Abstract

The transient regime of a nth-order CW Raman fiber laser is simulated from switch-on to the steady-state and from the steady-state to switch-off. The Stokes waves exhibit high-power spikes during the switch-on transition. We find that the high order Stokes fields reach steady-state faster than the low order ones and the pump.

©2004 Optical Society of America

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References

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  1. S. G. Grubb and al., “High-power 1.48µm cascaded Raman laser in germanosilicate fibers,” Proc. Topical Meeting on Optical Amplifiers and Amplifications, Optical Society of America, Washington DC Paper SaA4, 197 (1995)
  2. W. A. Reed, W. C. Coughran, and S. G. Grubb, “Numerical modeling of cascaded CW Raman fiber amplifiers and lasers,” Proc. Conf. on Optical Communications, OFC ’95, Optical Society of America, Washington DC Paper WD1 (1995)
  3. S. D. Jackson and P. H. Muir, “Theory and numerical simulation of nth-order cascaded CW Raman fiber lasers,” J. Opt. Soc. Am. B 18, 1297–1306 (2001).
    [Crossref]
  4. M. Rini, I. Cristiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded CW Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000)
    [Crossref]
  5. G. Vareille, O. Audouin, and E. Desurvire, “Numerical optimisation of power conversion efficiency in 1480nm multi-Stokes Raman fibre lasers,” Electron. Lett.675–676 (1998)
    [Crossref]
  6. B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
    [Crossref]
  7. M. Karasek and M. Menif, “Channel addition/removal response in Raman fiber amplifier: Modeling and experimentation,” J. Lightwave Technol. 20, 1680–1687 (2002).
    [Crossref]
  8. C. Headley III and G. P. Agrawal, “Noise Characteristics and statistics of picosecond Stokes pulses generated in optical fibers through stimulated Raman scattering,” IEEE J. Quantum Electron. 31, 2058–2067 (1995).
    [Crossref]
  9. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Integration of ordinary differential equations,” Numerical recipes in C: The art of scientific Computing 2nd ed., Cambridge University Press (1992), 714–722.

2002 (1)

2001 (1)

2000 (2)

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded CW Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000)
[Crossref]

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
[Crossref]

1995 (1)

C. Headley III and G. P. Agrawal, “Noise Characteristics and statistics of picosecond Stokes pulses generated in optical fibers through stimulated Raman scattering,” IEEE J. Quantum Electron. 31, 2058–2067 (1995).
[Crossref]

Agrawal, G. P.

C. Headley III and G. P. Agrawal, “Noise Characteristics and statistics of picosecond Stokes pulses generated in optical fibers through stimulated Raman scattering,” IEEE J. Quantum Electron. 31, 2058–2067 (1995).
[Crossref]

Audouin, O.

G. Vareille, O. Audouin, and E. Desurvire, “Numerical optimisation of power conversion efficiency in 1480nm multi-Stokes Raman fibre lasers,” Electron. Lett.675–676 (1998)
[Crossref]

Coughran, W. C.

W. A. Reed, W. C. Coughran, and S. G. Grubb, “Numerical modeling of cascaded CW Raman fiber amplifiers and lasers,” Proc. Conf. on Optical Communications, OFC ’95, Optical Society of America, Washington DC Paper WD1 (1995)

Cristiani, I.

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded CW Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000)
[Crossref]

Degiorgio, V.

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded CW Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000)
[Crossref]

Desurvire, E.

G. Vareille, O. Audouin, and E. Desurvire, “Numerical optimisation of power conversion efficiency in 1480nm multi-Stokes Raman fibre lasers,” Electron. Lett.675–676 (1998)
[Crossref]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Integration of ordinary differential equations,” Numerical recipes in C: The art of scientific Computing 2nd ed., Cambridge University Press (1992), 714–722.

Grubb, S. G.

W. A. Reed, W. C. Coughran, and S. G. Grubb, “Numerical modeling of cascaded CW Raman fiber amplifiers and lasers,” Proc. Conf. on Optical Communications, OFC ’95, Optical Society of America, Washington DC Paper WD1 (1995)

S. G. Grubb and al., “High-power 1.48µm cascaded Raman laser in germanosilicate fibers,” Proc. Topical Meeting on Optical Amplifiers and Amplifications, Optical Society of America, Washington DC Paper SaA4, 197 (1995)

Headley III, C.

C. Headley III and G. P. Agrawal, “Noise Characteristics and statistics of picosecond Stokes pulses generated in optical fibers through stimulated Raman scattering,” IEEE J. Quantum Electron. 31, 2058–2067 (1995).
[Crossref]

Jackson, S. D.

Karasek, M.

Lee, W. J.

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
[Crossref]

Menif, M.

Min, B.

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
[Crossref]

Muir, P. H.

Park, N.

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
[Crossref]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Integration of ordinary differential equations,” Numerical recipes in C: The art of scientific Computing 2nd ed., Cambridge University Press (1992), 714–722.

Reed, W. A.

W. A. Reed, W. C. Coughran, and S. G. Grubb, “Numerical modeling of cascaded CW Raman fiber amplifiers and lasers,” Proc. Conf. on Optical Communications, OFC ’95, Optical Society of America, Washington DC Paper WD1 (1995)

Rini, M.

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded CW Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000)
[Crossref]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Integration of ordinary differential equations,” Numerical recipes in C: The art of scientific Computing 2nd ed., Cambridge University Press (1992), 714–722.

Vareille, G.

G. Vareille, O. Audouin, and E. Desurvire, “Numerical optimisation of power conversion efficiency in 1480nm multi-Stokes Raman fibre lasers,” Electron. Lett.675–676 (1998)
[Crossref]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Integration of ordinary differential equations,” Numerical recipes in C: The art of scientific Computing 2nd ed., Cambridge University Press (1992), 714–722.

IEEE J. Quantum Electron. (2)

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded CW Raman fiber lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000)
[Crossref]

C. Headley III and G. P. Agrawal, “Noise Characteristics and statistics of picosecond Stokes pulses generated in optical fibers through stimulated Raman scattering,” IEEE J. Quantum Electron. 31, 2058–2067 (1995).
[Crossref]

IEEE Photon. Technol. Lett. (1)

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
[Crossref]

J. Lightwave Technol. (1)

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

Other (4)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Integration of ordinary differential equations,” Numerical recipes in C: The art of scientific Computing 2nd ed., Cambridge University Press (1992), 714–722.

G. Vareille, O. Audouin, and E. Desurvire, “Numerical optimisation of power conversion efficiency in 1480nm multi-Stokes Raman fibre lasers,” Electron. Lett.675–676 (1998)
[Crossref]

S. G. Grubb and al., “High-power 1.48µm cascaded Raman laser in germanosilicate fibers,” Proc. Topical Meeting on Optical Amplifiers and Amplifications, Optical Society of America, Washington DC Paper SaA4, 197 (1995)

W. A. Reed, W. C. Coughran, and S. G. Grubb, “Numerical modeling of cascaded CW Raman fiber amplifiers and lasers,” Proc. Conf. on Optical Communications, OFC ’95, Optical Society of America, Washington DC Paper WD1 (1995)

Supplementary Material (2)

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Figures (5)

Figure 1.
Figure 1. Scheme for a nth-order cascaded Raman fiber laser. λ j represents the wavelength of the jth Stokes wave. Only the output coupler (OC) is not highly reflective. The vertical lines represent the Bragg gratings used as reflectors with reflectivity R± j .

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Figure 2.
Figure 2. Evolution through time of Stokes power in the middle of the cavity at z=L/2 during switch-on. The laser is a 6 th -order cascade with a 150 m long cavity and 96.7% mirrors except for the 50% output coupler. The curves are offset by 10 W for comparison.

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Figure 3.
Figure 3. Evolution through the first 20 µs of Stokes power in the middle of the cavity during switch-on. The Stokes waves’ power levels are shown superimposed so as to highlight the transfer from one wave to the other.

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Figure 4.
Figure 4. Evolution of Stokes power in the cavity during switch-on. The colors white, red, green, blue, cyan, magenta and yellow stand for the pump and Stokes waves from n=1 to n=6. Note that the vertical scales change at t=20, 25, and 32 µs (2.6 MB).

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Figure 5.
Figure 5. Evolution of Stokes power in the cavity during switch-off. The colors white, red, green, blue, cyan, magenta and yellow stand for the pump and Stokes waves from n=1 to n=6. Note that the vertical scales change at t=8, 23, and 36 µs (1.8 MB).

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Tables (1)

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Table 1. Fiber characteristics.

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Equations (12)

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∂ P 0 ± ( z , t ) ∂ z ± 1 v g 0 ∂ P 0 ± ( z , t ) ∂ z = ∓ g 0 [ P 1 + ( z , t ) + P 1 − ( z , t ) + 4 h f 0 B 0 , + ] P 0 ± ( z , t )
∓ α 0 P 0 ± ( z , t )
∂ P j ± ( z , t ) ∂ z ± 1 v gj ∂ P j ± ( z , t ) ∂ t = ± g j [ P j − 1 + ( z , t ) + P j − 1 − ( z , t ) ] [ P j ± ( z , t ) + 2 h f j B j , − ]
∓ g j [ P j + 1 + ( z , t ) + P j + 1 − ( z , t ) + 4 h f j B j , + ] P j ± ( z , t )
∓ α j P j ± ( z , t ) for j = 1 to n − 1
∂ P n ± ( z , t ) ∂ z ± 1 v gn ∂ P n ± ( z , t ) ∂ t = ± g n [ P n − 1 + ( z , t ) + P n − 1 − ( z , t ) ] [ P n ± ( z , t ) + 2 h f n B n , − ]
∓ α n P n ± ( z , t )
B j , ± = 1 + 1 exp ∣ ± h ( f j ± 1 − f j ) k B T ∣ − 1
P 0 + ( 0 ) = P in P 0 − ( L ) = R 0 + P 0 + ( L )
P j + ( 0 ) = R j − P j − ( 0 ) P j − ( L ) = R j + P j + ( L ) for j = 1 to n
P j ± ( z , 0 ) = 0 except for P 0 + ( 0 , t ) = P in for t ≥ 0
τ = 2 L v g ≈ 300 m 2 · 10 8 m ⁄ s = 1.5 μ s

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