Abstract

An implicit equation for the oscillation threshold of stimulated Brillouin scattering from Raman amplified signals in fibers with external feedback is derived under the assumption of no depletion. This is compared to numerical investigations of Raman amplification schemes showing good agreement for high reflectivities. For low reflectivities and high attenuation or long fibers, the assumption of no depletion is shown not to be valid. In these cases the effects of the depletion on the self-pulsation is examined.

© 2009 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, Third Edition, (Academic Press, San Diego, 2001).
  2. E. P. Ippen, "Low-power quasi-cw Raman oscillator," Appl. Phys. Lett. 16, 303-305 (1970).
    [CrossRef]
  3. R. V. Johnson and J. H. Marburger, "Relaxation oscillation in stimulated Raman and Brillouin scattering," Phys. Rev. A 4, 1175-1182 (1971).
    [CrossRef]
  4. E. P. Ippen and R. H. Stolen, "Stimulated Brillouin scattering in optical fibers," Appl. Phys. Lett. 21, 539-541 (1972).
    [CrossRef]
  5. R. G. Smith, "Optical Power Handling Capacity of Low Loss Optical Fibers as Deterined by Stimulated Raman and Brillouin Scattering," Appl. Opt. 11, 2489-2494 (1972).
    [CrossRef]
  6. D. Cotter, "Stimulated Brillouin scattering in monomode optical fibers," Opt. Commun. 4, 10-19 (1983).
    [CrossRef]
  7. I. Bar-Joseph, A. A. Friesem, E. Lichtman, and R. G. Waarts, "Steady and relaxation oscillations of stimulated Brillouin scattering in single-mode optical fibers," J. Opt. Soc. Am. B. 2, 1606 (1985).
    [CrossRef]
  8. A. L. Gaeta and R. W. Boyd, "Stimulated Brillouin scattering in the presence of external feedback," J. Nonlinear Opt. Phys. Mater. 1, 581-594 (1992).
    [CrossRef]
  9. M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301-3309 (1993).
    [CrossRef] [PubMed]
  10. J. H. Lee, T. Tanemura, and K. Kikuchi, "Experimental comparison of a Kerr Nonlinearity figure of merit including the stimulated Brillouin scattering threshold for state-of-the-art nonlinear optical fibers," Opt. Lett. 30, 1968-1970 (2005).
    [CrossRef]
  11. V. I. Kovalev and R. G. Harrison, "Continuous wave stimulated Brillouin scattering in optical fibers: New results and applications for high power lasers," Proc. SPIE 5975, 59750L-1-13 (2006).
  12. J. W. Lou, F. K. Fatemi, and M. Currie, "Brillouin fibre laser enhanced by Raman amplification," Electron. Lett. 40, 1044-1046 (2004).
    [CrossRef]
  13. G. Ravet, A. A. Fotiadi, M. Blondel, and P. Mégret, "Passive Q-switching in all-fibre Raman laser with distributed Rayleigh feedback," Elect. Lett. 40, 528-529 (2004).
    [CrossRef]
  14. A. A. Fotiadi, P. Mégret, and M. Blondel, "Dynamics of a self-Q-switched fiber laser with a Rayleigh-stimulated Brillouin scattering ring mirror," Opt. Lett. 29, 1078-1080 (2004).
    [CrossRef] [PubMed]
  15. A. N. Pilipetskii and V. V. Shkunov, "Calculation of the threshold and of the efficiency of conversion by stimulated scattering in an amplifying medium," Sov. J. Quantum Electron. 15, 284-286 (1985).
    [CrossRef]
  16. M. E. V. Pedersen, J. R. Ott, and K. Rottwitt, "Self-Pulsation in Raman Fiber Amplifiers," presented at the Eleventh International Conference on Transparent Optical Networks, Island of São Miguel, Azores, Portugal, 28 June-2 July 2009.
  17. K. Rottwitt and A. J. Stentz, "Raman Amplification in Lightwave Communication Systems," in Optical Fiber Telecommunications, Chap. 5, (Academic Press, San Diego, Calif., 2002).
    [CrossRef]

2005

2004

J. W. Lou, F. K. Fatemi, and M. Currie, "Brillouin fibre laser enhanced by Raman amplification," Electron. Lett. 40, 1044-1046 (2004).
[CrossRef]

G. Ravet, A. A. Fotiadi, M. Blondel, and P. Mégret, "Passive Q-switching in all-fibre Raman laser with distributed Rayleigh feedback," Elect. Lett. 40, 528-529 (2004).
[CrossRef]

A. A. Fotiadi, P. Mégret, and M. Blondel, "Dynamics of a self-Q-switched fiber laser with a Rayleigh-stimulated Brillouin scattering ring mirror," Opt. Lett. 29, 1078-1080 (2004).
[CrossRef] [PubMed]

1993

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

1992

A. L. Gaeta and R. W. Boyd, "Stimulated Brillouin scattering in the presence of external feedback," J. Nonlinear Opt. Phys. Mater. 1, 581-594 (1992).
[CrossRef]

1985

I. Bar-Joseph, A. A. Friesem, E. Lichtman, and R. G. Waarts, "Steady and relaxation oscillations of stimulated Brillouin scattering in single-mode optical fibers," J. Opt. Soc. Am. B. 2, 1606 (1985).
[CrossRef]

A. N. Pilipetskii and V. V. Shkunov, "Calculation of the threshold and of the efficiency of conversion by stimulated scattering in an amplifying medium," Sov. J. Quantum Electron. 15, 284-286 (1985).
[CrossRef]

1983

D. Cotter, "Stimulated Brillouin scattering in monomode optical fibers," Opt. Commun. 4, 10-19 (1983).
[CrossRef]

1972

E. P. Ippen and R. H. Stolen, "Stimulated Brillouin scattering in optical fibers," Appl. Phys. Lett. 21, 539-541 (1972).
[CrossRef]

R. G. Smith, "Optical Power Handling Capacity of Low Loss Optical Fibers as Deterined by Stimulated Raman and Brillouin Scattering," Appl. Opt. 11, 2489-2494 (1972).
[CrossRef]

1971

R. V. Johnson and J. H. Marburger, "Relaxation oscillation in stimulated Raman and Brillouin scattering," Phys. Rev. A 4, 1175-1182 (1971).
[CrossRef]

1970

E. P. Ippen, "Low-power quasi-cw Raman oscillator," Appl. Phys. Lett. 16, 303-305 (1970).
[CrossRef]

Bar-Joseph, I.

I. Bar-Joseph, A. A. Friesem, E. Lichtman, and R. G. Waarts, "Steady and relaxation oscillations of stimulated Brillouin scattering in single-mode optical fibers," J. Opt. Soc. Am. B. 2, 1606 (1985).
[CrossRef]

Blondel, M.

G. Ravet, A. A. Fotiadi, M. Blondel, and P. Mégret, "Passive Q-switching in all-fibre Raman laser with distributed Rayleigh feedback," Elect. Lett. 40, 528-529 (2004).
[CrossRef]

A. A. Fotiadi, P. Mégret, and M. Blondel, "Dynamics of a self-Q-switched fiber laser with a Rayleigh-stimulated Brillouin scattering ring mirror," Opt. Lett. 29, 1078-1080 (2004).
[CrossRef] [PubMed]

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, "Stimulated Brillouin scattering in the presence of external feedback," J. Nonlinear Opt. Phys. Mater. 1, 581-594 (1992).
[CrossRef]

Cotter, D.

D. Cotter, "Stimulated Brillouin scattering in monomode optical fibers," Opt. Commun. 4, 10-19 (1983).
[CrossRef]

Currie, M.

J. W. Lou, F. K. Fatemi, and M. Currie, "Brillouin fibre laser enhanced by Raman amplification," Electron. Lett. 40, 1044-1046 (2004).
[CrossRef]

Dämmig, M.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

Fatemi, F. K.

J. W. Lou, F. K. Fatemi, and M. Currie, "Brillouin fibre laser enhanced by Raman amplification," Electron. Lett. 40, 1044-1046 (2004).
[CrossRef]

Fotiadi, A. A.

A. A. Fotiadi, P. Mégret, and M. Blondel, "Dynamics of a self-Q-switched fiber laser with a Rayleigh-stimulated Brillouin scattering ring mirror," Opt. Lett. 29, 1078-1080 (2004).
[CrossRef] [PubMed]

G. Ravet, A. A. Fotiadi, M. Blondel, and P. Mégret, "Passive Q-switching in all-fibre Raman laser with distributed Rayleigh feedback," Elect. Lett. 40, 528-529 (2004).
[CrossRef]

Friesem, A. A.

I. Bar-Joseph, A. A. Friesem, E. Lichtman, and R. G. Waarts, "Steady and relaxation oscillations of stimulated Brillouin scattering in single-mode optical fibers," J. Opt. Soc. Am. B. 2, 1606 (1985).
[CrossRef]

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, "Stimulated Brillouin scattering in the presence of external feedback," J. Nonlinear Opt. Phys. Mater. 1, 581-594 (1992).
[CrossRef]

Ippen, E. P.

E. P. Ippen and R. H. Stolen, "Stimulated Brillouin scattering in optical fibers," Appl. Phys. Lett. 21, 539-541 (1972).
[CrossRef]

E. P. Ippen, "Low-power quasi-cw Raman oscillator," Appl. Phys. Lett. 16, 303-305 (1970).
[CrossRef]

Johnson, R. V.

R. V. Johnson and J. H. Marburger, "Relaxation oscillation in stimulated Raman and Brillouin scattering," Phys. Rev. A 4, 1175-1182 (1971).
[CrossRef]

Kikuchi, K.

Lee, J. H.

Lichtman, E.

I. Bar-Joseph, A. A. Friesem, E. Lichtman, and R. G. Waarts, "Steady and relaxation oscillations of stimulated Brillouin scattering in single-mode optical fibers," J. Opt. Soc. Am. B. 2, 1606 (1985).
[CrossRef]

Lou, J. W.

J. W. Lou, F. K. Fatemi, and M. Currie, "Brillouin fibre laser enhanced by Raman amplification," Electron. Lett. 40, 1044-1046 (2004).
[CrossRef]

Marburger, J. H.

R. V. Johnson and J. H. Marburger, "Relaxation oscillation in stimulated Raman and Brillouin scattering," Phys. Rev. A 4, 1175-1182 (1971).
[CrossRef]

Mégret, P.

G. Ravet, A. A. Fotiadi, M. Blondel, and P. Mégret, "Passive Q-switching in all-fibre Raman laser with distributed Rayleigh feedback," Elect. Lett. 40, 528-529 (2004).
[CrossRef]

A. A. Fotiadi, P. Mégret, and M. Blondel, "Dynamics of a self-Q-switched fiber laser with a Rayleigh-stimulated Brillouin scattering ring mirror," Opt. Lett. 29, 1078-1080 (2004).
[CrossRef] [PubMed]

Mitschke, F.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

Pilipetskii, A. N.

A. N. Pilipetskii and V. V. Shkunov, "Calculation of the threshold and of the efficiency of conversion by stimulated scattering in an amplifying medium," Sov. J. Quantum Electron. 15, 284-286 (1985).
[CrossRef]

Ravet, G.

G. Ravet, A. A. Fotiadi, M. Blondel, and P. Mégret, "Passive Q-switching in all-fibre Raman laser with distributed Rayleigh feedback," Elect. Lett. 40, 528-529 (2004).
[CrossRef]

Shkunov, V. V.

A. N. Pilipetskii and V. V. Shkunov, "Calculation of the threshold and of the efficiency of conversion by stimulated scattering in an amplifying medium," Sov. J. Quantum Electron. 15, 284-286 (1985).
[CrossRef]

Smith, R. G.

Stolen, R. H.

E. P. Ippen and R. H. Stolen, "Stimulated Brillouin scattering in optical fibers," Appl. Phys. Lett. 21, 539-541 (1972).
[CrossRef]

Tanemura, T.

Waarts, R. G.

I. Bar-Joseph, A. A. Friesem, E. Lichtman, and R. G. Waarts, "Steady and relaxation oscillations of stimulated Brillouin scattering in single-mode optical fibers," J. Opt. Soc. Am. B. 2, 1606 (1985).
[CrossRef]

Welling, H.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

Zinner, G.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

E. P. Ippen, "Low-power quasi-cw Raman oscillator," Appl. Phys. Lett. 16, 303-305 (1970).
[CrossRef]

E. P. Ippen and R. H. Stolen, "Stimulated Brillouin scattering in optical fibers," Appl. Phys. Lett. 21, 539-541 (1972).
[CrossRef]

Elect. Lett.

G. Ravet, A. A. Fotiadi, M. Blondel, and P. Mégret, "Passive Q-switching in all-fibre Raman laser with distributed Rayleigh feedback," Elect. Lett. 40, 528-529 (2004).
[CrossRef]

Electron. Lett.

J. W. Lou, F. K. Fatemi, and M. Currie, "Brillouin fibre laser enhanced by Raman amplification," Electron. Lett. 40, 1044-1046 (2004).
[CrossRef]

J. Nonlinear Opt. Phys. Mater.

A. L. Gaeta and R. W. Boyd, "Stimulated Brillouin scattering in the presence of external feedback," J. Nonlinear Opt. Phys. Mater. 1, 581-594 (1992).
[CrossRef]

J. Opt. Soc. Am. B.

I. Bar-Joseph, A. A. Friesem, E. Lichtman, and R. G. Waarts, "Steady and relaxation oscillations of stimulated Brillouin scattering in single-mode optical fibers," J. Opt. Soc. Am. B. 2, 1606 (1985).
[CrossRef]

Opt. Commun.

D. Cotter, "Stimulated Brillouin scattering in monomode optical fibers," Opt. Commun. 4, 10-19 (1983).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301-3309 (1993).
[CrossRef] [PubMed]

R. V. Johnson and J. H. Marburger, "Relaxation oscillation in stimulated Raman and Brillouin scattering," Phys. Rev. A 4, 1175-1182 (1971).
[CrossRef]

Sov. J. Quantum Electron.

A. N. Pilipetskii and V. V. Shkunov, "Calculation of the threshold and of the efficiency of conversion by stimulated scattering in an amplifying medium," Sov. J. Quantum Electron. 15, 284-286 (1985).
[CrossRef]

Other

M. E. V. Pedersen, J. R. Ott, and K. Rottwitt, "Self-Pulsation in Raman Fiber Amplifiers," presented at the Eleventh International Conference on Transparent Optical Networks, Island of São Miguel, Azores, Portugal, 28 June-2 July 2009.

K. Rottwitt and A. J. Stentz, "Raman Amplification in Lightwave Communication Systems," in Optical Fiber Telecommunications, Chap. 5, (Academic Press, San Diego, Calif., 2002).
[CrossRef]

V. I. Kovalev and R. G. Harrison, "Continuous wave stimulated Brillouin scattering in optical fibers: New results and applications for high power lasers," Proc. SPIE 5975, 59750L-1-13 (2006).

G. P. Agrawal, Nonlinear Fiber Optics, Third Edition, (Academic Press, San Diego, 2001).

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Figures (5)

Fig. 1.
Fig. 1.

A fiber cavity of length L with power reflectivity R + i in the left end and R - i in the right end creates a cavity. AC Winput signal in this produce a Brillouin wave in the opposite direction. Both waves are amplified by a Raman amplifier. The signal output power, given by P out S (t)=(1-R - S)P + S (L,t), oscillates in case of high signal input power levels.

Fig. 2.
Fig. 2.

Oscillation power threshold for the discrete Raman amplifier vs. different round trip reflectivity, defined as 10log10(R 2). The blue solid lines corresponds to the scheme with a Raman gain of 20 dB, the green dashed lines show the threshold without the amplification and the red dash-dotted lines show the threshold for lossless fibers. The thick lines are the derived results and the thin lines with error bars are the numerically obtained results. The regions below the curves corresponds to CW output.

Fig. 3.
Fig. 3.

Oscillation power threshold for the distributed Raman amplifier vs. different round trip reflectivity, defined as 10log10(R 2). The blue solid lines corresponds to the scheme in which Raman amplification is used to counterbalance fiber losses as described in the text, the green dashed lines show the threshold without the amplification and the red dash-dotted lines show the threshold for lossless fibers. The thick lines are the derived results and the thin lines with error bars are the numerically obtained results. The regions below the curves corresponds to CW output.

Fig. 4.
Fig. 4.

The threshold for the distributed Raman amplified scheme, shown in Fig. 3, which is numerically calculated in the three cases of i) propagation including depletion, the thin blue solid line, ii) propagation without depletion on the Raman wave, the thin green dashed line, and iii) propagation without depletion on the Raman wave nor the signal wave, thin red dash dotted line, all with error bars. The thick black solid line show the derived threshold.

Fig. 5.
Fig. 5.

Comparison of forward, backward and bidirectional amplification and an investigation of the effect of propagation length, loss and amount of amplification. The general values of L=200 m, g B=0.8 (Wm)-1, g R=5 (Wm)-1 and α=0.8 dB/km when not explicitly stated otherwise. The thick lines indicates the analytically found threshold while the thin lines with error bars show the corresponding numerical calculations. Color codes are as follows: Blue: Backward amplification, 10 dB gain. Green: Forward amplification, 10 dB gain. Red: Bidirectional amplification, 10 dB gain. Light-blue: Backward amplification, 5 dB gain. Pink: Backward amplification, 10 dB gain, 1 km cavity. Yellow: No amplification. Black: No amplification nor loss.

Tables (1)

Tables Icon

Table 1. The used values of the amplifier schemes.

Equations (36)

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

1vg,RPR±t±PR±z=gRωRωSPR±(PS++PS+PB++PB)αRPR±,
1vg,SPS±t±PS±z=gBωBωSPS±PB+gRPS±(PR++PR)αSPS±,
1vg,BPB±t±PB±z=gBPSPB±+gRPB±(PR++PR)αBPB±,
PR+(0,t)=RR+PR(0,t)+PRin,+,PR(L,t)=RRPR+(L,t)+PRin,,
PS+(0,t)=RS+PS(0,t)+PSin,+,PS(L,t)=RSPS+(L,t),
PB+(0,t)=RB+PB(0,t)+ε+,PB(L,t)=RBPB+(L,t)+ε,
PB(0)= rPs+ (0).
PS+(z)=P˜SG+(z),
PS(z)=P˜SρSG+(L)G(z),
PB+(z)=P˜B+G+(z)exp[gBP˜SρSG+(L)J+(z)],
PB(z)=P˜BG+(L)G(z)exp[gBP˜S J (L)]exp[gBP˜SJ(z)],
G±(z)=exp {αz±gRαR[P˜R+(1eαRz)+P˜ReαRL(eαRz1)]},
P˜R±=PRin,±+R˜R±PRin,1R˜R+R˜R,
P˜S=PSin1ρS+ρS,P˜B±=ε±+ρB±ε1ρB+ρBexp{gBP˜S[ρSJ+(L)J(L)]},
J+(z)=G+(L)0zG(z)dz,J(z)=0zG+(z)dz,
J+(L)=J(L)=1exp(αL)α.
rPR=0thr=εG0+(L)exp[gBPR=0thrJR=0(L)],
P˜thrPR=0thr=G+(L)GR=0+(L)exp[gBPR=0thrJR=0(L)]ρBηexp{gB[P˜thrρSJ+(L)PR=0thrJR=0(L)]}exp[gBP˜thrJ(L)]ρB+ρBexp[gBP˜thrρSJ+(L)],
P˜thr=Pthr,in1ρS+ρS,
η=ε+ε.
PR+(z)=P˜R+exp(αRz),
PR(z)=P˜Rexp[αR(Lz)],
P˜R±=PRin,±+R˜R±PRin,±1R˜R+R˜R, R˜R±=RR±exp(αRL).
PS+(z)=P˜SG+(z),
PS(z)=ρP˜SG+(L)G(z),
P˜S=PSin1ρS+ρS, ρi±=Ri±G+(L),
G±(z)=exp{αz±gRαR[P˜R+(1eαRz)+P˜ReαRL(eαRz1)]}.
PB+(z)=P˜B+G+(z)exp[gBP˜SρJ+(z)],
PB(z)=P˜BG(z)exp[gBP˜SJ(L)]exp[gBP˜SJ(z)],
P˜B±=ε±+ρ˜B±ε±1ρ˜B+ρ˜B,J+(z)=G+(L)0zG(z')dz',J(z)=0zG+(z')dz',
ρ˜B=ρBexp[+gBP˜SρSJ+(L)], ρ˜B+=ρB+exp[gBP˜SJ(L)].
JS±(z)=0za±exp[α±z'b±exp(α±z')+c±exp(α±z')]dz',
JS±(x)=a±α±x(0)x(z)exp(b±x'+c±x'1)dx'
=a±α±x(0)x(z)exp{2b±c±2[b±c±x'(b±c±x')1]}dx'
=a±α± x(0)x(z)n=Jn(2b±c±)(b±c±x')ndx',
JS±(x)=a±α±n=n1Jn(2b±c±)n+1(b±c±)n(xn+11)+a±α±c±b±J1(2b±c±)ln(x).

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