Abstract

We show that the classic Raman threshold formula is unsuitable to accurately predict the onset of Raman scattering in high-power CW double-clad fiber amplifiers. Consequently new analytical formulas for the Raman threshold are obtained and their accuracy is tested. Using these new formulas, the dependence of the Raman threshold on various parameters is studied.

© 2009 Optical Society of America

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References

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  1. J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
    [CrossRef]
  2. D. Gapontsev, IPG Photonics, "6kW CW Single Mode Ytterbium Fiber Laser in All-Fiber Format," in "Solid State and Diode Laser Technology Review" (Albuquerque, 2008)
  3. S. W. Allison, G. T. Gillies, D. W. Magnuson, and T. S. Pagano, "Pulsed laser damage to optical fibers," Appl. Opt. 24, 3140-3145 (1985).
    [CrossRef] [PubMed]
  4. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, NY, 1995).
  5. J. Kim, P. Dupriez, C. Codemard, J. Nilsson, and J. K. Sahu, "Suppression of stimulated Raman scattering in a high power Yb-doped fiber amplifier using a W-type core with fundamental mode cut-off," Opt. Express 14, 5103-5113 (2006).
    [CrossRef] [PubMed]
  6. J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, "Extended single-mode photonic crystal fiber lasers," Opt. Express 14, 2715-2720 (2006)
    [CrossRef] [PubMed]
  7. 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]
  8. R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-Doped Fiber Amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
    [CrossRef]
  9. Y. Wang, "Stimulated Raman scattering in high-power double-clad fiber lasers and power amplifiers," Opt. Eng.  44, 114202-1 - 114202-12 (2005).
    [CrossRef]
  10. R. H. Stolen, "Polarization effects in fiber Raman and Brillouin lasers," IEEE J. Quantum Electron. QE-15, 1157-1160 (1979).
    [CrossRef]
  11. Y. Wang, C. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
    [CrossRef]
  12. F. Röser, D. N. Schimpf, J. Rothhardt, T. Eidam, J. Limpert, A. Tünnermann, and F. Salin, "Gain limitations and consequences for short length fiber amplifiers," in OSA Topical Meeting on Advanced Solid-State Photonics (ASSP, 2008), paper WB22.

2007

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
[CrossRef]

2006

2004

Y. Wang, C. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
[CrossRef]

1997

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-Doped Fiber Amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

1985

1979

R. H. Stolen, "Polarization effects in fiber Raman and Brillouin lasers," IEEE J. Quantum Electron. QE-15, 1157-1160 (1979).
[CrossRef]

1972

Allison, S. W.

Codemard, C.

Dupriez, P.

Eberhardt, R.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
[CrossRef]

Ermeneux, S.

Gillies, G. T.

Hanna, D. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-Doped Fiber Amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Kim, J.

Klingebiel, S.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
[CrossRef]

Limpert, J.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
[CrossRef]

J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, "Extended single-mode photonic crystal fiber lasers," Opt. Express 14, 2715-2720 (2006)
[CrossRef] [PubMed]

Magnuson, D. W.

Nilsson, J.

Pagano, T. S.

Paschotta, R.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-Doped Fiber Amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Peschel, T.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
[CrossRef]

Po, H.

Y. Wang, C. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
[CrossRef]

Röser, F.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
[CrossRef]

J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, "Extended single-mode photonic crystal fiber lasers," Opt. Express 14, 2715-2720 (2006)
[CrossRef] [PubMed]

Rothhardt, J.

Sahu, J. K.

Salin, F.

Schmidt, O.

Schreiber, T.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
[CrossRef]

J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, "Extended single-mode photonic crystal fiber lasers," Opt. Express 14, 2715-2720 (2006)
[CrossRef] [PubMed]

Smith, R. G.

Stolen, R. H.

R. H. Stolen, "Polarization effects in fiber Raman and Brillouin lasers," IEEE J. Quantum Electron. QE-15, 1157-1160 (1979).
[CrossRef]

Tropper, A. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-Doped Fiber Amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Tünnermann, A.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
[CrossRef]

J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, "Extended single-mode photonic crystal fiber lasers," Opt. Express 14, 2715-2720 (2006)
[CrossRef] [PubMed]

Wang, Y.

Y. Wang, C. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
[CrossRef]

Wirth, C.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
[CrossRef]

Xu, C.

Y. Wang, C. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
[CrossRef]

Yvernault, P.

Appl. Opt.

IEEE J. Quantum Electron.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-Doped Fiber Amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

R. H. Stolen, "Polarization effects in fiber Raman and Brillouin lasers," IEEE J. Quantum Electron. QE-15, 1157-1160 (1979).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, "The rising power of fiber lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 13, 537-545 (2007).
[CrossRef]

Opt. Commun.

Y. Wang, C. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
[CrossRef]

Opt. Express

Other

D. Gapontsev, IPG Photonics, "6kW CW Single Mode Ytterbium Fiber Laser in All-Fiber Format," in "Solid State and Diode Laser Technology Review" (Albuquerque, 2008)

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, NY, 1995).

Y. Wang, "Stimulated Raman scattering in high-power double-clad fiber lasers and power amplifiers," Opt. Eng.  44, 114202-1 - 114202-12 (2005).
[CrossRef]

F. Röser, D. N. Schimpf, J. Rothhardt, T. Eidam, J. Limpert, A. Tünnermann, and F. Salin, "Gain limitations and consequences for short length fiber amplifiers," in OSA Topical Meeting on Advanced Solid-State Photonics (ASSP, 2008), paper WB22.

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Figures (2)

Fig. 1.
Fig. 1.

CW fiber amplifier operating at the Raman thresholds as calculated with the new proposed formulas for a) co-propagating and b) counter-propagating pump configurations.

Fig. 2.
Fig. 2.

Map showing the dependence of the Raman threshold on the fiber length and doping concentration for a signal wavelength of 1064nm for a) counter-propagating and b) counter-propagating pump configuration. The white line represents the absorption length for each doping concentration (13dB total small signal pump absorption).

Tables (2)

Tables Icon

Table 1. Raman threshold predictions with the different formulas for a signal wavelength of 1064nm

Tables Icon

Table 2. Raman threshold predictions with the different formulas for a signal wavelength of 1030nm

Equations (39)

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Pth=16·Aeff/gRLeff
dPsignaldz=ωsignalωRgA PRAeff Psignal αsignal (z) Psignal
dPRdz=gR PsignalAeff PRαR (z) PR
Psignal(z)=Psignalo f (z)
PR(z)=PRo egRPsignaloAeff0Lf(z)dz0LαR(z)dz
PRoegRPsignalAeffLeffγR=Psignal(L)β
N=N1+N2
N2τ=ΓpλphcA [σapN1σepN2] Aeffp (Ip++Ip)+ΓsignalλsignalhcA[σasignalN1σesignalN2]Aeff Isignal+
±dIp±dz =Γp [σapN1σepN2] Ip±+αp Ip±
dIsignal+dz =Γsignal [σasignalN1σesignalN2] Isignal++αsignal Isignal+
Pp(z)Ppo eζ(Lz)
Psignal(z)C·Aeffαsignal·ζ(eζ·zeαsignalz)+Psignal0eαsignalz
ζ=Γp N (σesignalσapσasignalσep)σesignal+σasignal
C=Γsignal·ζΓpIpo
Psignal(L)=C·Aeffαsignal+ζ (eζ·LeαsignalL)+PsignaloeαsignalL
Leff=0LIsignal(z)dzIsignalo=C·(ζ·eαsignalLαsignaleζ·L+αsignalζ)Isignalo(αsignalζ)αsignalζ+1eαsignalLαlaser
Ppave=Ppo(1e(ζ+αp)L)(ζ+αp)L
PsignalavePpo[αsignalζ(eζ.L1)(eαsignal1)]Lαsignal +Psignalo
dPRdz=gR PsignalAeff PRΓR[σaRN1σeRN2]PRα'R PR
PR(L)=PRo . egRPsignalAeffLeff . eΓRNσeRσapσesignal+σasignal0LIp(z)Isignal(z)dzΓRNσesignalσaRσeRσasignalσesignal+σasignalLα'RL
0LIp(z)Isignal(z)dz=AeffζAeffpLn (1+PpoPsignalo(Psignalo+Ppo)eζLPsignalo(1+PsignaloPpo))
dPRdz=gRPsignalAeff (PR+PRspon)+ΓRσeRN2PRα'R PR +2σeRN2hc2ΔλASEλR3
PRspon=hcλRBeff
PR(z)2σeRN2avehc2ΔλASEλR3+gRPsignalaveAeffPRspongRPsignalaveAeff+ΓRσeRN2aveα'R e(gRPsignalaveAeff+ΓRσeRN2aveα'R)z
2σeRN2avehc2ΔλASEλR3+gRPsignalaveAeffPRspongRPsignalaveAeff+ΓRσeRN2aveα'RegRPpo[αsignalζ(eζL1)(eαsignalL1)]αsignal.Aeff+gRPsignaloLAeffγRPpo(eαsignalLeζL)+PsignaloeαsignalLβ
Psignal(L)=C·Aeff·eζ·Lαsignal+ζ(eζ·LeαsignalL) +PsignaloeαsignalL
Leff=C·eζ·L(ζ·eαsignalL+αsignaleζ·Lαsignalζ)Isignalo(αsignal+ζ)αsignalζ+1eαsignalLαlaser
Ppave=Ppo(1e(ζ+αp)L)(ζ+αp)L
PsignalavePpoeζ.L[αsignalζ(eζ.L1)+(eαsignalL1)]Lαsignal+Psignalo
0LIp(z)Isignal(z)dz=AeffζAeffp(1+PsignaloPpoeζ.L)Ln((PsignaloPpo1)eζ.L+(PsignaloPpoeζ.L+1).(1PpoPsignalo)(PsignaloPpo1).(1+eζ.L))
2σeRN2avehc2ΔλASEλR3+gRPsignalaveAeffPRspongRPsignalaveAeff+ΓRσeRN2aveα'RegRPpoeζ.L[αsignalζ(eζ.L1)+eαsignalL1]αsignal.Aeff+gRPsignaloLAeffγRPpo(1eζL)+PsignaloeαsignalLβ
2βσeRN̅2avehc2ΔλASEλR3Ppo(eαsignalLeζL)egRPp[αsignalζ(eζL1)eαsignalL1]αsignal.AeffgRPsignaloLAeff+γR
N̄2ave=(σapαsignalAeff+σasignalAeffpump(ζ+αp)[αsignalζ(eζ.L1)(eαsignal.L1)])N(σap+σep)αsignalAeff+(σasignal+σesignal)Aeffpump(ζ+αp)[αsignalζ(eζ.L1)(eαsignal.L1)
γ̅R=γR(Ppo=Psiganlo)+γR(Ppo=1000*Psignalo)2
f(x)=xBeAx+DA11+e(xxo)/dx with {A1=0.465eDBAxo=2.21BAdx=1.07A
PpAeffαsignalgR2.21(eαsignalLeζL)+1.07Ln(egRPsignaloLAeff+γ̄R(eαsignalLeζL)AeffαsignalβσeRN̅2avegR[αsignalζ(eζ.L1)(eαsignalL1)])+15αsignalζ(eζ.L1)(eαsignalL1)
Ppo(16AeffgRLPsignalo)L.αsignal[αsignalζ(eζ.L1)(eαsignalL1)]
PpoAeffαsignalgR2.21(1eζL)+1.07Ln(egRPsignaloLAeff+γ̄R(1eζL)AeffαsignalβσeRN̄2avegR[αsignalζ(eζ.L1)+(eαsignalL1)]eζ.L)+15αsignalζ(eζ.L1)+(eαsignalL1)eζ.L
Ppo(16AeffgRLPsignalo)L.αsignal[αsignalζ(eζ.L1)+(eαsignalL1)]eζ.L

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