Abstract

Semi-classical noise characteristics are derived for the cascade of a non-degenerate phase-insensitive (PI) and a phase-sensitive (PS) fiber optical parametric amplifier (FOPA). The analysis is proved to be consistent with the quantum theory under the large-photon number assumption. Based on this, we show that the noise figure (NF) of the PS-FOPA at the second stage can be obtained via relative-intensity-noise (RIN) subtraction method after averaging the signal and idler NFs. Negative signal and idler NFs are measured, and <2 dB NF at >16 dB PS gain is estimated when considering the combined signal and idler input, which is believed to be the lowest measured NF of a non-degenerate PS amplifier to this date. The limitation of the RIN subtraction method attributed to pump transferred noise and Raman phonon induced noise is also discussed.

© 2010 OSA

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    [CrossRef]
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    [CrossRef]
  3. K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007).
    [CrossRef]
  4. D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24(14), 984–986 (1999).
    [CrossRef]
  5. D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–, J. Phys. 56, 281–285 (2001).
    [CrossRef]
  6. W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954–1955 (1999).
    [CrossRef]
  7. W. Imajuku and A. Takada, “Error-free operation of in-line phase-sensitive amplifier,” Electron. Lett. 34(17), 1673–1674 (1998).
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    [CrossRef]
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    [CrossRef]
  13. C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12(21), 5037–5066 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-21-5037 .
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    [CrossRef]
  24. A. Mecozzi and P. Tombesi, “Parametric amplification and signal-to-noise ratio in optical transmission lines,” Opt. Commun. 75(3-4), 256–262 (1990).
    [CrossRef]
  25. N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7(7), 1071–1082 (1989).
    [CrossRef]
  26. E. Desuvire, “Comments on ‘The noise figure of optical amplifiers’,” IEEE Photon. Technol. Lett. 11(5), 620–621 (1999).
    [CrossRef]
  27. 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 (submitted to).
    [PubMed]
  28. M. Movassaghi, M. K. Jackson, V. M. Smith, and W. J. Hallam, “Noise figure of erbium-doped fiber amplifiers in saturated operation,” J. Lightwave Technol. 16(5), 1461–1465 (1998).
    [CrossRef]
  29. P. L. Voss and P. Kumar, “Raman-effect induced noise limits on χ(3) parametric amplifiers and wavelength converters,” J. Opt. B Quantum Semiclassical Opt. 6(8), 762–770 (2004) (and references therein).
    [CrossRef]
  30. P. Kylemark, P. –O. Hedekvist, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Noise characteristics of fiber optical parametric amplifiers,” J. Lightwave Technol. 22, 409–416 (2004) and 23, 2192 (2005).
    [CrossRef]
  31. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2884 .
    [CrossRef] [PubMed]
  32. P. Kylemark, M. Karlsson, and P. A. Andrekson, “Gain and wavelength dependence of the noise-figure in fiber optical parametric amplifiers,” IEEE Photon. Technol. Lett. 18(11), 1255–1257 (2006).
    [CrossRef]
  33. X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express 12(16), 3737–3744 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3737 .
    [CrossRef] [PubMed]

2010 (2)

2008 (1)

2007 (1)

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007).
[CrossRef]

2006 (3)

C. J. McKinstrie, M. G. Raymer, S. Radic, and M. Vasilyev, “Quantum mechanics of phase-sensitive amplification in a fiber,” Opt. Commun. 257(1), 146–163 (2006).
[CrossRef]

P. Kylemark, M. Karlsson, and P. A. Andrekson, “Gain and wavelength dependence of the noise-figure in fiber optical parametric amplifiers,” IEEE Photon. Technol. Lett. 18(11), 1255–1257 (2006).
[CrossRef]

P. L. Voss, K. G. Köprülü, and P. Kumar, “Raman-noise-induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” J. Opt. Soc. Am. B 23(4), 598–610 (2006).
[CrossRef]

2005 (4)

2004 (5)

2001 (1)

D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–, J. Phys. 56, 281–285 (2001).
[CrossRef]

1999 (3)

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954–1955 (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(14), 984–986 (1999).
[CrossRef]

E. Desuvire, “Comments on ‘The noise figure of optical amplifiers’,” IEEE Photon. Technol. Lett. 11(5), 620–621 (1999).
[CrossRef]

1998 (2)

M. Movassaghi, M. K. Jackson, V. M. Smith, and W. J. Hallam, “Noise figure of erbium-doped fiber amplifiers in saturated operation,” J. Lightwave Technol. 16(5), 1461–1465 (1998).
[CrossRef]

W. Imajuku and A. Takada, “Error-free operation of in-line phase-sensitive amplifier,” Electron. Lett. 34(17), 1673–1674 (1998).
[CrossRef]

1991 (1)

M. E. Marhic, C. H. Hsia, and J. M. Jeong, “Optical amplification in a nonlinear fibre interferometer,” Electron. Lett. 27(3), 210–211 (1991).
[CrossRef]

1990 (1)

A. Mecozzi and P. Tombesi, “Parametric amplification and signal-to-noise ratio in optical transmission lines,” Opt. Commun. 75(3-4), 256–262 (1990).
[CrossRef]

1989 (1)

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7(7), 1071–1082 (1989).
[CrossRef]

1982 (1)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982).
[CrossRef]

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 afiber-optic parametric amplifier in phase-sensitive and phase-insensitive operation,” Opt. Express 18(5), 4130–4137 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4130 .
[CrossRef] [PubMed]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2884 .
[CrossRef] [PubMed]

P. Kylemark, M. Karlsson, and P. A. Andrekson, “Gain and wavelength dependence of the noise-figure in fiber optical parametric amplifiers,” IEEE Photon. Technol. Lett. 18(11), 1255–1257 (2006).
[CrossRef]

P. Kylemark, P. –O. Hedekvist, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Noise characteristics of fiber optical parametric amplifiers,” J. Lightwave Technol. 22, 409–416 (2004) and 23, 2192 (2005).
[CrossRef]

P. Kylemark, P.-O. Hedekvist, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Noise characteristics of fiber optical parametric amplifiers,” J. Lightwave Technol. 22(2), 409–416 (2004).
[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-sensitive amplifiers,” Opt. Express (submitted to).
[PubMed]

Bogris, A.

Caves, C. M.

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982).
[CrossRef]

Chen, J.

Croussore, K.

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007).
[CrossRef]

Desuvire, E.

E. Desuvire, “Comments on ‘The noise figure of optical amplifiers’,” IEEE Photon. Technol. Lett. 11(5), 620–621 (1999).
[CrossRef]

Devgan, P.

R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, “Inline frequency-non-degenerate phase-sensitive fibre parametric amplifier for fibre-optic communication,” Electron. Lett. 41(19), 1072–1074 (2005).
[CrossRef]

Devgan, P. S.

Grigoryan, V. S.

Hallam, W. J.

M. Movassaghi, M. K. Jackson, V. M. Smith, and W. J. Hallam, “Noise figure of erbium-doped fiber amplifiers in saturated operation,” J. Lightwave Technol. 16(5), 1461–1465 (1998).
[CrossRef]

Hedekvist, P. –O.

Hedekvist, P.-O.

Hsia, C. H.

M. E. Marhic, C. H. Hsia, and J. M. Jeong, “Optical amplification in a nonlinear fibre interferometer,” Electron. Lett. 27(3), 210–211 (1991).
[CrossRef]

Imajuku, W.

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954–1955 (1999).
[CrossRef]

W. Imajuku and A. Takada, “Error-free operation of in-line phase-sensitive amplifier,” Electron. Lett. 34(17), 1673–1674 (1998).
[CrossRef]

Jackson, M. K.

M. Movassaghi, M. K. Jackson, V. M. Smith, and W. J. Hallam, “Noise figure of erbium-doped fiber amplifiers in saturated operation,” J. Lightwave Technol. 16(5), 1461–1465 (1998).
[CrossRef]

Jeong, J. M.

M. E. Marhic, C. H. Hsia, and J. M. Jeong, “Optical amplification in a nonlinear fibre interferometer,” Electron. Lett. 27(3), 210–211 (1991).
[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 afiber-optic parametric amplifier in phase-sensitive and phase-insensitive operation,” Opt. Express 18(5), 4130–4137 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4130 .
[CrossRef] [PubMed]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2884 .
[CrossRef] [PubMed]

P. Kylemark, M. Karlsson, and P. A. Andrekson, “Gain and wavelength dependence of the noise-figure in fiber optical parametric amplifiers,” IEEE Photon. Technol. Lett. 18(11), 1255–1257 (2006).
[CrossRef]

P. Kylemark, P. –O. Hedekvist, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Noise characteristics of fiber optical parametric amplifiers,” J. Lightwave Technol. 22, 409–416 (2004) and 23, 2192 (2005).
[CrossRef]

P. Kylemark, P.-O. Hedekvist, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Noise characteristics of fiber optical parametric amplifiers,” J. Lightwave Technol. 22(2), 409–416 (2004).
[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-sensitive amplifiers,” Opt. Express (submitted to).
[PubMed]

Köprülü, K. G.

Kumar, P.

R. Tang, P. S. Devgan, V. S. Grigoryan, P. Kumar, and M. Vasilyev, “In-line phase-sensitive amplification of multi-channel CW signals based on frequency nondegenerate four-wave-mixing in fiber,” Opt. Express 16(12), 9046–9053 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-12-9046 .
[CrossRef] [PubMed]

P. L. Voss, K. G. Köprülü, and P. Kumar, “Raman-noise-induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” J. Opt. Soc. Am. B 23(4), 598–610 (2006).
[CrossRef]

R. Tang, J. Lasri, P. S. Devgan, V. S. Grigoryan, P. Kumar, and M. Vasilyev, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13(26), 10483–10493 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-13-26-10483 .
[CrossRef] [PubMed]

R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, “Inline frequency-non-degenerate phase-sensitive fibre parametric amplifier for fibre-optic communication,” Electron. Lett. 41(19), 1072–1074 (2005).
[CrossRef]

P. L. Voss and P. Kumar, “Raman-effect induced noise limits on χ(3) parametric amplifiers and wavelength converters,” J. Opt. B Quantum Semiclassical Opt. 6(8), 762–770 (2004) (and references therein).
[CrossRef]

X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express 12(16), 3737–3744 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3737 .
[CrossRef] [PubMed]

D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–, J. Phys. 56, 281–285 (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(14), 984–986 (1999).
[CrossRef]

Kylemark, P.

Lasri, J.

Levandovsky, D.

D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–, J. Phys. 56, 281–285 (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(14), 984–986 (1999).
[CrossRef]

Li, G.

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007).
[CrossRef]

Li, X.

Lundström, C.

Marhic, M. E.

M. E. Marhic, C. H. Hsia, and J. M. Jeong, “Optical amplification in a nonlinear fibre interferometer,” Electron. Lett. 27(3), 210–211 (1991).
[CrossRef]

McKinstrie, C. J.

C. J. McKinstrie, M. G. Raymer, S. Radic, and M. Vasilyev, “Quantum mechanics of phase-sensitive amplification in a fiber,” Opt. Commun. 257(1), 146–163 (2006).
[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), http://www.opticsinfobase.org/oe/abstract.cfm?uri=OE-13-13-4986 .
[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(21), 5037–5066 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-21-5037 .
[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 (submitted to).
[PubMed]

Mecozzi, A.

A. Mecozzi and P. Tombesi, “Parametric amplification and signal-to-noise ratio in optical transmission lines,” Opt. Commun. 75(3-4), 256–262 (1990).
[CrossRef]

Movassaghi, M.

M. Movassaghi, M. K. Jackson, V. M. Smith, and W. J. Hallam, “Noise figure of erbium-doped fiber amplifiers in saturated operation,” J. Lightwave Technol. 16(5), 1461–1465 (1998).
[CrossRef]

Olsson, N. A.

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7(7), 1071–1082 (1989).
[CrossRef]

Parmigiani, F.

Petropoulos, P.

Radic, S.

Raymer, M. G.

Richardson, D. J.

Sharping, J.

Smith, V. M.

M. Movassaghi, M. K. Jackson, V. M. Smith, and W. J. Hallam, “Noise figure of erbium-doped fiber amplifiers in saturated operation,” J. Lightwave Technol. 16(5), 1461–1465 (1998).
[CrossRef]

Sunnerud, H.

Takada, A.

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954–1955 (1999).
[CrossRef]

W. Imajuku and A. Takada, “Error-free operation of in-line phase-sensitive amplifier,” Electron. Lett. 34(17), 1673–1674 (1998).
[CrossRef]

Tang, R.

Tombesi, P.

A. Mecozzi and P. Tombesi, “Parametric amplification and signal-to-noise ratio in optical transmission lines,” Opt. Commun. 75(3-4), 256–262 (1990).
[CrossRef]

Tong, Z.

Vasilyev, M.

Voss, P.

Voss, P. L.

P. L. Voss, K. G. Köprülü, and P. Kumar, “Raman-noise-induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” J. Opt. Soc. Am. B 23(4), 598–610 (2006).
[CrossRef]

P. L. Voss and P. Kumar, “Raman-effect induced noise limits on χ(3) parametric amplifiers and wavelength converters,” J. Opt. B Quantum Semiclassical Opt. 6(8), 762–770 (2004) (and references therein).
[CrossRef]

Yamabayashi, Y.

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954–1955 (1999).
[CrossRef]

Yu, M.

Electron. Lett. (4)

M. E. Marhic, C. H. Hsia, and J. M. Jeong, “Optical amplification in a nonlinear fibre interferometer,” Electron. Lett. 27(3), 210–211 (1991).
[CrossRef]

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954–1955 (1999).
[CrossRef]

W. Imajuku and A. Takada, “Error-free operation of in-line phase-sensitive amplifier,” Electron. Lett. 34(17), 1673–1674 (1998).
[CrossRef]

R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, “Inline frequency-non-degenerate phase-sensitive fibre parametric amplifier for fibre-optic communication,” Electron. Lett. 41(19), 1072–1074 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007).
[CrossRef]

E. Desuvire, “Comments on ‘The noise figure of optical amplifiers’,” IEEE Photon. Technol. Lett. 11(5), 620–621 (1999).
[CrossRef]

P. Kylemark, M. Karlsson, and P. A. Andrekson, “Gain and wavelength dependence of the noise-figure in fiber optical parametric amplifiers,” IEEE Photon. Technol. Lett. 18(11), 1255–1257 (2006).
[CrossRef]

J. Lightwave Technol. (4)

J. Opt. B Quantum Semiclassical Opt. (1)

P. L. Voss and P. Kumar, “Raman-effect induced noise limits on χ(3) parametric amplifiers and wavelength converters,” J. Opt. B Quantum Semiclassical Opt. 6(8), 762–770 (2004) (and references therein).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

C. J. McKinstrie, M. G. Raymer, S. Radic, and M. Vasilyev, “Quantum mechanics of phase-sensitive amplification in a fiber,” Opt. Commun. 257(1), 146–163 (2006).
[CrossRef]

A. Mecozzi and P. Tombesi, “Parametric amplification and signal-to-noise ratio in optical transmission lines,” Opt. Commun. 75(3-4), 256–262 (1990).
[CrossRef]

Opt. Express (9)

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 (submitted to).
[PubMed]

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[CrossRef]

Other (6)

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Z. Tong, C. Lundström, A. Bogris, M. Karlsson, P. Andrekson, and D. Syvridis, “Measurement of sub-1 dB noise figure in a non-degenerate cascaded phase-sensitive fiber parametric amplifier,” in European Conference on Optical Communications, paper Mo. 1.1.2 (2009).

G. Obarski, “Precise calibration for optical amplifier noise figure measurement using the RIN subtraction method,” in Optical Fiber Communications Conference, paper ThZ3 (2003).

E. Desuvire, Erbium-doped fiber amplifiers (John Wiley and Sons, 1994), Chap. 2.

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,” in European Conference on Optical Communications, paper Mo. 1.1.1 (2009).

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Figures (8)

Fig. 1
Fig. 1

Schematic of a non-degenerate PIA+ATT+PSA cascade, and the principle diagram of the RIN subtraction measurement. Sin and Sout are the noise PSD measured at the PSA input and output.

Fig. 2
Fig. 2

Comparison of the minimum ideal and equivalent NF vs. PSA gain, according to Eq. (21) and (26), respectively. The PIA gain is fixed at 10 dB.

Fig. 3
Fig. 3

Measurement setup. NFA: Noise figure analyzer; ESA: Electrical spectrum analyzer; OSA: Optical spectrum analyzer; PC: Polarization controller; ATT: Variable attenuator. Inset (a) shows the theoretical and measured shot noise level after calibration vs. the detected photocurrent, and Inset (b) shows the electrical noise spectrum measured by the ESA, where the spurious tones are due to the pump phase- to intensity-modulation transfer.

Fig. 4
Fig. 4

Measured PSA, PIA gain and PSA NF spectra of the signal wave at a) the anti-Stokes and b) Stokes bands, and the PSA gain and NF spectra of the idler wave at c) the anti-Stokes and d) Stokes bands.

Fig. 5
Fig. 5

Output PSA noise spectra with a) 3 m and b) 7 m mid-stage SMF. The OSA resolution bandwidth is 0.1 nm.

Fig. 6
Fig. 6

Measured PSA, PIA gain and PSA NF spectra of the signal wave at a) the anti-Stokes and b) Stokes bands, and the PSA gain and NF spectra of the idler wave at c) the anti-Stokes and d) Stokes bands.

Fig. 7
Fig. 7

Averaged PSA gain and equivalent NF spectra by taking average of the signal and idler gains and NFs [Eq. (27)] at a) the anti-Stokes and b) the Stokes bands.

Fig. 8
Fig. 8

Measured signal and idler NF as a function of input power, and the estimated equivalent NF at averaged input power. Minimum −1dB equivalent NF can be observed.

Equations (47)

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[ A s A i * ] = [ μ ν ν * μ * ] [ A s 0 A i 0 * ] = G [ A s 0 A i 0 * ] ,
[ A s , P I A A i , P I A * ] = [ μ 1 ν 1 ν 1 * μ 1 * ] [ A s 0 + δ A s δ A i * ] = G 1 [ A s 0 + δ A s δ A i * ] ,
[ A s , P I A + A T T A i , P I A + A T T * ] = [ T s 0 0 T i ] [ A s , P I A A i , P I A * ] + [ 1 T s δ A s ' 1 T i δ A i ' ] = T ^ [ A s , P I A A i , P I A * ] ,
[ A s , P I A + A T T + P S A A i , P I A + A T T + P S A * ] = [ μ 2 ν 2 ν 2 * μ 2 * ] [ e j φ 1 0 0 e j φ 2 ] [ A s , P I A + A T T A i , P I A + A T T * ] = G 2 D [ A s , P I A + A T T A i , P I A + A T T * ] ,
[ A s , P I A + A T T + P S A A i , P I A + A T T + P S A * ] = G 2 D T ^ G 1 [ A s 0 + δ A s δ A i * ] = T [ μ s 12 ν s 12 ν i 12 * μ i 12 * ] [ A s 0 + δ A s δ A i * ] + 1 T [ μ 2 e j φ 1 ν 2 e j φ 2 ν 2 * e j φ 1 μ 2 * e j φ 2 ] [ δ A s ' δ A i * ' ] , = T [ μ s 12 ν s 12 ν i 12 * μ i 12 * ] [ A s 0 + δ A s δ A i * ] + 1 T [ μ 2 e j φ 1 ν 2 e j φ 2 ν 2 * e j φ 1 μ 2 * e j φ 2 ] [ δ A s ' δ A i * ' ] ,
μ s 12 = μ 1 μ 2 e j φ 1 + ν 1 * ν 2 e j φ 2 , ν s 12 = ν 1 μ 2 e j φ 1 + μ 1 * ν 2 e j φ 2 , μ i 12 = μ 1 μ 2 e j φ 2 + ν 1 * ν 2 e j φ 1 , ν i 12 = ν 1 μ 2 e j φ 2 + μ 1 * ν 2 e j φ 1 .
G 12 ( ϕ ) = | μ s 12 | 2 = | μ i 12 | 2 = | μ 1 μ 2 | 2 + | ν 1 ν 2 | 2 + 2 | μ 1 μ 2 ν 1 ν 2 | cos ( ϕ ) = G 1 G 2 + ( G 1 1 ) ( G 2 1 ) + 2 G 1 G 2 ( G 1 1 ) ( G 2 1 ) cos ( ϕ ) ,
G 12 ( ϕ ) 1 = | ν s 12 | 2 = | ν i 12 | 2 = | ν 1 μ 2 | 2 + | μ 1 ν 2 | 2 + 2 | μ 1 μ 2 ν 1 ν 2 | cos ( ϕ ) = ( G 1 1 ) G 2 + G 1 ( G 2 1 ) + 2 G 1 G 2 ( G 1 1 ) ( G 2 1 ) cos ( ϕ ) ,
G s , P S A ( ϕ ) = G 12 ( ϕ ) / G 1 , G i , P S A ( ϕ ) = [ G 12 ( ϕ ) 1 ] / ( G 1 1 ) .
G s , P S A ( 2 m π ) = ( | μ 1 μ 2 | + | ν 1 ν 2 | ) 2 / | μ 1 | 2 = [ G 1 G 2 + ( G 1 1 ) ( G 2 1 ) ] 2 / G 1 ,
G i , P S A ( 2 m π ) = ( | ν 1 μ 2 | + | μ 1 ν 2 | ) 2 / | ν 1 | 2 = [ ( G 1 1 ) G 2 + G 1 ( G 2 1 ) ] 2 / ( G 1 1 ) .
G s , P S A ( 2 m π ) G i , P S A ( 2 m π ) 4 G 2 ,
G s , P S A [ ( 2 m + 1 ) π ] ) ( G 1 + G 2 ) 2 / 4 G 1 2 G 2 , G i , P S A [ ( 2 m + 1 ) π ] ( G 1 G 2 ) 2 / 4 G 1 2 G 2 ,
S s , o u t = 4 R 2 P s 0 T G 12 ( ϕ ) h v s 2 { [ 2 G 12 ( ϕ ) 1 ] T + ( 2 G 2 1 ) ( 1 T ) } ,
S i , o u t = 4 R 2 P s 0 T [ G 12 ( ϕ ) 1 ] h v s 2 { [ 2 G 12 ( ϕ ) 1 ] T + ( 2 G 2 1 ) ( 1 T ) } ,
N F s , i = ( 2 G 1 ) / G P S A ( ϕ ) ,
N F s = 1 / G s , P S A + P s 0 T G 1 ( S s , o u t S s , i n ) / ( 2 h v s I s , o u t 2 ) , N F i = 1 / G i , P S A + P s 0 T ( G 1 1 ) ( S i , o u t S i , i n ) / ( 2 h v i I i , o u t 2 ) ,
T a = G k , P S A T T b ,
I s , o u t = R P s 0 G 12 T T b , I i , o u t = R P s 0 ( G 12 1 ) T T b .
S k , i n = 4 R 2 G 1 T a P s 0 h v k 2 [ 2 G 1 T a + ( 1 T a ) ] ,
S k , o u t = 4 R 2 P s 0 T T b G 12 ( ϕ ) h v k 2 { [ 2 G 12 ( ϕ ) T + ( 2 G 2 1 ) ( 1 T ) ] T b + ( 1 T b ) } ,
N F i d e a l ( ϕ ) = [ G P S A ( φ ) T + ( 2 G 2 1 ) ( 1 T ) ] / G P S A ( ϕ ) ,
S s , i n = 4 R 2 G 1 T a P s 0 h v s 2 [ ( 2 G 1 1 ) T a + ( 1 T a ) ] ,
S s , o u t = 4 R 2 P s 0 T T b G 12 ( ϕ ) h v s 2 { [ ( 2 G 12 ( ϕ ) T + 2 G 2 ( 1 T ) 1 ] T b + ( 1 T b ) } .
N F s ( ϕ ) = [ 2 G 2 2 G 2 T + 2 G s , P S A ( ϕ ) T 1 ] / G s , P S A ( ϕ ) .
N F i ( ϕ ) = [ 2 G 2 2 G 2 T + 2 T 1 ] / G i , P S A ( ϕ ) ,
N F e q = ( N F s + N F i ) / 2 N F i d e a l ,
Δ S k , i n P T N = 4 [ R P s 0 ( G 1 P P ) T a P P ] 2 / ( 2 O S N R Δ v ) ,
Δ S k , o u t P T N = 4 [ R P s 0 ( G 12 ( ϕ ) P P ) T T b P P ] 2 / ( 2 O S N R Δ v ) ,
Δ N F k P T N = P s 0 P P 2 T [ ( G P S A P P ) 2 G 1 + 2 ( G 1 P P ) ( G P S A P P ) G P S A ] O S N R G P S A 2 h v k Δ v ,
Δ S k , i n u c = r 4 R 2 G 1 2 T a 2 P s 0 h v k ,
Δ S k , o u t u c = r 4 R 2 G 12 2 ( ϕ ) T 2 T b 2 P s 0 ( 2 G 2 1 ) h v k / G P S A .
Δ N F k u c = 2 r G 1 T ( 2 G 2 G P S A 1 ) / G P S A .
Δ N F k u c r G 1 T ,
b s = μ a s + ν a i ,
b i = μ a i + ν a s ,
b s = τ a s + ρ a l ,
b l = ρ * a s + τ * a l ,
c s = ( τ s μ 1 ) a s + ( τ s ν 1 ) a i + ρ s a l ,
c i = ( τ i μ 1 ) a i + ( τ i ν 1 ) a s + ρ i a m ,
δ n s _ P I A + A T T 2 = | τ μ 1 | 4 n s + | τ μ 1 | 2 ( | τ ν 1 | 2 + | ρ | 2 ) n s + | τ ν 1 | 2 ( | τ μ 1 | 2 + | ρ | 2 ) ,
δ n i _ P I A + A T T 2 = | τ ν 1 | 4 n s + | τ ν 1 | 2 ( | τ μ 1 | 2 + | ρ | 2 ) n s + | τ ν 1 | 2 ( | τ μ 1 | 2 + | ρ | 2 ) ,
d s = μ 11 a s + ν 12 a i + μ 13 a l + ν 14 a m ,
d i = ν 21 a s + μ 22 a i + ν 23 a l + μ 24 a m .
μ 11 = μ 2 μ 1 τ e j φ 1 + ν 2 ν 1 * τ * e j φ 2 , μ 22 = μ 2 μ 1 τ e j φ 2 + ν 2 ν 1 * τ * e j φ 1 , ν 12 = μ 2 ν 1 τ e j φ 1 + ν 2 μ 1 * τ * e j φ 2 , ν 21 = μ 2 ν 1 τ e j φ 2 + ν 2 μ 1 * τ * e j φ 1 , μ 13 = μ 24 = μ 2 ρ , ν 14 = ν 23 = ν 2 ρ * ,
δ n s _ P I A + A T T + P S A 2 = | μ 11 | 4 n s + | μ 11 | 2 ( | ν 12 | 2 + | μ 13 | 2 + | ν 14 | 2 ) n s + ( | μ 11 | 2 + | μ 13 | 2 ) ( | ν 12 | 2 + | ν 14 | 2 ) ,
δ n i _ P I A + A T T + P S A 2 = | ν 21 | 4 n s + | ν 21 | 2 ( | μ 22 | 2 + | ν 23 | 2 + | μ 24 | 2 ) n s + ( | μ 22 | 2 + | μ 24 | 2 ) ( | ν 21 | 2 + | ν 23 | 2 ) ,

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