Abstract

We propose a phase-sensitive amplifier scheme that balances fiber loss and parametric gain everywhere in a fiber span. We show that, for long links, such a distributed phase-sensitive amplifier has a 3-dB lower noise figure than an ideal distributed phase-insensitive amplifier (e.g. Raman), even if simple direct detection is employed. This sets the ultimate limit for the optimum noise-nonlinearity trade-off in transmission systems.

© 2005 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  5. J. A. Levenson, I. Abram, T. Rivera, and P. Grainger, “Reduction of quantum-noise in optical parametric amplification,” J. Opt. Soc. Am. B 10, 2233 (1993).
    [Crossref]
  6. Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Quantum noise reduction in optical amplification,” Phys. Rev. Lett. 70, 3239 (1993).
    [Crossref] [PubMed]
  7. S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless Optical Amplification of Images,” Phys. Rev. Lett. 83, 1938 (1999).
    [Crossref]
  8. M. E. Marhic, C. H. Hsia, and J.-M. Jeong, Electron. Lett. 27, 210 (1991).
    [Crossref]
  9. G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, “All-optical storage of a picosecond-pulse packet using parametric amplification,” IEEE Photonics Technol. Lett. 9, 1020 (1997).
    [Crossref]
  10. K. Croussore, I. Kim, Y. Han, C. Kim, G. Li, and S. Radic, “Demonstration of phase-regeneration of DPSK signals based on phase-sensitive amplification,” Opt. Express 13, 3945 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-3945 .
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    [Crossref]
  14. W. Imajuku and A. Takada, “In-line optical phase-sensitive amplifier with pump light source controlled by optical phase-lock loop,” J. Lightwave Technol. 17, 637 (1999).
    [Crossref]
  15. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
    [Crossref]
  16. D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24, 984 (1999).
    [Crossref]
  17. D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA-Journal of Physics 56, 281 (2001).
    [Crossref]
  18. W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35, 1954 (1999).
    [Crossref]
  19. S. Radic and C. J. McKinstrie, “Two pump fiber parametric amplifiers,” Opt. Fiber Technol. 9, 7 (2003).
    [Crossref]
  20. P. L. Voss and P. Kumar, “Raman-noise-induced noise-figure limit for ?(3) parametric amplifiers,” Opt. Lett. 29, 445 (2004).
    [Crossref] [PubMed]
  21. P. L. Voss, K. G. Koprulu, and P. Kumar “Raman-noise induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” submitted to J. Opt. Soc. Am. B.
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  23. C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13, 4986 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-4986 .
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  24. R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-Line Frequency-Nondegenerate Phase-Sensitive Fiber-Optical Parametric Amplifier,” IEEE Photonics Technol. Lett. 17, 1845 (2005).
    [Crossref]
  25. R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, “In-line frequency-non-degenerate phase-sensitive fiber parametric amplifier for fiber-optic communications,” to appear in Electron. Lett.
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    [Crossref] [PubMed]
  27. M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, “Reduction of Raman MPI and noise figure in dispersion-managed fibre,” Electron. Lett. 38, 271 (2002).
    [Crossref]
  28. M. Vasilyev, “Raman-assisted transmission: toward ideal distributed amplification,” Optical Fiber Communication Conference 2003, Technical Digest (OSA, Washington, D.C.2003), Vol. 1, pp. 303–305, paper WB1.
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    [Crossref]
  30. J.-C. Bouteiller, K. Brar, and C. Headley, “Quasi-constant signal power transmission,” European Conference on Optical Communication 2002, paper S3.04.
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  32. Here, conventional fiber is assumed to be averaging the nonlinear interaction over the signal states of polarization while preserving the relative orientation of the pump and signal. Coefficients a, b, ε, and εP are straightforwardly derived from Eq. (4.2.10) of [33], as done, for example, in [34].
  33. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003), Chap. 4.2.
  34. M. Vasilyev, lecture notes for Nonlinear Optics course (University of Texas at Arlington, 2004).
  35. C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4973 .
    [Crossref] [PubMed]
  36. L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, “Solitons in high bit-rate, long-distance transmission,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997), pp. 373–460.
  37. I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600 (1998).
    [Crossref]
  38. A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photonics Technol. Lett. 12, 392 (2000).
    [Crossref]
  39. M. Vasilyev and T. Lakoba, “All-optical multi-channel 2R regeneration in a fiber-based device,” Opt. Lett. 30, 1458 (2005).
    [Crossref] [PubMed]
  40. G. P. Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 1995).
  41. G. Kalogerakis, K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, “Transmission of optical communication signals by distributed parametric amplification,” in Conference on Lasers and Electro-Optics 2005 (Optical Society of America, Washington, DC, 2005), paper CTuT2.
    [Crossref]

2005 (4)

2004 (3)

2003 (1)

S. Radic and C. J. McKinstrie, “Two pump fiber parametric amplifiers,” Opt. Fiber Technol. 9, 7 (2003).
[Crossref]

2002 (1)

M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, “Reduction of Raman MPI and noise figure in dispersion-managed fibre,” Electron. Lett. 38, 271 (2002).
[Crossref]

2001 (1)

D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA-Journal of Physics 56, 281 (2001).
[Crossref]

2000 (1)

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photonics Technol. Lett. 12, 392 (2000).
[Crossref]

1999 (4)

D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24, 984 (1999).
[Crossref]

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35, 1954 (1999).
[Crossref]

W. Imajuku and A. Takada, “In-line optical phase-sensitive amplifier with pump light source controlled by optical phase-lock loop,” J. Lightwave Technol. 17, 637 (1999).
[Crossref]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless Optical Amplification of Images,” Phys. Rev. Lett. 83, 1938 (1999).
[Crossref]

1998 (2)

A. Takada and W. Imajuku, “In-line optical phase-sensitive amplifier employing pump laser injection-locked to input signal light,” Electron. Lett. 34, 274 (1998).
[Crossref]

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600 (1998).
[Crossref]

1997 (1)

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, “All-optical storage of a picosecond-pulse packet using parametric amplification,” IEEE Photonics Technol. Lett. 9, 1020 (1997).
[Crossref]

1993 (3)

1992 (2)

1991 (2)

1990 (1)

1986 (1)

1985 (1)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
[Crossref]

1982 (1)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D. 26, 1817 (1982).
[Crossref]

Abram, I.

Agrawal, G. P.

G. P. Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 1995).

Bar-Joseph, I.

Bartolini, G. D.

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, “All-optical storage of a picosecond-pulse packet using parametric amplification,” IEEE Photonics Technol. Lett. 9, 1020 (1997).
[Crossref]

Bayer, P. W.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
[Crossref]

Bergman, K.

Bouteiller, J.-C.

J.-C. Bouteiller, K. Brar, and C. Headley, “Quasi-constant signal power transmission,” European Conference on Optical Communication 2002, paper S3.04.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003), Chap. 4.2.

Brar, K.

J.-C. Bouteiller, K. Brar, and C. Headley, “Quasi-constant signal power transmission,” European Conference on Optical Communication 2002, paper S3.04.

Caves, C. M.

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D. 26, 1817 (1982).
[Crossref]

Choi, S.-K.

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless Optical Amplification of Images,” Phys. Rev. Lett. 83, 1938 (1999).
[Crossref]

Clausen, C. B.

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photonics Technol. Lett. 12, 392 (2000).
[Crossref]

Croussore, K.

Devgan, P.

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-Line Frequency-Nondegenerate Phase-Sensitive Fiber-Optical Parametric Amplifier,” IEEE Photonics Technol. Lett. 17, 1845 (2005).
[Crossref]

R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, “In-line frequency-non-degenerate phase-sensitive fiber parametric amplifier for fiber-optic communications,” to appear in Electron. Lett.

Evans, A. F.

M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, “Reduction of Raman MPI and noise figure in dispersion-managed fibre,” Electron. Lett. 38, 271 (2002).
[Crossref]

A. F. Evans, A. Kobyakov, and M. Vasilyev, “Distributed Raman transmission: applications and fiber issues,” in Raman Amplifiers in Telecommunications 2: Sub-Systems and Systems, ed. by M. N. Islam, Springer, New York, 2004, pp. 383–412.
[Crossref]

Friesem, A. A.

Gordon, J. P.

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, “Solitons in high bit-rate, long-distance transmission,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997), pp. 373–460.

Grainger, P.

Grigoryan, V. S.

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-Line Frequency-Nondegenerate Phase-Sensitive Fiber-Optical Parametric Amplifier,” IEEE Photonics Technol. Lett. 17, 1845 (2005).
[Crossref]

R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, “In-line frequency-non-degenerate phase-sensitive fiber parametric amplifier for fiber-optic communications,” to appear in Electron. Lett.

Grochocinski, J. M.

M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, “Reduction of Raman MPI and noise figure in dispersion-managed fibre,” Electron. Lett. 38, 271 (2002).
[Crossref]

Han, Y.

Haus, H. A.

Headley, C.

J.-C. Bouteiller, K. Brar, and C. Headley, “Quasi-constant signal power transmission,” European Conference on Optical Communication 2002, paper S3.04.

Hsia, C. H.

M. E. Marhic, C. H. Hsia, and J.-M. Jeong, Electron. Lett. 27, 210 (1991).
[Crossref]

Imajuku, W.

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35, 1954 (1999).
[Crossref]

W. Imajuku and A. Takada, “In-line optical phase-sensitive amplifier with pump light source controlled by optical phase-lock loop,” J. Lightwave Technol. 17, 637 (1999).
[Crossref]

A. Takada and W. Imajuku, “In-line optical phase-sensitive amplifier employing pump laser injection-locked to input signal light,” Electron. Lett. 34, 274 (1998).
[Crossref]

Jeong, J.-M.

M. E. Marhic, C. H. Hsia, and J.-M. Jeong, Electron. Lett. 27, 210 (1991).
[Crossref]

Kalogerakis, G.

G. Kalogerakis, K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, “Transmission of optical communication signals by distributed parametric amplification,” in Conference on Lasers and Electro-Optics 2005 (Optical Society of America, Washington, DC, 2005), paper CTuT2.
[Crossref]

Kath, W. L.

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, “All-optical storage of a picosecond-pulse packet using parametric amplification,” IEEE Photonics Technol. Lett. 9, 1020 (1997).
[Crossref]

J. N. Kutz, W. L. Kath, R.-D. Li, and P. Kumar, “Long-distance propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers,” Opt. Lett. 18, 802 (1993).
[Crossref] [PubMed]

Kawanishi, S.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600 (1998).
[Crossref]

Kazovsky, L. G.

G. Kalogerakis, K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, “Transmission of optical communication signals by distributed parametric amplification,” in Conference on Lasers and Electro-Optics 2005 (Optical Society of America, Washington, DC, 2005), paper CTuT2.
[Crossref]

Kim, C.

Kim, I.

Kimble, H. J.

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Quantum noise reduction in optical amplification,” Phys. Rev. Lett. 70, 3239 (1993).
[Crossref] [PubMed]

Kobyakov, A.

A. F. Evans, A. Kobyakov, and M. Vasilyev, “Distributed Raman transmission: applications and fiber issues,” in Raman Amplifiers in Telecommunications 2: Sub-Systems and Systems, ed. by M. N. Islam, Springer, New York, 2004, pp. 383–412.
[Crossref]

Koprulu, K. G.

P. L. Voss, K. G. Koprulu, and P. Kumar “Raman-noise induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” submitted to J. Opt. Soc. Am. B.

Kumar, P.

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-Line Frequency-Nondegenerate Phase-Sensitive Fiber-Optical Parametric Amplifier,” IEEE Photonics Technol. Lett. 17, 1845 (2005).
[Crossref]

P. L. Voss and P. Kumar, “Raman-noise-induced noise-figure limit for ?(3) parametric amplifiers,” Opt. Lett. 29, 445 (2004).
[Crossref] [PubMed]

D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA-Journal of Physics 56, 281 (2001).
[Crossref]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless Optical Amplification of Images,” Phys. Rev. Lett. 83, 1938 (1999).
[Crossref]

D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24, 984 (1999).
[Crossref]

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, “All-optical storage of a picosecond-pulse packet using parametric amplification,” IEEE Photonics Technol. Lett. 9, 1020 (1997).
[Crossref]

J. N. Kutz, W. L. Kath, R.-D. Li, and P. Kumar, “Long-distance propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers,” Opt. Lett. 18, 802 (1993).
[Crossref] [PubMed]

P. L. Voss, K. G. Koprulu, and P. Kumar “Raman-noise induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” submitted to J. Opt. Soc. Am. B.

R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, “In-line frequency-non-degenerate phase-sensitive fiber parametric amplifier for fiber-optic communications,” to appear in Electron. Lett.

Kutz, J. N.

Lakoba, T.

Levandovsky, D.

D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA-Journal of Physics 56, 281 (2001).
[Crossref]

D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24, 984 (1999).
[Crossref]

Levenson, J. A.

Levenson, M. D.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
[Crossref]

Li, G.

Li, R.-D.

Mamyshev, P. V.

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, “Solitons in high bit-rate, long-distance transmission,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997), pp. 373–460.

Marhic, M. E.

M. E. Marhic, C. H. Hsia, and J.-M. Jeong, Electron. Lett. 27, 210 (1991).
[Crossref]

G. Kalogerakis, K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, “Transmission of optical communication signals by distributed parametric amplification,” in Conference on Lasers and Electro-Optics 2005 (Optical Society of America, Washington, DC, 2005), paper CTuT2.
[Crossref]

McKinstrie, C. J.

Mecozzi, A.

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photonics Technol. Lett. 12, 392 (2000).
[Crossref]

Mollenauer, L. F.

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, “Solitons in high bit-rate, long-distance transmission,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997), pp. 373–460.

Mori, K.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600 (1998).
[Crossref]

Mu, Y.

Ou, Z. Y.

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Quantum noise reduction in optical amplification,” Phys. Rev. Lett. 70, 3239 (1993).
[Crossref] [PubMed]

Pereira, S. F.

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Quantum noise reduction in optical amplification,” Phys. Rev. Lett. 70, 3239 (1993).
[Crossref] [PubMed]

Radic, S.

Raymer, M. G.

Rivera, T.

Savage, C. M.

Serkland, D. K.

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, “All-optical storage of a picosecond-pulse packet using parametric amplification,” IEEE Photonics Technol. Lett. 9, 1020 (1997).
[Crossref]

Shake, I.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600 (1998).
[Crossref]

Shelby, R. M.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
[Crossref]

Shirasaki, M.

Shtaif, M.

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photonics Technol. Lett. 12, 392 (2000).
[Crossref]

Szalabofka, B.

M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, “Reduction of Raman MPI and noise figure in dispersion-managed fibre,” Electron. Lett. 38, 271 (2002).
[Crossref]

Takada, A.

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35, 1954 (1999).
[Crossref]

W. Imajuku and A. Takada, “In-line optical phase-sensitive amplifier with pump light source controlled by optical phase-lock loop,” J. Lightwave Technol. 17, 637 (1999).
[Crossref]

A. Takada and W. Imajuku, “In-line optical phase-sensitive amplifier employing pump laser injection-locked to input signal light,” Electron. Lett. 34, 274 (1998).
[Crossref]

Takara, H.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600 (1998).
[Crossref]

Tang, R.

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-Line Frequency-Nondegenerate Phase-Sensitive Fiber-Optical Parametric Amplifier,” IEEE Photonics Technol. Lett. 17, 1845 (2005).
[Crossref]

R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, “In-line frequency-non-degenerate phase-sensitive fiber parametric amplifier for fiber-optic communications,” to appear in Electron. Lett.

Tsuda, S.

M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, “Reduction of Raman MPI and noise figure in dispersion-managed fibre,” Electron. Lett. 38, 271 (2002).
[Crossref]

Vasilyev, M.

M. Vasilyev and T. Lakoba, “All-optical multi-channel 2R regeneration in a fiber-based device,” Opt. Lett. 30, 1458 (2005).
[Crossref] [PubMed]

M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, “Reduction of Raman MPI and noise figure in dispersion-managed fibre,” Electron. Lett. 38, 271 (2002).
[Crossref]

D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA-Journal of Physics 56, 281 (2001).
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A. F. Evans, A. Kobyakov, and M. Vasilyev, “Distributed Raman transmission: applications and fiber issues,” in Raman Amplifiers in Telecommunications 2: Sub-Systems and Systems, ed. by M. N. Islam, Springer, New York, 2004, pp. 383–412.
[Crossref]

M. Vasilyev, lecture notes for Nonlinear Optics course (University of Texas at Arlington, 2004).

M. Vasilyev, “Squeezing and fiber-optic communication,” 9th International Conference on Squeezed States and Uncertainty Relations 2005, May 2005, Besançon, France, paper I 79.

Voss, P. L.

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-Line Frequency-Nondegenerate Phase-Sensitive Fiber-Optical Parametric Amplifier,” IEEE Photonics Technol. Lett. 17, 1845 (2005).
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Wong, K. K. Y.

G. Kalogerakis, K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, “Transmission of optical communication signals by distributed parametric amplification,” in Conference on Lasers and Electro-Optics 2005 (Optical Society of America, Washington, DC, 2005), paper CTuT2.
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[Crossref]

M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, “Reduction of Raman MPI and noise figure in dispersion-managed fibre,” Electron. Lett. 38, 271 (2002).
[Crossref]

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600 (1998).
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D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA-Journal of Physics 56, 281 (2001).
[Crossref]

Other (12)

P. L. Voss, K. G. Koprulu, and P. Kumar “Raman-noise induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” submitted to J. Opt. Soc. Am. B.

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, “Solitons in high bit-rate, long-distance transmission,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997), pp. 373–460.

R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, “In-line frequency-non-degenerate phase-sensitive fiber parametric amplifier for fiber-optic communications,” to appear in Electron. Lett.

M. Vasilyev, “Raman-assisted transmission: toward ideal distributed amplification,” Optical Fiber Communication Conference 2003, Technical Digest (OSA, Washington, D.C.2003), Vol. 1, pp. 303–305, paper WB1.

A. F. Evans, A. Kobyakov, and M. Vasilyev, “Distributed Raman transmission: applications and fiber issues,” in Raman Amplifiers in Telecommunications 2: Sub-Systems and Systems, ed. by M. N. Islam, Springer, New York, 2004, pp. 383–412.
[Crossref]

J.-C. Bouteiller, K. Brar, and C. Headley, “Quasi-constant signal power transmission,” European Conference on Optical Communication 2002, paper S3.04.

M. Vasilyev, “Squeezing and fiber-optic communication,” 9th International Conference on Squeezed States and Uncertainty Relations 2005, May 2005, Besançon, France, paper I 79.

Here, conventional fiber is assumed to be averaging the nonlinear interaction over the signal states of polarization while preserving the relative orientation of the pump and signal. Coefficients a, b, ε, and εP are straightforwardly derived from Eq. (4.2.10) of [33], as done, for example, in [34].

R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003), Chap. 4.2.

M. Vasilyev, lecture notes for Nonlinear Optics course (University of Texas at Arlington, 2004).

G. P. Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 1995).

G. Kalogerakis, K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, “Transmission of optical communication signals by distributed parametric amplification,” in Conference on Lasers and Electro-Optics 2005 (Optical Society of America, Washington, DC, 2005), paper CTuT2.
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1.

Optical amplifier evolution quantified by the net NF limits of a fiber span. Numbers next to arrows show the signal-to-noise-ratio improvement for a 100-km-long span, accounting for signal-power adjustment by (ln G)/(1–1/G) between lumped and distributed amplifiers due to their difference in nonlinear path integrals. Dashed box shows focus of this paper.

Fig. 2.
Fig. 2.

Example of wideband square-law optical detector. The local oscillator LO with phase φ and cw wave are assumed to be separated by more than 2∆ω=ωS- ω I , i.e. WDM coupler can be used for their multiplexing. The output optical spectrum is related to the spectrum of fictitious homodyne photocurrent.

Fig. 3.
Fig. 3.

Left: comparison of the quantum limit 2-1/G for PIA NF (dashed) and direct-detected PSA NF of Eq. (7) increased by 3 dB to account for effective input SNR based on total power of signal and idler (solid). Right: comparison of overall link NF limits for different amplifiers (α=0.25 dB/km, span length between lumped amplifiers is L=100 km). Direct-detected distributed PSA is close to the distributed PSA limit for z >100 km. Lumped-case NFs have been adjusted by a ratio (1-e L )/(αL) to account for the difference between lumped and distributed path-averaged powers responsible for nonlinear penalties.

Fig. 4.
Fig. 4.

Transmission link with cascaded distributed PSAs. OPLL-optical phase-locked loop. PIA/BS-PIA or nonlinear beam splitter (BS). DSF-dispersion-shifted fiber. WDM-wavelength-division-multiplexing coupler for signal and Raman-pump bands. Inset diagrams show relative polarizations of the signal and idler with respect to the parametric and Raman pumps.

Equations (14)

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d A S , I dz = i γε [ 2 a ( P 1 + P 2 ) A S , I + 2 b A 1 A 2 A I , S + e i Δβz ] ,
d A 1 , 2 dz = i γε ( P 1,2 + 2 ε P P 2,1 ) A 1,2 .
A S ( z ) = μ A S ( 0 ) + v A I + ( 0 ) ,
A I ( z ) = μ A I ( 0 ) + v A S + ( 0 ) ,
μ = e i [ κ 2 + 2 γε a ( P 1 + P 2 ) ] z [ cosh gz i κ 2 g sinh gz ] ,
v = i e i [ κ 2 + 2 γε a ( P 1 + P 2 ) ] z 2 γε b g P 1 P 2 e i ( θ 1 + θ 2 ) sinh gz ,
A + = A S + A I 2 , A = A S A I 2 ,
X ± ( z ) = A ± ( z ) + A ± + ( z ) 2 = ( μ ± v ) X ± ( 0 ) ,
Y ± ( z ) = A ± ( z ) A ± + ( z ) 2 i = ( μ v ) Y ± ( 0 ) .
G PSA = ( μ + v ) 2 = ( G PIA + G PIA 1 ) 2 = exp ( 2 gz )
1 / G PSA = ( μ + v ) 2 = ( G PIA G PIA 1 ) 2 = exp ( 2 gz )
NF SIG PSA = 2 G PIA 1 ( G PIA + G PIA 1 ) 2 1 2
A S , I ( z ) = e αz / 2 [ μ A I , S ( 0 ) + v A I , S + ( 0 ) ] +
+ α 0 z e α ( z ' z ) / 2 { μ ( z ) [ μ * ( z ' ) c S ( z ' ) v ( z ' ) c I + ( z ' ) ] v ( z ) [ v * ( z ' ) c S ( z ' ) μ ( z ' ) c I + ( z ' ) ] } dz ' ,

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