Abstract

We present an experimental and theoretical study of the transition from linear to nonlinear amplification of classical pump noise in a fiber Raman generator. In particular, we focus on the conversion of fluctuations in the fine temporal structure of Q-switched pump pulses into Stokes pulse energy fluctuations. We show that there is a distinct pump power domain where large scale fluctuations in the Stokes pulse energy result from the amplification of fluctuations in the temporal structure of pump pulses with stable energies. Dramatic changes in the shape of the Stokes pulse energy probability distribution also occur as the pump power is swept through the domain of large scale energy fluctuations.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. S. V. Chernikov, N. S. Platonov, D. V. Gapontsev, D. I. Chang, M. J. Guy, and J. R. Taylor, �??Raman Fibre Laser Operating at 1.24 µm,�?? Electron. Lett. 34, 680 (1998).
    [CrossRef]
  2. Y. Emori, K. Tanaka, and S. Namiki, �??100 nm Bandwidth Flat-Gain Raman Amplifiers Pumped and Gain Equalized by 12-Wavelength-Channel WDM Laser Diode Unit,�?? Electron. Lett. 35, 1355 (1999).
    [CrossRef]
  3. D. V. Gapontsev, S. V. Chernikov, and J. R. Taylor, �??Fibre Raman Amplifiers for Broadband Operation at 1.3 µm,�?? Opt. Commun. 166, 85�??88 (1999).
    [CrossRef]
  4. S. A. E. Lewis, S. V. Chernikov, and J. R. Taylor, �??Fibre-Optic Tunable CW Raman Laser Operating Around 1.3 µm,�?? Opt. Commun. 182, 403�??405 (2000).
    [CrossRef]
  5. M. Prabhua, N. S. Kim, L. Jianrena, and K.-I. Ueda, �??Simultaneous Two-Color CW Raman Fiber Laser With Maximum Output Power of 1.05 W/1239 nm and 0.95 W/1484 nm Using Phosphosilicate Fiber,�?? Opt. Commun. 182, 305�??309 (2000).
    [CrossRef]
  6. L. F. Mollenauer, A. R. Grant, and P. V. Mamyshev, �??Time-Division Multiplexing of Pump Wavelengths to Achieve Ultrabroadband, Flat, Backward-Pumped Raman Gain,�?? Opt. Lett. 27, 592�??594 (2002).
    [CrossRef]
  7. D. A. Chestnut, C. J. S. de Matos, P. C. Reeves-Hall, and J. R. Taylor, �??Copropagating and Counterpropagating Pumps in Second-Order Pumped Discrete Fiber Raman Amplifiers,�?? Opt. Lett. 27, 1708�??1710 (2002).
    [CrossRef]
  8. R. Waarts, V. Dominic, D. Giltner, and D. Mehuys, �??Raman Amplification Enhances System Operation,�?? WDM Solutions pp. 27�??32 (2000).
  9. I. A. Walmsley and M. G. Raymer, �??Observation of Macroscopic Quantum Fluctuations in Stimulated Raman Scattering,�?? Phys. Rev. Lett. 50, 962�??965 (1983).
    [CrossRef]
  10. N. Fabricius, K. Nattermann, and D. von der Linde, �??Macroscopic Manifestations of Quantum Fluctuations in Transient Stimulated Raman Scattering,�?? Phys. Rev. Lett. 52, 113�??116 (1984).
    [CrossRef]
  11. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, �??Quantum Fluctuations in the Stimulated-Raman-Scattering Linewidth,�?? Phys. Rev. Lett. 23, 66�??69 (1988).
    [CrossRef]
  12. R. G. Smith, �??Optical Power Handling Capacity of Low Loss Optical Fibers as Determined by Stimulated Raman and Brillouin Scattering,�?? Appl. Opt. 11, 2489�??2494 (1972).
    [CrossRef] [PubMed]
  13. J. Auyeung and A. Yariv, �??Spontaneous and Stimulated Raman Scattering in Long Low Loss Fibers,�?? IEEE J. Quantum Electron. 14, 347�??352 (1978).
    [CrossRef]
  14. F. R. Barbosa, �??Quasi-Stationary Multiple Stimulated Raman Generation in the Visible Using Optical Fibers,�?? Appl. Opt. 22, 3859�??3863 (1983).
    [CrossRef] [PubMed]
  15. R. H. Stolen, C. Lee, and R. K. Jain, �??Development of the Stimulated Raman Spectrum in Single-Mode Silica Fibers,�?? J. Opt. Soc. Am. B 1, 652�??657 (1984).
    [CrossRef]
  16. K. X. Liu and E. Garmire, �??Understanding the Formation of the SRS Stokes Spectrum in Fused Silica Fibers,�?? IEEE J. Quantum Electron. 27, 1022�??1030 (1991).
    [CrossRef]
  17. C. Yijiang and A. W. Snyder, �??Saturation and Depletion Effect of Raman Scattering in Optical Fibers,�?? J. Lightwave Technol. 7, 1109�??1116 (1989).
    [CrossRef]
  18. D. Dahan, A. Bilenca, and G. Eisenstein, �??Noise-Reduction Capabilities of a Raman-Mediated Wavelength Converter,�?? Opt. Lett. 28, 634�??636 (2003).
    [CrossRef] [PubMed]
  19. M. Lewenstein, �??Fluctuations in the Nonlinear Regime of Stimulated Raman Scattering,�?? Zeitschrift für Physik B 56, 69�??75 (1984).
    [CrossRef]
  20. I. A. Walmsley, M. G. Raymer, T. S. II, I. N. D. III, and J. D. Kafka, �??Stabilization of Stokes Pulse Energies in the Nonlinear Regime of Stimulated Raman Scattering,�?? Opt. Commun. 53, 137�??140 (1985).
    [CrossRef]
  21. A. T. Georges, �??Theory of Stimulated Raman Scattering in a Chaotic Incoherent Pump Field,�?? Opt. Commun. 41, 61�??66 (1982).
    [CrossRef]
  22. M. Trippenbach, K. Rz�?żewski, and M. G. Raymer, �??Stimulated Raman Scattering of Colored Chaotic Light,�?? J. Opt. Soc. Am. B 1, 671�??675 (1984).
    [CrossRef]
  23. A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, �??Pulse-Energy Statistics in the Linear Regime of Stimulated Raman Scattering with a Broad-Band Pump,�?? Phys. Rev. A 56, 1666�??1669 (1997).
    [CrossRef]
  24. L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, �??Influence of Classical Pump Noise on Long-Pulse Multiorder Stimulated Raman Scattering in Optical Fiber,�?? J. Opt. Soc. Am. B 19, 2727�??2736 (2002).
    [CrossRef]
  25. H.-S. Seo and K. Oh, �??Optimization of Silica Fiber Raman Amplifier Using the Raman Frequency Modeling for an Arbitrary GeO2 Concentration in the Core,�?? Opt. Commun. 181, 145�??151 (2000).
    [CrossRef]
  26. W. P. Urquhart and P. J. R. Laybourn, �??Stimulated Raman Scattering in Optical Fibers With Nonconstant Loss: A Multiwavelength Model,�?? Appl. Opt. 25, 2592�??2599 (1986).
    [CrossRef] [PubMed]
  27. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic Press, Boston, 1995).
  28. J. Correa, E. Manzano, R. Tracy, and J. R. Thompson, �??Correlations Between Intensity Fluctuations Within Stimulated Brillouin Waveforms Generated by Scattering of Q-Switched Pulses in Optical Fiber,�?? Opt. Commun. 242, 267�??278 (2004).
    [CrossRef]

Appl. Opt. (3)

Electron. Lett. (2)

S. V. Chernikov, N. S. Platonov, D. V. Gapontsev, D. I. Chang, M. J. Guy, and J. R. Taylor, �??Raman Fibre Laser Operating at 1.24 µm,�?? Electron. Lett. 34, 680 (1998).
[CrossRef]

Y. Emori, K. Tanaka, and S. Namiki, �??100 nm Bandwidth Flat-Gain Raman Amplifiers Pumped and Gain Equalized by 12-Wavelength-Channel WDM Laser Diode Unit,�?? Electron. Lett. 35, 1355 (1999).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. Auyeung and A. Yariv, �??Spontaneous and Stimulated Raman Scattering in Long Low Loss Fibers,�?? IEEE J. Quantum Electron. 14, 347�??352 (1978).
[CrossRef]

K. X. Liu and E. Garmire, �??Understanding the Formation of the SRS Stokes Spectrum in Fused Silica Fibers,�?? IEEE J. Quantum Electron. 27, 1022�??1030 (1991).
[CrossRef]

J. Lightwave Technol. (1)

C. Yijiang and A. W. Snyder, �??Saturation and Depletion Effect of Raman Scattering in Optical Fibers,�?? J. Lightwave Technol. 7, 1109�??1116 (1989).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (7)

J. Correa, E. Manzano, R. Tracy, and J. R. Thompson, �??Correlations Between Intensity Fluctuations Within Stimulated Brillouin Waveforms Generated by Scattering of Q-Switched Pulses in Optical Fiber,�?? Opt. Commun. 242, 267�??278 (2004).
[CrossRef]

H.-S. Seo and K. Oh, �??Optimization of Silica Fiber Raman Amplifier Using the Raman Frequency Modeling for an Arbitrary GeO2 Concentration in the Core,�?? Opt. Commun. 181, 145�??151 (2000).
[CrossRef]

I. A. Walmsley, M. G. Raymer, T. S. II, I. N. D. III, and J. D. Kafka, �??Stabilization of Stokes Pulse Energies in the Nonlinear Regime of Stimulated Raman Scattering,�?? Opt. Commun. 53, 137�??140 (1985).
[CrossRef]

A. T. Georges, �??Theory of Stimulated Raman Scattering in a Chaotic Incoherent Pump Field,�?? Opt. Commun. 41, 61�??66 (1982).
[CrossRef]

D. V. Gapontsev, S. V. Chernikov, and J. R. Taylor, �??Fibre Raman Amplifiers for Broadband Operation at 1.3 µm,�?? Opt. Commun. 166, 85�??88 (1999).
[CrossRef]

S. A. E. Lewis, S. V. Chernikov, and J. R. Taylor, �??Fibre-Optic Tunable CW Raman Laser Operating Around 1.3 µm,�?? Opt. Commun. 182, 403�??405 (2000).
[CrossRef]

M. Prabhua, N. S. Kim, L. Jianrena, and K.-I. Ueda, �??Simultaneous Two-Color CW Raman Fiber Laser With Maximum Output Power of 1.05 W/1239 nm and 0.95 W/1484 nm Using Phosphosilicate Fiber,�?? Opt. Commun. 182, 305�??309 (2000).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, �??Pulse-Energy Statistics in the Linear Regime of Stimulated Raman Scattering with a Broad-Band Pump,�?? Phys. Rev. A 56, 1666�??1669 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

I. A. Walmsley and M. G. Raymer, �??Observation of Macroscopic Quantum Fluctuations in Stimulated Raman Scattering,�?? Phys. Rev. Lett. 50, 962�??965 (1983).
[CrossRef]

N. Fabricius, K. Nattermann, and D. von der Linde, �??Macroscopic Manifestations of Quantum Fluctuations in Transient Stimulated Raman Scattering,�?? Phys. Rev. Lett. 52, 113�??116 (1984).
[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, �??Quantum Fluctuations in the Stimulated-Raman-Scattering Linewidth,�?? Phys. Rev. Lett. 23, 66�??69 (1988).
[CrossRef]

WDM Solutions (1)

R. Waarts, V. Dominic, D. Giltner, and D. Mehuys, �??Raman Amplification Enhances System Operation,�?? WDM Solutions pp. 27�??32 (2000).

Zeitschrift für Physik B (1)

M. Lewenstein, �??Fluctuations in the Nonlinear Regime of Stimulated Raman Scattering,�?? Zeitschrift für Physik B 56, 69�??75 (1984).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic Press, Boston, 1995).

Supplementary Material (2)

» Media 1: MOV (655 KB)     
» Media 2: MOV (1552 KB)     

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.

Distribution of the modulation amplitudes used in the simulations.

Fig. 2.
Fig. 2.

Relative noise in the first Stokes energy as a function of input pump power. Circles: experimental data; Solid line: simulation results (classical fluctuations only); Dashed line: simulation results (classical and quantum fluctuations).

Fig. 3.
Fig. 3.

First Stokes pulse energy distributions for an input peak pump power of 11.5 watts. The simulation results include fluctuations from the pump pulse temporal modulations; green shading indicates pump pulses with a modulation depth greater than 45%. (Accompanying animation 660 kB.)

Fig. 4.
Fig. 4.

First Stokes pulse energy distributions for an input peak pump power of 11.5 watts. The simulation results include fluctuations from quantum initiation noise and the pump pulse temporal modulations; green shading indicates pump pulses with a modulation depth greater than 45%. (Accompanying animation 1592 kB.)

Fig. 5.
Fig. 5.

Experimental data for the relative noise in the first Stokes energy as a function of input pump power. Circles: multi-mode pump; Squares: single-mode pump.

Equations (10)

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

A u = S + r P ,
A f = T S S + r T P P ,
T S S A f = T S T S T P [ 1 T P A u A f ] .
σ A = σ S 2 + σ P 2 + σ n 2 .
A f = T S S + r T P P ,
σ S T S S = σ S 2 σ P 2 σ n 2 A f r T P P .
d P 0 d z = j = 1 N g 0 j ( P j + η 0 ) P 0 ,
d P i d z = λ 0 λ i j = 1 i g i j , i ( P i + η i j ) P i j λ 0 λ i j = 1 N i g i , i + j ( P i + j + η i ) P i .
η i = f ε i j = 1 N g i j , where ε i = π ( n 1 2 n 2 2 ) β λ i 4 ,
g i j = G 0 λ 0 λ i [ 1 + ( Δ Ω i j Δ Ω max Δ Ω F W 2 ) 2 ] 1 .

Metrics