Abstract

We theoretically and experimentally analyze the dominant impairment mechanisms affecting the fidelity of optical phase in parametric amplifiers and converters in media characterized by third-order (Kerr) optical nonlinearity. The critical role of narrow-band pump filtering in parametric mixers is quantified with respect to frequency stability of amplified and converted waves. The analysis is generally applicable to all four-photon devices used to generate new frequencies or translate spectral bands.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Radic, “Parametric amplification and processing in optical fibers,” Laser Photon. Rev. 2(6), 498–513 (2008).
    [CrossRef]
  2. R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (2006).
    [CrossRef]
  3. J. M. Chavez Boggio, S. Moro, B. P.-P. Kuo, N. Alic, B. Stossel, and S. Radic, “Tunable All-Fiber Short-Wavelength-IR Transmitter,” Optical Fiber Communications Conference, paper PDPC9 (2009).
  4. 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]
  5. W. H. Louisell, Radiation and Noise in Quantum Electronics (McGraw-Hill, 1964).
  6. 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).
    [CrossRef] [PubMed]
  7. 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]
  8. A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-Induced Changes in Optical Polarization in Glasses,” Phys. Rev. B 5(2), 628–633 (1972).
    [CrossRef]
  9. 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]
  10. Y. Kim, S. Kim, Y.-J. Kim, H. Hussein, and S.-W. Kim, “Er-doped fiber frequency comb with mHz relative linewidth,” Opt. Express 17(14), 11972–11977 (2009).
    [CrossRef] [PubMed]
  11. N. Nishizawa and J. Takayanagi, “Octave spanning high-quality supercontinuum generation in all-fiber system,” J. Opt. Soc. Am. B 24(8), 1786–1792 (2007).
    [CrossRef]
  12. N. R. Newbury and W. C. Swann, “Low-noise fiber-laser frequency combs,” J. Opt. Soc. Am. B 24(8), 1756–1770 (2007).
    [CrossRef]
  13. S. J. McNaught, J. E. Rothenberg, P. A. Thielen, M. G. Wickham, M. E. Weber, and G. D. Goodno, “Coherent Combining of a 1.26-kW Fiber Amplifier,” Advanced in Solid-State Photonics, paper AMA2 (2010).
  14. K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005), Chap. 5.
  15. M. Sköld, J. Yang, H. Sunnerud, M. Karlsson, S. Oda, and P. A. Andrekson, “Constellation diagram analysis of DPSK signal regeneration in a saturated parametric amplifier,” Opt. Express 16(9), 5974–5982 (2008).
    [CrossRef] [PubMed]
  16. M. Skold, M. Karlsson, S. Oda, H. Sunnerud, and P. A. Andrekson, “Constellation diagram measurements of induced phase noise in a regenerating parametric amplifier,” Optical Fiber Communications Conference, paper OML4 (2008).
  17. M. Matsumoto, “Phase noise generation in an amplitude limiter using saturation of a fiber-optic parametric amplifier,” Opt. Lett. 33(15), 1638–1640 (2008).
    [CrossRef] [PubMed]
  18. R. Elschner, and K. 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).
  19. H. Kim, “Cross-Phase-Modulation-Induced Nonlinear Phase Noise in WDM Direct-Detection DPSK Systems,” J. Lightwave Technol. 21(8), 1770–1774 (2003).
    [CrossRef]
  20. R. Loudon, The Quantum Theory of Light (Oxford University Press, 2000).
  21. 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]
  22. J. W. Goodman, Statistical Optics (Wiley, 1985), Chap. 3.
  23. P. G. Hoel, S. C. Port, and C. J. Stone, Introduction to Stochastic Processes (Waveland Press, 1987).
  24. S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of Equalized Broadband Parametric Gain by Localized Dispersion Mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
    [CrossRef]
  25. G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2007).

2010 (1)

2009 (1)

2008 (4)

M. Sköld, J. Yang, H. Sunnerud, M. Karlsson, S. Oda, and P. A. Andrekson, “Constellation diagram analysis of DPSK signal regeneration in a saturated parametric amplifier,” Opt. Express 16(9), 5974–5982 (2008).
[CrossRef] [PubMed]

M. Matsumoto, “Phase noise generation in an amplitude limiter using saturation of a fiber-optic parametric amplifier,” Opt. Lett. 33(15), 1638–1640 (2008).
[CrossRef] [PubMed]

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

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of Equalized Broadband Parametric Gain by Localized Dispersion Mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[CrossRef]

2007 (2)

2006 (1)

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (2006).
[CrossRef]

2005 (2)

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]

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]

2003 (1)

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]

1972 (1)

A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-Induced Changes in Optical Polarization in Glasses,” Phys. Rev. B 5(2), 628–633 (1972).
[CrossRef]

Alic, N.

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of Equalized Broadband Parametric Gain by Localized Dispersion Mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[CrossRef]

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (2006).
[CrossRef]

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]

Bogris, A.

Chavez Boggio, J. M.

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of Equalized Broadband Parametric Gain by Localized Dispersion Mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[CrossRef]

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]

Fainman, Y.

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (2006).
[CrossRef]

Ford, J.

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (2006).
[CrossRef]

George, N.

A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-Induced Changes in Optical Polarization in Glasses,” Phys. Rev. B 5(2), 628–633 (1972).
[CrossRef]

Gordon, J. P.

Hellwarth, R. W.

A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-Induced Changes in Optical Polarization in Glasses,” Phys. Rev. B 5(2), 628–633 (1972).
[CrossRef]

Hussein, H.

Jiang, R.

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (2006).
[CrossRef]

Karlsson, M.

Kim, H.

Kim, S.

Kim, S.-W.

Kim, Y.

Kim, Y.-J.

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]

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]

Matsumoto, M.

McKinstrie, C.

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (2006).
[CrossRef]

McKinstrie, C. J.

Mollenauer, L. F.

Moro, S.

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of Equalized Broadband Parametric Gain by Localized Dispersion Mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[CrossRef]

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.

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of Equalized Broadband Parametric Gain by Localized Dispersion Mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[CrossRef]

Newbury, N. R.

Nezhad, M.

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (2006).
[CrossRef]

Nishizawa, N.

Oda, S.

Owyoung, A.

A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-Induced Changes in Optical Polarization in Glasses,” Phys. Rev. B 5(2), 628–633 (1972).
[CrossRef]

Radic, S.

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

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of Equalized Broadband Parametric Gain by Localized Dispersion Mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[CrossRef]

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (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).
[CrossRef] [PubMed]

Raymer, M. G.

Saperstein, R.

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (2006).
[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]

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]

Takayanagi, J.

Tong, Z.

Windmiller, J. R.

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of Equalized Broadband Parametric Gain by Localized Dispersion Mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[CrossRef]

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 Photon. Technol. Lett. (2)

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “Parametric Wavelength Conversion from Conventional Near-Infrared to Visible Band,” IEEE Photon. Technol. Lett. 18(23), 2445–2447 (2006).
[CrossRef]

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of Equalized Broadband Parametric Gain by Localized Dispersion Mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[CrossRef]

J. Lightwave Technol. (1)

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

Laser Photon. Rev. (1)

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

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. B (1)

A. Owyoung, R. W. Hellwarth, and N. George, “Intensity-Induced Changes in Optical Polarization in Glasses,” Phys. Rev. B 5(2), 628–633 (1972).
[CrossRef]

Other (10)

W. H. Louisell, Radiation and Noise in Quantum Electronics (McGraw-Hill, 1964).

S. J. McNaught, J. E. Rothenberg, P. A. Thielen, M. G. Wickham, M. E. Weber, and G. D. Goodno, “Coherent Combining of a 1.26-kW Fiber Amplifier,” Advanced in Solid-State Photonics, paper AMA2 (2010).

K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005), Chap. 5.

M. Skold, M. Karlsson, S. Oda, H. Sunnerud, and P. A. Andrekson, “Constellation diagram measurements of induced phase noise in a regenerating parametric amplifier,” Optical Fiber Communications Conference, paper OML4 (2008).

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

J. M. Chavez Boggio, S. Moro, B. P.-P. Kuo, N. Alic, B. Stossel, and S. Radic, “Tunable All-Fiber Short-Wavelength-IR Transmitter,” Optical Fiber Communications Conference, paper PDPC9 (2009).

J. W. Goodman, Statistical Optics (Wiley, 1985), Chap. 3.

P. G. Hoel, S. C. Port, and C. J. Stone, Introduction to Stochastic Processes (Waveland Press, 1987).

G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2007).

R. Elschner, and K. 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).

Cited By

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

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic for analytical derivation of NPN/NC statistics; Acronyms: OBPF - optical band-pass filter.

Fig. 2
Fig. 2

(a) Schematic illustrating the influence of ω2 weighting factor on two different noise power spectral densities; Standard deviation of (b) NPN and (c) NC vs. pump OSNR and 3-dB optical Gaussian noise filter bandwidth.

Fig. 3
Fig. 3

Experimental setup for noise-induced NC measurement; Left inset: measured optical filter transfer functions; Right inset: optical spectrum after HNLF propagation; Acronyms: AM – amplitude modulator, EDFA – Erbium doped fiber amplifier, CWDM – coarse wavelength division multiplexer, OBPF – optical band-pass filter, VOA – variable optical attenuator, SMF – single-mode fiber, Rx – optical receiver.

Fig. 4
Fig. 4

(a) Measured pump SNR vs. optical filter bandwidth following PM-to-AM in SMF; (b) Standard deviation of NPN and NC vs. optical filter bandwidth.

Fig. 5
Fig. 5

Schematic for semi-analytical model of PM-to-AM in optical fiber.

Equations (11)

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

Δ ϕ N L ( t ) = 2 γ P p L n ' r ( t ) + γ L | n ' ( t ) | 2 ,
σ 2 Δ ϕ N L = 2 γ 2 L 2 P p S n ' ( ω ) d ω ,
Δ f N L ( t ) = 1 2 π d [ Δ ϕ N L ( t ) ] d t = γ P p L π d n ' r ( t ) d t .
E { | d n ' ( t ) d t | 2 } = 2 t s R ( t , s ) | t = s = R ( 2 ) ( 0 ) = ω 2 S n ' ( ω ) d ω ,
σ 2 Δ f N L = γ 2 L 2 P p 2 π 2 ω 2 S n ' ( ω ) d ω .
ρ ( t ) = P p + n ( t ) h i n ( t ) .
ρ ' ( t ) = ρ ( t ) × e j γ L | ρ ( t ) | 2 = ρ ( t ) × e j ϕ N L ( t ) .
ρ ' ' ( t ) = 1 { { ρ ' ( t ) } × e j D ^ ( ω ) L S M F } ,
D ^ ( ω ) = β 2 ( ω r e f ) 2 ( ω ω r e f ) 2 + β 3 ( ω r e f ) 6 ( ω ω r e f ) 3 .
ρ ' ' ' ( t ) = | ρ ' ' ( t ) | 2 h e l e c ( t ) ,
S N R = ρ ' ' ' ( t ) 2 σ 2 ρ ' ' ' ( t ) ,

Metrics