [ 1 + σ x ( 0 ) / σ v s L ] 1 / 2 .
σ x ( s ) = σ x ( 0 ) / L 2 s ,
σ n ( s ) = 1 / L 2 s + ( 1 1 / L 2 s ) / ( L + 1 ) = ( 1 + 1 / L 2 s 1 ) / ( L + 1 ) .
C i ( s ) ln [ 1 + σ x ( 0 ) / σ v L 2 s 1 ] 1 / 2 .
y 1 ( 1 ) = ( μ τ ) y 1 ( 0 ) + ( ν τ ) y 2 ( 0 ) + ( μ ρ ) v k ( 1 ) + ( ν ρ ) v l ( 1 ) ,
y 2 ( 1 ) = ( ν τ ) y 1 ( 0 ) + ( μ τ ) y 2 ( 0 ) + ( ν ρ ) v k ( 1 ) + ( μ ρ ) v l ( 1 ) ,
y 1 ( s ) = τ s [ p s y 1 ( 0 ) + q s y 2 ( 0 ) ] + ρ r = 1 s τ s r [ p s r + 1 v k ( r ) + q s r + 1 v l ( r ) ] ,
y 2 ( s ) = τ s [ q s y 1 ( 0 ) + p s y 2 ( 0 ) ] + ρ r = 1 s τ s r [ q s r + 1 v k ( r ) + p s r + 1 v l ( r ) ] ,
p s = [ ( μ + ν ) s + ( μ ν ) s ] / 2 ,
q s = [ ( μ + ν ) s ( μ ν ) s ] / 2 .
x i x j = [ ( μ + ν ) τ ] 2 s σ t / 2 ,
n j 2 / σ v = τ 2 s ( p s 2 + q s 2 ) + ρ 2 r = 1 s τ 2 ( s r ) ( p s r + 1 2 + q s r + 1 2 ) ,
n 1 n 2 / σ v = τ 2 s ( 2 p s q s ) + ρ 2 r = 1 s τ 2 ( s r ) ( 2 p s r + 1 q s r + 1 ) ,
n j 2 / σ v = [ 1 + s ( L 1 ) + ( 1 + 1 / L 2 s 1 ) / ( L + 1 ) ] / 2 ,
n 1 n 2 / σ v = [ 1 + s ( L 1 ) ( 1 + 1 / L 2 s 1 ) / ( L + 1 ) ] / 2 .
K y = [ ( α + β + γ ) ( α + β γ ) ( α + β γ ) ( α + β + γ ) ] , K n = [ ( β + γ ) ( β γ ) ( β γ ) ( β + γ ) ] ,
C j = ln [ 1 + α / ( β + γ ) ] 1 / 2 .
C t = ln ( 1 + α / β ) 1 / 2 .
C ln ( 1 + σ t / σ v s L ) 1 / 2 .
y ± ( 1 ) = ( λ ± τ ) y ± ( 0 ) + ( λ ± ρ ) v ± ( 1 ) .
n + 2 / σ v = 1 + s ( L 1 ) ,
n 2 / σ v = ( 1 + 1 / L 2 n 1 ) / ( L + 1 ) .
K y = [ α + + β + 0 0 α + β ] , K n = [ β + 0 0 β ] ,
C ± = ln ( 1 + α ± / β ± ) 1 / 2 ,
a | α = α | α ,
q ( θ ) = ( a e i θ + a e i θ ) / 2 1 / 2 ,
b j = Σ k ( μ j k a k + ν j k a k ) ,
Σ l ( μ j l ν k l μ k l ν j l ) = 0 ,
Σ l ( μ j l μ k l * ν j l ν k l * ) = δ j k .
a j = α j + v j , b j = β j + w j ,
δ q i ( θ i ) δ q j ( θ j ) = ( w i e i θ i + w i e i θ i ) ( w j e i θ j + w j e i θ j ) / 2 .
w i w j = Σ k μ i k ν j k , w i w j = Σ k μ i k μ j k * , w i w j = Σ k ν i k * ν j k , w i w j = Σ k ν i k * μ j k * ,
δ q i ( θ i ) δ q j ( θ j ) = Σ k ( μ i k e i θ i + ν i k * e i θ i ) ( μ j k * e i θ j + ν j k e i θ j ) / 2 .
w i w j = Σ k μ i k ν j k , w i w j = Σ k μ i k μ j k * δ i j / 2 , w i w j = Σ k ν i k * ν j k + δ i j / 2 , w i w j = Σ k ν i k * μ j k * .

Metrics