Abstract

We investigate the combined effect of Raman and parametric gain on single-pump parametric amplifiers. The phasematched parametric gain is shown to depend strongly on the real part of the complex Raman susceptibility. In fused silica fibers this results in a significant reduction in the available parametric gain for signal detunings beyond 10 THz. We are able to experimentally measure this effect for signal detunings ranging from 7 to 22 THz. Finally we discuss the implications of these results for the design of broadband optical parametric amplifiers.

© 2007 Optical Society of America

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  1. G. P. Agrawal, , Nonlinear Fiber Optics, Optics and Photonics Series (Academic, San Diego, Calif., 2001).
  2. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, , “Fiber–based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum. Electron. 8, 506–520 (2002).
    [Crossref]
  3. C. Headley and G. P. Agrawal, , eds., Raman Amplification in Optical Fiber Communications, (Elsevier, San Diego, Calif., 2005).
  4. N. Bloembergen and Y. R. Shen, , “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
    [Crossref]
  5. M. D. Duncan, R. Mahon, J. Reintjes, and L. L. Tankersley, “Parametric Raman gain suppression in D2 and H2,” Opt. Lett. 11, 803–805 (1986).
    [Crossref] [PubMed]
  6. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [Crossref]
  7. S. Trillo and S. Wabnitz, “Parametric and Raman amplification in birefringent fibers,” J. Opt. Soc. Am. B 9, 1061–1082 (1992).
    [Crossref]
  8. E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
    [Crossref]
  9. F. Vanholsbeeck, P. Emplit, and S. Coen, “Complete experimental characterization of the influence of parametric four-wave mixing on stimulated Raman gain,” Opt. Lett. 281960–1962 (2003).
    [Crossref] [PubMed]
  10. A. S. Y. Hsieh, S. G. Murdoch, S. Coen, R. Leonhardt, and J. D. Harvey, “Influence of Raman susceptibility on parametric amplification in optical fibers,” Opt. Lett. 32, 521–523 (2007).
    [Crossref] [PubMed]
  11. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989).
    [Crossref]
  12. P.Tchofo Dinda, E. Seve, G. Millot, T. Sylvestre, H. Maillotte, and E. Lantz, “Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion,” Opt. Commun. 192, 107–121 (2001).
    [Crossref]
  13. M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21, 573–575 (1996).
    [Crossref] [PubMed]
  14. 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, 194–196 (2001).
    [Crossref]
  15. S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
    [Crossref]
  16. J. S. Y. Chen, S. G. Murdoch, R. Leonhardt, and J. D. Harvey, “Effect of dispersion fluctuations on widely tunable optical parametric amplification in photonic crystal fibers,” Opt. Express 14, 9491–9501 (2006).
    [Crossref] [PubMed]
  17. S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
    [Crossref]
  18. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber” Opt. Lett. 28, 2225–2227 (2003).
    [Crossref] [PubMed]
  19. M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wideband tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum. Electron. 10, 1133–1141 (2004).
    [Crossref]
  20. S. Wabnitz, “Broadband parametric amplification in photonic crystal fibers with two zero-dispersion wavelengths,” J. Lightwave Tech. 24, 1732–1738 (2006).
    [Crossref]
  21. M. Hirano, T. Nakanishi, T. Okunko, and M. Onishi, “Selective FWM-based wavelength conversion realized by highly nonlinear fiber” in Proc. European conference on optical communications, September 2006, Cannes, France, paper Th. 1.3.5.
  22. C. J. Mckinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum. Electron. 8, 538–547 (2002).
    [Crossref]

2007 (1)

2006 (3)

J. S. Y. Chen, S. G. Murdoch, R. Leonhardt, and J. D. Harvey, “Effect of dispersion fluctuations on widely tunable optical parametric amplification in photonic crystal fibers,” Opt. Express 14, 9491–9501 (2006).
[Crossref] [PubMed]

S. Wabnitz, “Broadband parametric amplification in photonic crystal fibers with two zero-dispersion wavelengths,” J. Lightwave Tech. 24, 1732–1738 (2006).
[Crossref]

M. Hirano, T. Nakanishi, T. Okunko, and M. Onishi, “Selective FWM-based wavelength conversion realized by highly nonlinear fiber” in Proc. European conference on optical communications, September 2006, Cannes, France, paper Th. 1.3.5.

2004 (1)

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wideband tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum. Electron. 10, 1133–1141 (2004).
[Crossref]

2003 (3)

2002 (3)

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
[Crossref]

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, , “Fiber–based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum. Electron. 8, 506–520 (2002).
[Crossref]

C. J. Mckinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum. Electron. 8, 538–547 (2002).
[Crossref]

2001 (2)

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, 194–196 (2001).
[Crossref]

P.Tchofo Dinda, E. Seve, G. Millot, T. Sylvestre, H. Maillotte, and E. Lantz, “Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion,” Opt. Commun. 192, 107–121 (2001).
[Crossref]

1996 (1)

1992 (1)

1990 (1)

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

1989 (2)

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989).
[Crossref]

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

1986 (1)

1964 (1)

N. Bloembergen and Y. R. Shen, , “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, , Nonlinear Fiber Optics, Optics and Photonics Series (Academic, San Diego, Calif., 2001).

C. Headley and G. P. Agrawal, , eds., Raman Amplification in Optical Fiber Communications, (Elsevier, San Diego, Calif., 2005).

Andrekson, P. A.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, , “Fiber–based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum. Electron. 8, 506–520 (2002).
[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, 194–196 (2001).
[Crossref]

Bloembergen, N.

N. Bloembergen and Y. R. Shen, , “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[Crossref]

Blow, K. J.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

Chen, J. S. Y.

Chiang, T. K.

Chraplyvy, A. R.

C. J. Mckinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum. Electron. 8, 538–547 (2002).
[Crossref]

Coen, S.

Dianov, E. M.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

Dinda, P.Tchofo

P.Tchofo Dinda, E. Seve, G. Millot, T. Sylvestre, H. Maillotte, and E. Lantz, “Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion,” Opt. Commun. 192, 107–121 (2001).
[Crossref]

Duncan, M. D.

Emplit, P.

Golovchenko, E.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

Gordon, J. P.

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, , “Fiber–based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum. Electron. 8, 506–520 (2002).
[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, 194–196 (2001).
[Crossref]

Harvey, J. D.

Haus, H. A.

Headley, C.

C. Headley and G. P. Agrawal, , eds., Raman Amplification in Optical Fiber Communications, (Elsevier, San Diego, Calif., 2005).

Hedekvist, P.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, , “Fiber–based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum. Electron. 8, 506–520 (2002).
[Crossref]

Hirano, M.

M. Hirano, T. Nakanishi, T. Okunko, and M. Onishi, “Selective FWM-based wavelength conversion realized by highly nonlinear fiber” in Proc. European conference on optical communications, September 2006, Cannes, France, paper Th. 1.3.5.

Hsieh, A. S. Y.

Kagi, N.

Kazovsky, L. G.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wideband tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum. Electron. 10, 1133–1141 (2004).
[Crossref]

M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21, 573–575 (1996).
[Crossref] [PubMed]

Knight, J. C.

Lantz, E.

P.Tchofo Dinda, E. Seve, G. Millot, T. Sylvestre, H. Maillotte, and E. Lantz, “Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion,” Opt. Commun. 192, 107–121 (2001).
[Crossref]

Leonhardt, R.

Li, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, , “Fiber–based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum. Electron. 8, 506–520 (2002).
[Crossref]

Mahon, R.

Maillotte, H.

P.Tchofo Dinda, E. Seve, G. Millot, T. Sylvestre, H. Maillotte, and E. Lantz, “Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion,” Opt. Commun. 192, 107–121 (2001).
[Crossref]

Mamyshev, P. V.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

Marhic, M. E.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wideband tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum. Electron. 10, 1133–1141 (2004).
[Crossref]

M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21, 573–575 (1996).
[Crossref] [PubMed]

Mckinstrie, C. J.

C. J. Mckinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum. Electron. 8, 538–547 (2002).
[Crossref]

Millot, G.

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
[Crossref]

P.Tchofo Dinda, E. Seve, G. Millot, T. Sylvestre, H. Maillotte, and E. Lantz, “Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion,” Opt. Commun. 192, 107–121 (2001).
[Crossref]

Murdoch, S. G.

Nakanishi, T.

M. Hirano, T. Nakanishi, T. Okunko, and M. Onishi, “Selective FWM-based wavelength conversion realized by highly nonlinear fiber” in Proc. European conference on optical communications, September 2006, Cannes, France, paper Th. 1.3.5.

Okunko, T.

M. Hirano, T. Nakanishi, T. Okunko, and M. Onishi, “Selective FWM-based wavelength conversion realized by highly nonlinear fiber” in Proc. European conference on optical communications, September 2006, Cannes, France, paper Th. 1.3.5.

Onishi, M.

M. Hirano, T. Nakanishi, T. Okunko, and M. Onishi, “Selective FWM-based wavelength conversion realized by highly nonlinear fiber” in Proc. European conference on optical communications, September 2006, Cannes, France, paper Th. 1.3.5.

Pilipetskii, A. N.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

Pitois, S.

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
[Crossref]

Radic, S.

C. J. Mckinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum. Electron. 8, 538–547 (2002).
[Crossref]

Reintjes, J.

Russell, P. St. J.

Seve, E.

P.Tchofo Dinda, E. Seve, G. Millot, T. Sylvestre, H. Maillotte, and E. Lantz, “Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion,” Opt. Commun. 192, 107–121 (2001).
[Crossref]

Shen, Y. R.

N. Bloembergen and Y. R. Shen, , “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[Crossref]

Stolen, R. H.

Sylvestre, T.

P.Tchofo Dinda, E. Seve, G. Millot, T. Sylvestre, H. Maillotte, and E. Lantz, “Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion,” Opt. Commun. 192, 107–121 (2001).
[Crossref]

Tankersley, L. L.

Tomlinson, W. J.

Trillo, S.

Vanholsbeeck, F.

Wabnitz, S.

S. Wabnitz, “Broadband parametric amplification in photonic crystal fibers with two zero-dispersion wavelengths,” J. Lightwave Tech. 24, 1732–1738 (2006).
[Crossref]

S. Trillo and S. Wabnitz, “Parametric and Raman amplification in birefringent fibers,” J. Opt. Soc. Am. B 9, 1061–1082 (1992).
[Crossref]

Wadsworth, W. J.

Wardle, D. A.

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
[Crossref]

Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, , “Fiber–based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum. Electron. 8, 506–520 (2002).
[Crossref]

Wong, G. K. L.

Wong, K. K. Y.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wideband tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum. Electron. 10, 1133–1141 (2004).
[Crossref]

Wood, D.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

IEEE J. Quantum Electron. (2)

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

IEEE J. Sel. Top. Quantum. Electron. (3)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, , “Fiber–based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum. Electron. 8, 506–520 (2002).
[Crossref]

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wideband tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum. Electron. 10, 1133–1141 (2004).
[Crossref]

C. J. Mckinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum. Electron. 8, 538–547 (2002).
[Crossref]

IEEE Photon. Technol. Lett. (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, 194–196 (2001).
[Crossref]

J. Lightwave Tech. (1)

S. Wabnitz, “Broadband parametric amplification in photonic crystal fibers with two zero-dispersion wavelengths,” J. Lightwave Tech. 24, 1732–1738 (2006).
[Crossref]

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

Opt. Commun. (2)

P.Tchofo Dinda, E. Seve, G. Millot, T. Sylvestre, H. Maillotte, and E. Lantz, “Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion,” Opt. Commun. 192, 107–121 (2001).
[Crossref]

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
[Crossref]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. Lett. (2)

N. Bloembergen and Y. R. Shen, , “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[Crossref]

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
[Crossref]

Other (3)

G. P. Agrawal, , Nonlinear Fiber Optics, Optics and Photonics Series (Academic, San Diego, Calif., 2001).

C. Headley and G. P. Agrawal, , eds., Raman Amplification in Optical Fiber Communications, (Elsevier, San Diego, Calif., 2005).

M. Hirano, T. Nakanishi, T. Okunko, and M. Onishi, “Selective FWM-based wavelength conversion realized by highly nonlinear fiber” in Proc. European conference on optical communications, September 2006, Cannes, France, paper Th. 1.3.5.

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Figures (7)

Fig. 1.
Fig. 1.

Measured real and imaginary parts of the complex Raman susceptibility of fused silica (after Ref. [11]).

Fig. 2.
Fig. 2.

Normalized Raman-parametric gain coefficient gn as a function of normalized wavevector mismatch K and the signal detuning Ω. This calculation uses the complex Raman susceptibility curve of Fig. 1. Inset is the graph of gn versus Ω for a phasematched process (K = 1).

Fig. 3.
Fig. 3.

Sideband power asymmetry as a function of normalized wavevector mismatch K and the signal detuning Ω. This calculation uses the complex Raman susceptibility curve of Fig. 1. Inset is the graph of the power asymmetry versus Ω for a phasematched process (K = 1).

Fig. 4.
Fig. 4.

Schematic diagram of the experimental setup: PC - fiber polarization controller, ISO -optical isolator, ECL - tunable external cavity laser.

Fig. 5.
Fig. 5.

Spectrum of spontaneous parametric sidebands for eight pump wavelengths: 1558.0, 1556.0, 1554.5, 1553.7, 1552.5, 1551.9, 1550.6 and 1548.4 nm. The input pump peak power was 82 W. The smallest frequency shift sidebands correspond to the highest pump wavelength.

Fig. 6.
Fig. 6.

Measured parametric gain for an anti-Stokes seed as a function of seed detuning (circles). The solid line is the prediction of Eq. (8) with γ = 2.53 W-1km-1 and f = 0.18. The pump wavelength is 1555.7 nm, and the input pump peak power is 82 W.

Fig. 7.
Fig. 7.

Measured phasematched parametric gain for an anti-Stokes seed as a function of detuning (circles). The solid line is the prediction of Eq. (8) with γ = 2.53 W-1km-1 and f = 0.18. The input pump peak power is 82 W.

Equations (17)

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

A z t z = i β 2 2 2 A z t t 2 + β 3 6 3 A z t t 3 + i β 4 24 4 A z t t 4 + [ ( 1 f ) A z t 2 + f t χ R ( 3 ) ( t t ) | A ( z , t ' ) | 2 dt ] A z t
1 d A a d z = A a 2 A a + ( 1 + q ( 2 Ω ) ) A s 2 A a + ( 1 + q ( Ω ) ) A p 2 A a + q ( Ω ) A p 2 A s * exp ( kz )
1 d A p d z = A p 2 A p + ( 1 + q ( Ω ) ) A s 2 A p + ( 1 + q ( Ω ) ) A a 2 A p + q ( Ω ) + q ( Ω ) A a A s A p * exp ( kz )
1 d A s d z = A s 2 A s + ( 1 + q ( 2 Ω ) ) A a 2 A s + ( 1 + q ( Ω ) ) A p 2 A s + q ( Ω ) A p 2 A a * exp ( kz )
Δ k ( Ω ) = β 2 Ω 2 + β 4 Ω 4 12
B a * ( z ) = 1 2 R { [ ( R iq + iK ) B a * ( 0 ) iq B s ( 0 ) ] exp ( γRPz ) + [ ( R iq + iK ) B a * ( 0 ) iq B s ( 0 ) ] exp ( γRPz ) }
B s * ( z ) = 1 2 R { [ iq B a * ( 0 ) + ( R iq + iK ) B s ( 0 ) ] exp ( γRPz ) + [ iq B a * ( 0 ) + ( R iq + iK ) B s ( 0 ] exp ( γRPz ) }
G = cosh ( γRPL ) ± i ( K q ) R sinh ( γRPL ) 2
G = 1 4 1 ± i ( K q ) R 2 exp ( 2 γP Re ( R ) L )
g = γP Re ( R ) .
G = exp ( 2 γP Im ( q ) L ) = exp ( 2 γPf Im ( χ ˜ R (3) (Ω) ) L )
G = cosh ( γ 2 q 1 PL ) ± i ( 1 q ) 2 q 1 sinh ( γ 2 q 1 PL ) 2
G = 1 4 1 ± i ( 1 q ) q 2 exp ( 2 γP Re ( q ) L )
g p m = 2 γP ( 1 f + f Re ( χ ˜ R ( 3 ) ( Ω ) ) )
P a P s = K q ( iR ) tanh ( γRPL ) q 2
P a P s = q K q + ( iR ) tanh ( γRPL ) 2
P a P s = K q iR q 2

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