Abstract

In a previous paper [Opt. Express 13, 4986 (2005)], formulas were derived for the field-quadrature and photon-number variances produced by multiple-mode parametric processes. In this paper, formulas are derived for the quadrature and number correlations. The number formulas are used to analyze the properties of basic devices, such as two-mode amplifiers, attenuators and frequency convertors, and composite systems made from these devices, such as cascaded parametric amplifiers and communication links. Amplifiers generate idlers that are correlated with the amplified signals, or correlate pre-existing pairs of modes, whereas attenuators decorrelate pre-existing modes. Both types of device modify the signal-to-noise ratios (SNRs) of the modes on which they act. Amplifiers decrease or increase the mode SNRs, depending on whether they are operated in phase-insensitive (PI) or phase-sensitive (PS) manners, respectively, whereas attenuators always decrease these SNRs. Two-mode PS links are sequences of transmission fibers (attenuators) followed by two-mode PS amplifiers. Not only do these PS links have noise figures that are 6-dB lower than those of the corresponding PI links, they also produce idlers that are (almost) completely correlated with the signals. By detecting the signals and idlers, one can eliminate the effects of electronic noise in the detectors.

© 2010 Optical Society of America

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  1. J. Hansryd, P. A. Andrekson, M. Westland, 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]
  2. S. Radic, and C. J. McKinstrie, “Optical amplification and signal processing in highly nonlinear optical fiber,” IEICE Trans. Electron,” E 88-C, 859–869 (2005).
    [CrossRef]
  3. P. A. Andrekson, and M. Westlund, “Nonlinear optical fiber based all-optical waveform sampling,” Laser Photon. Rev. 1, 231–248 (2007).
    [CrossRef]
  4. S. Radic, “Parametric amplification and processing in optical fibers,” Laser Photon. Rev. 2, 489–513 (2008).
    [CrossRef]
  5. 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]
  6. C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13, 4986–5012 (2005).
    [CrossRef]
  7. R. Loudon, and P. L. Knight, “Squeezed light,” J. Mod. Opt. 34, 709–759 (1987).
    [CrossRef]
  8. S. M. Barnett, and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 1997).
  9. N. Christensen, R. Leonhardt, and J. D. Harvey, “Noise characteristics of cross-phase modulation instability light,” Opt. Commun. 101, 205–212 (1993).
    [CrossRef]
  10. J. E. Sharping, M. Fiorentino, and P. Kumar, “Observation of twin-beam-type quantum correlation in optical fiber,” Opt. Lett. 26, 367–369 (2001).
    [CrossRef]
  11. R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-line frequency-nondegenerate phase-sensitive fiber-optical parametric amplifier,” IEEE Photon. Technol. Lett. 17, 1845–1847 (2005).
    [CrossRef]
  12. R. Tang, J. Lasri, P. S. Devgan, V. 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]
  13. C. Lundström, J. Kakande, P. A. Andrekson, Z. Tong, M. Karlsson, P. Petropoulos, F. Parmigiani and D. J. Richardson, “Experimental comparison of gain and saturation characteristics of a parametric amplifier in phase-sensitive and phase-insensitive mode,” ECOC 2009, paper 1.1.1.
  14. 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]
  15. R. Loudon, “Theory of noise accumulation in linear optical-amplifier chains,” J. Quantum Electron. 21, 766–773 (1985).
    [CrossRef]
  16. R. E. Slusher, and B. Yurke, “Squeezed light for coherent communications,” J. Lightwave Technol. 8, 466–477 (1990).
    [CrossRef]
  17. M. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13, 7563–7571 (2005).
    [CrossRef]
  18. C. J. McKinstrie, S. Radic, R. M. Jopson, and A. R. Chraplyvy, “Quantum noise limits on optical monitoring with parametric devices,” Opt. Commun. 259, 309–320 (2006).
    [CrossRef]
  19. J. M. Manley, and H. E. Rowe, “Some general properties of nonlinear elements–Part I. General energy relations,” Proc. IRE 44, 904–913 (1956).
  20. M. T. Weiss, “Quantum derivation of energy relations analogous to those for nonlinear reactances,” Proc. IRE 45, 1012–1013 (1957).
  21. C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
    [CrossRef]
  22. M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
    [CrossRef]
  23. Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18, 14820–14835 (2010).
    [CrossRef]
  24. 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-sensative amplifiers,” Opt. Express 18, 15426–15439 (2010).
    [CrossRef]
  25. L. A. Krivitsky, U. L. Andersen, R. Dong, A. Huck, C. Wittmann, and G. Leuchs, “Electronic noise-free measurements of squeezed light,” Opt. Lett. 33, 2395–2397 (2008).
    [CrossRef]
  26. C. J. McKinstrie, S. Radic, M. G. Raymer, and M. V. Vasilyev, “Quantum mechanics of phase-sensitive amplification in fibers,” Opt. Commun. 257, 146–163 (2006).
    [CrossRef]

2010 (4)

2008 (2)

2007 (1)

P. A. Andrekson, and M. Westlund, “Nonlinear optical fiber based all-optical waveform sampling,” Laser Photon. Rev. 1, 231–248 (2007).
[CrossRef]

2006 (2)

C. J. McKinstrie, S. Radic, R. M. Jopson, and A. R. Chraplyvy, “Quantum noise limits on optical monitoring with parametric devices,” Opt. Commun. 259, 309–320 (2006).
[CrossRef]

C. J. McKinstrie, S. Radic, M. G. Raymer, and M. V. Vasilyev, “Quantum mechanics of phase-sensitive amplification in fibers,” Opt. Commun. 257, 146–163 (2006).
[CrossRef]

2005 (6)

2004 (1)

2002 (1)

J. Hansryd, P. A. Andrekson, M. Westland, 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 (1)

1993 (1)

N. Christensen, R. Leonhardt, and J. D. Harvey, “Noise characteristics of cross-phase modulation instability light,” Opt. Commun. 101, 205–212 (1993).
[CrossRef]

1990 (1)

R. E. Slusher, and B. Yurke, “Squeezed light for coherent communications,” J. Lightwave Technol. 8, 466–477 (1990).
[CrossRef]

1987 (1)

R. Loudon, and P. L. Knight, “Squeezed light,” J. Mod. Opt. 34, 709–759 (1987).
[CrossRef]

1985 (1)

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

Andersen, U. L.

Andrekson, P. A.

Bogris, A.

Chraplyvy, A. R.

C. J. McKinstrie, S. Radic, R. M. Jopson, and A. R. Chraplyvy, “Quantum noise limits on optical monitoring with parametric devices,” Opt. Commun. 259, 309–320 (2006).
[CrossRef]

Christensen, N.

N. Christensen, R. Leonhardt, and J. D. Harvey, “Noise characteristics of cross-phase modulation instability light,” Opt. Commun. 101, 205–212 (1993).
[CrossRef]

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 Photon. Technol. Lett. 17, 1845–1847 (2005).
[CrossRef]

Devgan, P. S.

Dong, R.

Fiorentino, M.

Grigoryan, V.

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 Photon. Technol. Lett. 17, 1845–1847 (2005).
[CrossRef]

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westland, 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]

Harvey, J. D.

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
[CrossRef]

N. Christensen, R. Leonhardt, and J. D. Harvey, “Noise characteristics of cross-phase modulation instability light,” Opt. Commun. 101, 205–212 (1993).
[CrossRef]

Hedekvist, P. O.

J. Hansryd, P. A. Andrekson, M. Westland, 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]

Huck, A.

Jopson, R. M.

C. J. McKinstrie, S. Radic, R. M. Jopson, and A. R. Chraplyvy, “Quantum noise limits on optical monitoring with parametric devices,” Opt. Commun. 259, 309–320 (2006).
[CrossRef]

Kakande, J.

Karlsson, M.

Knight, P. L.

R. Loudon, and P. L. Knight, “Squeezed light,” J. Mod. Opt. 34, 709–759 (1987).
[CrossRef]

Krivitsky, L. A.

Kumar, P.

Lasri, J.

Leonhardt, R.

N. Christensen, R. Leonhardt, and J. D. Harvey, “Noise characteristics of cross-phase modulation instability light,” Opt. Commun. 101, 205–212 (1993).
[CrossRef]

Leuchs, G.

Li, J.

J. Hansryd, P. A. Andrekson, M. Westland, 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, and P. L. Knight, “Squeezed light,” J. Mod. Opt. 34, 709–759 (1987).
[CrossRef]

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

Lundström, C.

McGuinness, H. J.

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[CrossRef]

McKinstrie, C. J.

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-sensative amplifiers,” Opt. Express 18, 15426–15439 (2010).
[CrossRef]

Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18, 14820–14835 (2010).
[CrossRef]

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[CrossRef]

C. J. McKinstrie, S. Radic, R. M. Jopson, and A. R. Chraplyvy, “Quantum noise limits on optical monitoring with parametric devices,” Opt. Commun. 259, 309–320 (2006).
[CrossRef]

C. J. McKinstrie, S. Radic, M. G. Raymer, and M. V. Vasilyev, “Quantum mechanics of phase-sensitive amplification in fibers,” Opt. Commun. 257, 146–163 (2006).
[CrossRef]

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
[CrossRef]

S. Radic, and C. J. McKinstrie, “Optical amplification and signal processing in highly nonlinear optical fiber,” IEICE Trans. Electron,” E 88-C, 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]

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]

Parmigiani, F.

Petropoulos, P.

Radic, S.

S. Radic, “Parametric amplification and processing in optical fibers,” Laser Photon. Rev. 2, 489–513 (2008).
[CrossRef]

C. J. McKinstrie, S. Radic, R. M. Jopson, and A. R. Chraplyvy, “Quantum noise limits on optical monitoring with parametric devices,” Opt. Commun. 259, 309–320 (2006).
[CrossRef]

C. J. McKinstrie, S. Radic, M. G. Raymer, and M. V. Vasilyev, “Quantum mechanics of phase-sensitive amplification in fibers,” Opt. Commun. 257, 146–163 (2006).
[CrossRef]

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (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]

S. Radic, and C. J. McKinstrie, “Optical amplification and signal processing in highly nonlinear optical fiber,” IEICE Trans. Electron,” E 88-C, 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]

Raymer, M. G.

Richardson, D. J.

Sharping, J. E.

Slusher, R. E.

R. E. Slusher, and B. Yurke, “Squeezed light for coherent communications,” J. Lightwave Technol. 8, 466–477 (1990).
[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 Photon. Technol. Lett. 17, 1845–1847 (2005).
[CrossRef]

R. Tang, J. Lasri, P. S. Devgan, V. 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]

Tong, Z.

van Enk, S. J.

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[CrossRef]

Vasilyev, M.

Vasilyev, M. V.

C. J. McKinstrie, S. Radic, M. G. Raymer, and M. V. Vasilyev, “Quantum mechanics of phase-sensitive amplification in fibers,” Opt. Commun. 257, 146–163 (2006).
[CrossRef]

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 Photon. Technol. Lett. 17, 1845–1847 (2005).
[CrossRef]

Westland, M.

J. Hansryd, P. A. Andrekson, M. Westland, 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]

Westlund, M.

P. A. Andrekson, and M. Westlund, “Nonlinear optical fiber based all-optical waveform sampling,” Laser Photon. Rev. 1, 231–248 (2007).
[CrossRef]

Wittmann, C.

Yu, M.

Yurke, B.

R. E. Slusher, and B. Yurke, “Squeezed light for coherent communications,” J. Lightwave Technol. 8, 466–477 (1990).
[CrossRef]

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

J. Hansryd, P. A. Andrekson, M. Westland, 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. Technol. Lett. (1)

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-line frequency-nondegenerate phase-sensitive fiber-optical parametric amplifier,” IEEE Photon. Technol. Lett. 17, 1845–1847 (2005).
[CrossRef]

IEICE Trans. Electron. E (1)

S. Radic, and C. J. McKinstrie, “Optical amplification and signal processing in highly nonlinear optical fiber,” IEICE Trans. Electron,” E 88-C, 859–869 (2005).
[CrossRef]

J. Lightwave Technol. (1)

R. E. Slusher, and B. Yurke, “Squeezed light for coherent communications,” J. Lightwave Technol. 8, 466–477 (1990).
[CrossRef]

J. Mod. Opt. (1)

R. Loudon, and P. L. Knight, “Squeezed light,” J. Mod. Opt. 34, 709–759 (1987).
[CrossRef]

J. Quantum Electron. (1)

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

Laser Photon. Rev. (2)

P. A. Andrekson, and M. Westlund, “Nonlinear optical fiber based all-optical waveform sampling,” Laser Photon. Rev. 1, 231–248 (2007).
[CrossRef]

S. Radic, “Parametric amplification and processing in optical fibers,” Laser Photon. Rev. 2, 489–513 (2008).
[CrossRef]

Opt. Commun. (4)

N. Christensen, R. Leonhardt, and J. D. Harvey, “Noise characteristics of cross-phase modulation instability light,” Opt. Commun. 101, 205–212 (1993).
[CrossRef]

C. J. McKinstrie, S. Radic, R. M. Jopson, and A. R. Chraplyvy, “Quantum noise limits on optical monitoring with parametric devices,” Opt. Commun. 259, 309–320 (2006).
[CrossRef]

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[CrossRef]

C. J. McKinstrie, S. Radic, M. G. Raymer, and M. V. Vasilyev, “Quantum mechanics of phase-sensitive amplification in fibers,” Opt. Commun. 257, 146–163 (2006).
[CrossRef]

Opt. Express (8)

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
[CrossRef]

Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18, 14820–14835 (2010).
[CrossRef]

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-sensative amplifiers,” Opt. Express 18, 15426–15439 (2010).
[CrossRef]

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

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]

R. Tang, J. Lasri, P. S. Devgan, V. 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]

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]

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

Opt. Lett. (2)

Other (4)

S. M. Barnett, and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 1997).

C. Lundström, J. Kakande, P. A. Andrekson, Z. Tong, M. Karlsson, P. Petropoulos, F. Parmigiani and D. J. Richardson, “Experimental comparison of gain and saturation characteristics of a parametric amplifier in phase-sensitive and phase-insensitive mode,” ECOC 2009, paper 1.1.1.

J. M. Manley, and H. E. Rowe, “Some general properties of nonlinear elements–Part I. General energy relations,” Proc. IRE 44, 904–913 (1956).

M. T. Weiss, “Quantum derivation of energy relations analogous to those for nonlinear reactances,” Proc. IRE 45, 1012–1013 (1957).

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