## Combined effect of Raman and parametric gain on single-pump parametric amplifiers.

Optics Express, Vol. 15, Issue 13, pp. 8104-8114 (2007)

http://dx.doi.org/10.1364/OE.15.008104

Acrobat PDF (332 KB)

### 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

## 1. Introduction

02. 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]

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

05. 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]

05. 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]

08. 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]

08. 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]

09. F. Vanholsbeeck, P. Emplit, and S. Coen, “Complete experimental characterization of the influence of parametric four-wave mixing on stimulated Raman gain,” Opt. Lett. **28**1960–1962 (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]

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]

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]

## 2. Theory.

*A*(

*z*,

*t*) is the electric field envelope,

*γ*is the nonlinear interaction coefficient,

*χ*

_{R}^{(3)}(

*t*) is the temporal Raman response function, and

*f*is the fractional strength of the Raman susceptibility to the Kerr nonlinearity (for fused silica

*f*≈ 0.18 [11

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]

*β*=

_{n}*d*

^{n}*β*/

*dω*is the n

^{n}^{th}order dispersion coefficient. Closely following the approach of Ref. [8

08. 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]

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]

*k*is the linear wavevector mismatch and can be expressed in terms of the even orders of dispersion expanded around the pump frequency:

*q*(Ω) is defined as

*q*(Ω) ≡ 1-

*f*+

*f*

χ ˜

_{R}^{(3)}(-Ω) [9

09. F. Vanholsbeeck, P. Emplit, and S. Coen, “Complete experimental characterization of the influence of parametric four-wave mixing on stimulated Raman gain,” Opt. Lett. **28**1960–1962 (2003). [CrossRef] [PubMed]

χ ˜

_{R}^{(3)}(Ω) the complex Raman susceptibility (the Fourier transform of

*χ*

_{R}^{(t)}normalized such that

χ ˜

_{R}^{(0)}= 1 [11

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]

χ ˜

_{R}^{(3)}is obtained from direct measurement of the Raman gain as a function of signal detuning, and the real part calculated from the imaginary part via the Kramers-Kronig relations. In Fig. 1 we plot the measured complex Raman susceptibility of a fused silica optical fiber presented in Ref. [11

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]

**26**, 1815–1820 (1990). [CrossRef]

*B*=

_{j}*A*exp(-

_{j}*i*(

*γP*- Δ

*k*/2)

*z*),

*P*is the pump power,

*R*= √

*K*(2

*q*-

*K*) , and

*K*= -Δ

*k*/(2

*γP*) is the normalized mismatch parameter. Phasematched parametric amplification corresponds to a value of

*K*= 1, and the parametric gain bandwidth is set by the range of detunings that satisfy the condition 0 <

*K*(Ω) < 2. These two equations, first derived in Ref. [8

**26**, 1815–1820 (1990). [CrossRef]

*L*as:

*γP*Re(

*R*)

*L*≫ 1) Eq. (8) reduces to:

09. F. Vanholsbeeck, P. Emplit, and S. Coen, “Complete experimental characterization of the influence of parametric four-wave mixing on stimulated Raman gain,” Opt. Lett. **28**1960–1962 (2003). [CrossRef] [PubMed]

*K*∣ ≫ 1). Here the small-signal intensity gain of the amplifier, given by Eq. (8), reduces to:

χ ˜

_{R}^{(3)}. The second case of interest is the gain at small values of the linear wavevector mismatch (

*K*→ 0). Under these conditions exponential gain coefficient falls to zero and the signal experiences only a weak quadratic amplification. This prediction was experimentally verified in Ref. [9

**28**1960–1962 (2003). [CrossRef] [PubMed]

*K*= 1). Here Eq. (8) reduces to:

*f*is small we may expand the square root term as √2

*q*-1 ≈

*q*via the binomial expansion which gives the phasematched gain of the amplifier in the high-gain limit (

*γP*Re(

*R*)

*L*≫ 1) as:

χ ˜

_{R}^{(3)}and an exponential gain that depends only on the real part. In the high-gain limit the exponential term dominates and so the phasematched gain is a strong function of the real part of

χ ˜

_{R}^{(3)}and only a weak function of the imaginary part. In the absence of Raman scattering (

*f*= 0) Eq. (13) reduces to

*G*= 0.25exp(2

*γPL*) which is the standard expression for the small-signal gain of a single-pump parametric amplifier [2

02. 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]

*g*as:

_{pm}*f*) reduction in the phasematched parametric gain coefficient at this detuning compared the gain coefficient at small detunings. The presence of this strong dip in the parametric gain at 15.5 THz was experimentally verified in Ref [10

**32**, 521–523 (2007). [CrossRef] [PubMed]

χ ˜

_{R}^{(3)}) . However if the phasematched parametric gain is measured at two different pump powers

*P*

_{1}and

*P*

_{2}, then Eq. (13) gives the ratio of these two parametric gains as exp(2

*γ*(

*P*

_{1}-

*P*

_{2})Re(

*q*)

*L*). If

*γ*and

*f*are known the real part of the Raman susceptibility is directly accessible from this ratio.

*γ*

*P*Re(

*R*)

*L*≫ 1) the tanh terms of Eqs. (15) and (16) tend to unity and both these expression give the same fixed ratio between the Stokes and anti-Stokes powers [7

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

**26**, 1815–1820 (1990). [CrossRef]

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

**26**, 1815–1820 (1990). [CrossRef]

*K*and the detuning

*Ω*for the entire range of detunings over which the Raman susceptibility has a non-zero value. Figure 3 shows that far from the phasematch condition (∣

*k*∣ ≫ 1) most of the power is to be found in the Stokes sideband as might be expected for a purely Raman amplifier. Reference [15

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]

*K*= 1) the ratio between the two sidebands depends primarily on the value of the imaginary part of

χ ˜

_{R}^{(3)}(the Raman gain). Where the Raman gain is low (at detunings close to zero, and above 25 THz) the ratio is close to unity over the entire parametric gain bandwidth (0 <

*K*< 2). Where the Raman gain is maximum (at a detuning of 13.4 THz) the power asymmetry is at its largest.

## 3. Experiment

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]

*β*

_{2}= 0.095 ps

^{2}/km and

*β*

^{4}= -5.5 × 10

^{-4}ps

^{4}/km, and the nonlinear parameter γ = 2.53 W

^{-1}km

^{-1}. The parameter

*f*is set to its accepted value (

*f*= 0.18 [11

**6**, 1159–1166 (1989). [CrossRef]

**6**, 1159–1166 (1989). [CrossRef]

χ ˜

_{R}^{(3)}returns to zero.

## 4. Conclusion

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]

## References and links

01. | G. P. Agrawal, , |

02. | 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. |

03. | C. Headley and G. P. Agrawal, , eds., |

04. | N. Bloembergen and Y. R. Shen, , “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. |

05. | M. D. Duncan, R. Mahon, J. Reintjes, and L. L. Tankersley, “Parametric Raman gain suppression in D2 and H2,” Opt. Lett. |

06. | K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. |

07. | S. Trillo and S. Wabnitz, “Parametric and Raman amplification in birefringent fibers,” J. Opt. Soc. Am. B |

08. | 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. |

09. | F. Vanholsbeeck, P. Emplit, and S. Coen, “Complete experimental characterization of the influence of parametric four-wave mixing on stimulated Raman gain,” Opt. Lett. |

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. |

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 |

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. |

13. | M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. |

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. |

15. | S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. |

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 |

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. |

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. |

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. |

20. | S. Wabnitz, “Broadband parametric amplification in photonic crystal fibers with two zero-dispersion wavelengths,” J. Lightwave Tech. |

21. | M. Hirano, T. Nakanishi, T. Okunko, and M. Onishi, “Selective FWM-based wavelength conversion realized by highly nonlinear fiber” in |

22. | C. J. Mckinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum. Electron. |

**OCIS Codes**

(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 7, 2007

Revised Manuscript: May 19, 2007

Manuscript Accepted: May 30, 2007

Published: June 13, 2007

**Citation**

A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, "Combined effect of Raman and parametric gain on single-pump parametric amplifiers," Opt. Express **15**, 8104-8114 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8104

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### References

- G. P. Agrawal, Nonlinear Fiber Optics, Optics and Photonics Series (Academic, San Diego, Calif., 2001).
- 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. Headley and G. P. Agrawal, eds., Raman Amplification in Optical Fiber Communications, (Elsevier, San Diego, Calif., 2005).
- N. Bloembergen and Y. R. Shen, "Coupling between vibrations and light waves in Raman laser media," Phys. Rev. Lett. 12, 504-507 (1964). [CrossRef]
- 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]
- 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]
- S. Trillo and S. Wabnitz, "Parametric and Raman amplification in birefringent fibers," J. Opt. Soc. Am. B 9, 1061-1082 (1992). [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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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. 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. 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]
- 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]
- 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]
- 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.
- 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]

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