Abstract

We present a theoretical analysis describing the spectral dependence of phase noise in one-pump fiber parametric amplifiers and converters. The analytical theory is experimentally validated and found to have high predictive accuracy. The implications related to phase-coded sensing and communications systems are discussed.

©2010 Optical Society of America

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  1. S. Radic, “Parametric amplification and processing in optical fibers,” Laser Photon. Rev. 2(6), 498–513 (2008).
    [Crossref]
  2. P. Kylemark, M. Karlsson, T. Torounidis, and P. A. Andrekson, “Noise Statistics in Fiber Optical Parametric Amplifiers,” J. Lightwave Technol. 25(2), 612–620 (2007).
    [Crossref]
  3. Z. Tong, A. Bogris, M. Karlsson, and P. A. Andrekson, “Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers,” Opt. Express 18(3), 2884–2893 (2010).
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  7. S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
    [Crossref]
  8. A. Durécu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump phase modulation on system performances of fiber optical parametric amplifiers,” Electron. Lett. 41(6), 350–352 (2005).
    [Crossref]
  9. P. Kylemark, J. Ren, Y. Myslivets, N. Alic, S. Radic, P. A. Andrekson, and M. Karlsson, “Impact of Pump Phase-Modulation on the Bit-Error Rate in Fiber-Optical Parametric-Amplifier-Based Systems,” IEEE Photon. Technol. Lett. 19(1), 79–81 (2007).
    [Crossref]
  10. R. Elschner, C.-A. Bunge, B. Huttl, A. G. i Coca, C. L. Schmidt, R. Ludwig, C. Schubert, and K. Petermann, “Impact of Pump-Phase Modulation on FWM-Based Wavelength Conversion of D(Q)PSK Signals,” IEEE J. Sel. Top. Quantum Electron. 14(3), 666–673 (2008).
    [Crossref]
  11. R. Jiang, C.-S. Bres, N. Alic, E. Myslivets, and S. Radic, “Translation of Gbps Phase-Modulated Optical Signal From Near-Infrared to Visible Band,” J. Lightwave Technol. 26(1), 131–137 (2008).
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  21. R. Elschner, and L. Petermann, “Impact of Pump-Induced Nonlinear Phase Noise on Parametric Amplification and Wavelength Conversion of Phase-Modulated Signals,” European Conference in Optical Communications, paper 3.3.4 (2009).
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  24. N. Alić, G. C. Papen, R. E. Saperstein, L. B. Milstein, and Y. Fainman, “Signal statistics and maximum likelihood sequence estimation in intensity modulated fiber optic links containing a single optical preamplifier,” Opt. Express 13(12), 4568–4579 (2005).
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  25. R. H. Stolen and J. E. Bjorkholm, “Parametric Amplification and Frequency Conversion in Optical Fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
    [Crossref]
  26. G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2007), Chap. 10.
  27. J. Hansryd and P. A. Andrekson, “Broad-Band Continuous-Wave-Pumped Fiber Optical Parametric Amplifier with 49-dB Gain and Wavelength-Conversion Efficiency,” IEEE Photon. Technol. Lett. 13(3), 194–196 (2001).
    [Crossref]
  28. J. B. Coles, B. P.-P. Kuo, N. Alic, S. Moro, C.-S. Bres, J. M. C. Boggio, P. A. Andrekson, M. Karlsson, and S. Radic, “Bandwidth-efficient phase modulation techniques for stimulated Brillouin scattering suppression in fiber optic parametric amplifiers,” Opt. Express 18(17), 18138–18150 (2010).
    [Crossref] [PubMed]
  29. J. M. Chavez Boggio, S. Moro, B. P.-P. Kuo, N. Alic, B. Stossel, and S. Radic, “Tunable Parametric All-Fiber Short-Wavelength IR Transmitter,” J. Lightwave Technol. 28(4), 443–447 (2010).
    [Crossref]
  30. J. W. Goodman, Statistical Optics (Wiley, 1985), Chap. 2.
  31. K. Shimoda, H. Takahasi, and C. H. Townes, “Fluctuations in Amplification of Quanta with Application to Maser Amplifiers,” J. Phys. Soc. Jpn. 12(6), 686–700 (1957).
    [Crossref]
  32. J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129(1), 481–485 (1963).
    [Crossref]
  33. C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13(13), 4986–5012 (2005).
    [Crossref] [PubMed]
  34. A. V. Kozlovskii, “Photodetection of a weak light signal in various quantum states by using an optical amplifier,” Quantum Electron. 36(3), 280–286 (2006).
    [Crossref]

2010 (3)

2009 (1)

2008 (5)

2007 (4)

2006 (1)

A. V. Kozlovskii, “Photodetection of a weak light signal in various quantum states by using an optical amplifier,” Quantum Electron. 36(3), 280–286 (2006).
[Crossref]

2005 (3)

2003 (1)

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
[Crossref]

2002 (1)

2001 (1)

J. Hansryd and P. A. Andrekson, “Broad-Band Continuous-Wave-Pumped Fiber Optical Parametric Amplifier with 49-dB Gain and Wavelength-Conversion Efficiency,” IEEE Photon. Technol. Lett. 13(3), 194–196 (2001).
[Crossref]

1990 (1)

1982 (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric Amplification and Frequency Conversion in Optical Fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[Crossref]

1963 (1)

J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129(1), 481–485 (1963).
[Crossref]

1957 (1)

K. Shimoda, H. Takahasi, and C. H. Townes, “Fluctuations in Amplification of Quanta with Application to Maser Amplifiers,” J. Phys. Soc. Jpn. 12(6), 686–700 (1957).
[Crossref]

Alic, N.

Andrekson, P. A.

Bayart, D.

A. Durécu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump phase modulation on system performances of fiber optical parametric amplifiers,” Electron. Lett. 41(6), 350–352 (2005).
[Crossref]

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, “Parametric Amplification and Frequency Conversion in Optical Fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[Crossref]

Boggio, J. M. C.

Bogris, A.

Brar, K.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
[Crossref]

Bres, C.-S.

Bunge, C.-A.

R. Elschner, C.-A. Bunge, B. Huttl, A. G. i Coca, C. L. Schmidt, R. Ludwig, C. Schubert, and K. Petermann, “Impact of Pump-Phase Modulation on FWM-Based Wavelength Conversion of D(Q)PSK Signals,” IEEE J. Sel. Top. Quantum Electron. 14(3), 666–673 (2008).
[Crossref]

Centanni, J. C.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
[Crossref]

Chavez Boggio, J. M.

Chraplyvy, A. R.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
[Crossref]

Coles, J. B.

Durécu-Legrand, A.

A. Durécu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump phase modulation on system performances of fiber optical parametric amplifiers,” Electron. Lett. 41(6), 350–352 (2005).
[Crossref]

Elschner, R.

R. Elschner, C.-A. Bunge, B. Huttl, A. G. i Coca, C. L. Schmidt, R. Ludwig, C. Schubert, and K. Petermann, “Impact of Pump-Phase Modulation on FWM-Based Wavelength Conversion of D(Q)PSK Signals,” IEEE J. Sel. Top. Quantum Electron. 14(3), 666–673 (2008).
[Crossref]

Fainman, Y.

Gordon, J. P.

J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15(23), 1351–1353 (1990).
[Crossref] [PubMed]

J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129(1), 481–485 (1963).
[Crossref]

Hansryd, J.

J. Hansryd and P. A. Andrekson, “Broad-Band Continuous-Wave-Pumped Fiber Optical Parametric Amplifier with 49-dB Gain and Wavelength-Conversion Efficiency,” IEEE Photon. Technol. Lett. 13(3), 194–196 (2001).
[Crossref]

Headley, C.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
[Crossref]

Ho, M.

Hussein, H.

Huttl, B.

R. Elschner, C.-A. Bunge, B. Huttl, A. G. i Coca, C. L. Schmidt, R. Ludwig, C. Schubert, and K. Petermann, “Impact of Pump-Phase Modulation on FWM-Based Wavelength Conversion of D(Q)PSK Signals,” IEEE J. Sel. Top. Quantum Electron. 14(3), 666–673 (2008).
[Crossref]

i Coca, A. G.

R. Elschner, C.-A. Bunge, B. Huttl, A. G. i Coca, C. L. Schmidt, R. Ludwig, C. Schubert, and K. Petermann, “Impact of Pump-Phase Modulation on FWM-Based Wavelength Conversion of D(Q)PSK Signals,” IEEE J. Sel. Top. Quantum Electron. 14(3), 666–673 (2008).
[Crossref]

Jiang, R.

Jopson, R. M.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
[Crossref]

Jorgensen, C. G.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
[Crossref]

Karlsson, M.

Kazovsky, L.

Kim, S.

Kim, S.-W.

Kim, Y.

Kim, Y.-J.

Kozlovskii, A. V.

A. V. Kozlovskii, “Photodetection of a weak light signal in various quantum states by using an optical amplifier,” Quantum Electron. 36(3), 280–286 (2006).
[Crossref]

Kuo, B. P.-P.

Kylemark, P.

P. Kylemark, M. Karlsson, T. Torounidis, and P. A. Andrekson, “Noise Statistics in Fiber Optical Parametric Amplifiers,” J. Lightwave Technol. 25(2), 612–620 (2007).
[Crossref]

P. Kylemark, J. Ren, Y. Myslivets, N. Alic, S. Radic, P. A. Andrekson, and M. Karlsson, “Impact of Pump Phase-Modulation on the Bit-Error Rate in Fiber-Optical Parametric-Amplifier-Based Systems,” IEEE Photon. Technol. Lett. 19(1), 79–81 (2007).
[Crossref]

Lantz, E.

A. Durécu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump phase modulation on system performances of fiber optical parametric amplifiers,” Electron. Lett. 41(6), 350–352 (2005).
[Crossref]

Louisell, W. H.

J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129(1), 481–485 (1963).
[Crossref]

Ludwig, R.

R. Elschner, C.-A. Bunge, B. Huttl, A. G. i Coca, C. L. Schmidt, R. Ludwig, C. Schubert, and K. Petermann, “Impact of Pump-Phase Modulation on FWM-Based Wavelength Conversion of D(Q)PSK Signals,” IEEE J. Sel. Top. Quantum Electron. 14(3), 666–673 (2008).
[Crossref]

Maillotte, H.

A. Durécu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump phase modulation on system performances of fiber optical parametric amplifiers,” Electron. Lett. 41(6), 350–352 (2005).
[Crossref]

Marhic, M. E.

Matsumoto, M.

McKinstrie, C. J.

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

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
[Crossref]

Milstein, L. B.

Mollenauer, L. F.

Moro, S.

Mussot, A.

A. Durécu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump phase modulation on system performances of fiber optical parametric amplifiers,” Electron. Lett. 41(6), 350–352 (2005).
[Crossref]

Myslivets, E.

Myslivets, Y.

P. Kylemark, J. Ren, Y. Myslivets, N. Alic, S. Radic, P. A. Andrekson, and M. Karlsson, “Impact of Pump Phase-Modulation on the Bit-Error Rate in Fiber-Optical Parametric-Amplifier-Based Systems,” IEEE Photon. Technol. Lett. 19(1), 79–81 (2007).
[Crossref]

Newbury, N. R.

Nishizawa, N.

Oda, S.

Papen, G. C.

Petermann, K.

R. Elschner, C.-A. Bunge, B. Huttl, A. G. i Coca, C. L. Schmidt, R. Ludwig, C. Schubert, and K. Petermann, “Impact of Pump-Phase Modulation on FWM-Based Wavelength Conversion of D(Q)PSK Signals,” IEEE J. Sel. Top. Quantum Electron. 14(3), 666–673 (2008).
[Crossref]

Radic, S.

J. B. Coles, B. P.-P. Kuo, N. Alic, S. Moro, C.-S. Bres, J. M. C. Boggio, P. A. Andrekson, M. Karlsson, and S. Radic, “Bandwidth-efficient phase modulation techniques for stimulated Brillouin scattering suppression in fiber optic parametric amplifiers,” Opt. Express 18(17), 18138–18150 (2010).
[Crossref] [PubMed]

J. M. Chavez Boggio, S. Moro, B. P.-P. Kuo, N. Alic, B. Stossel, and S. Radic, “Tunable Parametric All-Fiber Short-Wavelength IR Transmitter,” J. Lightwave Technol. 28(4), 443–447 (2010).
[Crossref]

S. Radic, “Parametric amplification and processing in optical fibers,” Laser Photon. Rev. 2(6), 498–513 (2008).
[Crossref]

R. Jiang, C.-S. Bres, N. Alic, E. Myslivets, and S. Radic, “Translation of Gbps Phase-Modulated Optical Signal From Near-Infrared to Visible Band,” J. Lightwave Technol. 26(1), 131–137 (2008).
[Crossref]

P. Kylemark, J. Ren, Y. Myslivets, N. Alic, S. Radic, P. A. Andrekson, and M. Karlsson, “Impact of Pump Phase-Modulation on the Bit-Error Rate in Fiber-Optical Parametric-Amplifier-Based Systems,” IEEE Photon. Technol. Lett. 19(1), 79–81 (2007).
[Crossref]

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

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
[Crossref]

Raymer, M. G.

Ren, J.

P. Kylemark, J. Ren, Y. Myslivets, N. Alic, S. Radic, P. A. Andrekson, and M. Karlsson, “Impact of Pump Phase-Modulation on the Bit-Error Rate in Fiber-Optical Parametric-Amplifier-Based Systems,” IEEE Photon. Technol. Lett. 19(1), 79–81 (2007).
[Crossref]

Saperstein, R. E.

Schmidt, C. L.

R. Elschner, C.-A. Bunge, B. Huttl, A. G. i Coca, C. L. Schmidt, R. Ludwig, C. Schubert, and K. Petermann, “Impact of Pump-Phase Modulation on FWM-Based Wavelength Conversion of D(Q)PSK Signals,” IEEE J. Sel. Top. Quantum Electron. 14(3), 666–673 (2008).
[Crossref]

Schubert, C.

R. Elschner, C.-A. Bunge, B. Huttl, A. G. i Coca, C. L. Schmidt, R. Ludwig, C. Schubert, and K. Petermann, “Impact of Pump-Phase Modulation on FWM-Based Wavelength Conversion of D(Q)PSK Signals,” IEEE J. Sel. Top. Quantum Electron. 14(3), 666–673 (2008).
[Crossref]

Shimoda, K.

K. Shimoda, H. Takahasi, and C. H. Townes, “Fluctuations in Amplification of Quanta with Application to Maser Amplifiers,” J. Phys. Soc. Jpn. 12(6), 686–700 (1957).
[Crossref]

Simonneau, C.

A. Durécu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump phase modulation on system performances of fiber optical parametric amplifiers,” Electron. Lett. 41(6), 350–352 (2005).
[Crossref]

Sköld, M.

Stolen, R. H.

R. H. Stolen and J. E. Bjorkholm, “Parametric Amplification and Frequency Conversion in Optical Fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[Crossref]

Stossel, B.

Sunnerud, H.

Swann, W. C.

Sylvestre, T.

A. Durécu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump phase modulation on system performances of fiber optical parametric amplifiers,” Electron. Lett. 41(6), 350–352 (2005).
[Crossref]

Takahasi, H.

K. Shimoda, H. Takahasi, and C. H. Townes, “Fluctuations in Amplification of Quanta with Application to Maser Amplifiers,” J. Phys. Soc. Jpn. 12(6), 686–700 (1957).
[Crossref]

Takayanagi, J.

Tong, Z.

Torounidis, T.

Townes, C. H.

K. Shimoda, H. Takahasi, and C. H. Townes, “Fluctuations in Amplification of Quanta with Application to Maser Amplifiers,” J. Phys. Soc. Jpn. 12(6), 686–700 (1957).
[Crossref]

Walker, L. R.

J. P. Gordon, W. H. Louisell, and L. R. Walker, “Quantum fluctuations and noise in parametric processes II,” Phys. Rev. 129(1), 481–485 (1963).
[Crossref]

Wong, K. Y. K.

Yang, J.

Yu, M.

Electron. Lett. (1)

A. Durécu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump phase modulation on system performances of fiber optical parametric amplifiers,” Electron. Lett. 41(6), 350–352 (2005).
[Crossref]

IEEE J. Quantum Electron. (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric Amplification and Frequency Conversion in Optical Fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Elschner, C.-A. Bunge, B. Huttl, A. G. i Coca, C. L. Schmidt, R. Ludwig, C. Schubert, and K. Petermann, “Impact of Pump-Phase Modulation on FWM-Based Wavelength Conversion of D(Q)PSK Signals,” IEEE J. Sel. Top. Quantum Electron. 14(3), 666–673 (2008).
[Crossref]

IEEE Photon. Technol. Lett. (3)

P. Kylemark, J. Ren, Y. Myslivets, N. Alic, S. Radic, P. A. Andrekson, and M. Karlsson, “Impact of Pump Phase-Modulation on the Bit-Error Rate in Fiber-Optical Parametric-Amplifier-Based Systems,” IEEE Photon. Technol. Lett. 19(1), 79–81 (2007).
[Crossref]

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, “Selective Suppression of Idler Spectral Broadening in Two-Pump Parametric Architectures,” IEEE Photon. Technol. Lett. 15(5), 673–675 (2003).
[Crossref]

J. Hansryd and P. A. Andrekson, “Broad-Band Continuous-Wave-Pumped Fiber Optical Parametric Amplifier with 49-dB Gain and Wavelength-Conversion Efficiency,” IEEE Photon. Technol. Lett. 13(3), 194–196 (2001).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. B (2)

J. Phys. Soc. Jpn. (1)

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[Crossref]

Laser Photon. Rev. (1)

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[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. (1)

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[Crossref]

Quantum Electron. (1)

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[Crossref]

Other (10)

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Figures (9)

Fig. 1
Fig. 1 FOPA model schematic used in the derivation of NPN statistics; Acronyms: OBPF - optical band-pass filter; the rest of the symbols are defined within the text.

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Fig. 2
Fig. 2 (a) Nonlinear phase SNR vs. pump OSNR and optical Gaussian noise filter 3-dB bandwidth; (b) Signal and idler phase and amplitude SNR spectra due to NPN.

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Fig. 3
Fig. 3 Spectral dependence of signal phase SNR when only PMN is present (a) for a range of RF noise bandwidths, (b) for 600MHz RF noise bandwidth.

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Fig. 4
Fig. 4 Schematic of parametric amplification of quantum noise in a one-pump FOPA. Acronyms: Ps – signal power, νs – signal frequency, νp – pump frequency, Pp – pump power, OBPF – optical band-pass filter, νi – idler frequency, Gs – signal gain, Δν – optical filter bandwidth, AQN – amplified quantum noise.

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Fig. 5
Fig. 5 Analytical/numerical signal phase SNR (when only AQN is present): (a) spectrum for two different input signal powers; (b) dependence on input signal power at the signal wavelength of 1545.0nm.

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Fig. 6
Fig. 6 Experimental setup for measurement of phase noise of a FOPA; Inset: electrical waveforms observed after intra-dyne detection of the two output ports of the 90° hybrid. Acronyms: PM – phase modulator, LPF – low-pass (RF) filter, VOA – variable optical attenuator, EDFA – Erbium-doped fiber amplifier, CWDM – coarse wavelength-division multiplexer, HNLF – highly nonlinear fiber, OBPF – optical band-pass filter, LO – local oscillator, ADC – analog-to-digital converter.

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Fig. 7
Fig. 7 (a) Optical spectra for two different signal wavelengths, (b) Measured FOPA gain spectrum.

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Fig. 8
Fig. 8 (a) Optical spectra of pump/signal/idler after HNLF; (b) Signal spectrum before and after FOPA. The three disjoint spectral bands centered around the three characteristic wavelengths (signal - 1545.0nm, pump - 1568.0nm, and idler - 1591.7nm) have been shifted for easier comparison.

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Fig. 9
Fig. 9 Measured, simulated, and analytically predicted signal phase and amplitude SNR spectra for input pump OSNR of 40dB.

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Tables (1)

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Table 1 FOPA simulation/experimental parameters

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Equations (11)

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ρ ' ( t ) = P p + n ( t ) ⊗ h i n ( t ) = P p + n ' ( t ) ,
ρ ' ' ( t ) = ( P p + n ' ( t ) ) e j γ L | P p + n ' ( t ) | 2 = ( P p + n ' ( t ) ) e j ϕ N L ( t ) .
ϕ N L ( t ) = γ P p L + 2 γ P p L n ' r ( t ) + γ L | n ' ( t ) | 2 .
p Φ N L ( ϕ N L ) = 1 γ L N 0 ' e − ϕ N L + γ P p L γ L N 0 ' I 0 ( 4 P p γ L N 0 ' 2 ϕ N L ) .
κ ( t ) = Δ β ( t ) + 2 γ | P p + n ' ( t ) | 2 ,
g ( t ) = ( γ | P p + n ' ( t ) | 2 ) 2 − ( κ ( t ) 2 ) 2 .
ϕ s ( t , L ) = ϕ s ( t , 0 ) + tan − 1 ( κ ( t ) sinh [ g ( t ) L ] 2 g ( t ) cosh [ g ( t ) L ] ) + γ | P p + n ' ( t ) | 2 L − Δ β ( t ) L 2 + Δ ϕ s , A Q N ,
ϕ i ( t , L ) = [ 2 ϕ p ( t , 0 ) − ϕ s ( t , 0 ) ] + π 2 + γ | P p + n ' ( t ) | 2 L − Δ β ( t ) L 2 + Δ ϕ i , A Q N .
Δ β ( t ) = − 2 π c ν p 2 ( t ) S ( c ν p ( t ) − λ o ) ( c / λ s − ν p ( t ) ) 2 .
P A Q N = h ν 2 ( G s + G s − 1 ) Δ ν = h ν 2 ( 2 G s − 1 ) Δ ν .
S N R p h a s e = 1 σ 2 Δ ϕ A Q N = 4 G s P s h ν ( 2 G s − 1 ) Δ ν .

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