Abstract

An analysis of Rayleigh backscattering (RBS) and amplified spontaneous emission (ASE) in strongly pumped ytterbium fiber amplifiers is presented. The ytterbium (three-level) system is compared with four-level systems that were studied previously. Both approximate expressions and exact numerical solutions for ASE and RBS as well as for the amplifier noise figure are examined. The results suggest that ASE is apparently stronger in three-level systems, which implies a preferable pumping strategy.

© 1999 Optical Society of America

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References

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  1. M. J. F. Digonnet, Rare Earth Doped Fiber Lasers and Amplifiers (Marcel Dekker, New York 1993).
  2. R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997).
    [CrossRef]
  3. E. Desurvire and J. R. Simpson, “Amplification of spontaneous emission in erbium doped single mode fibers,” J. Lightwave Technol. 7, 835–845 (1989).
    [CrossRef]
  4. R. Olshansky, “Noise figure for erbium doped optical fibre amplifiers,” Electron. Lett. 24, 1363–1365 (1988).
    [CrossRef]
  5. A. Bjarklev, Optical Fiber Amplifiers: Design and System Applications (Artech House, Boston, Mass. 1993).
  6. M. N. Zervas and R. I. Laming, “Rayleigh scattering effect on the gain efficiency and noise of erbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 31, 468–471 (1995).
    [CrossRef]
  7. E. G. Neumann, Single Mode Fibers Fundamentals (Springer-Verlag, New York, 1988), pp. 108–111.
  8. A. A. Hardy and R. Oron, “Amplified spontaneous emission and Rayleigh backscattering in strongly pumped fiber amplifiers,” J. Lightwave Technol. 16, 1865–1873 (1998).
    [CrossRef]
  9. B. Rossi, “Commercial fiber lasers take on industrial markets,” Laser Focus World 33(5), 143–149 (1997).
  10. I. Kelson and A. A. Hardy, “Strongly pumped fiber lasers,” IEEE J. Quantum Electron. 34, 1570–1577 (1998).
    [CrossRef]
  11. A. Hardy and R. Oron, “Signal amplification in strongly pumped fiber amplifiers,” IEEE J. Quantum Electron. 33, 307–313 (1997).
    [CrossRef]
  12. R. Oron and A. Hardy, “Approximate analytical expressions for signal amplification in strongly pumped fiber amplifiers,” IEE Proc.: Optoelectron. 145, 138–140 (1998).
  13. C. H. Henry, “Theory of spontaneous emission noise and its application to lasers and optical amplifiers,” J. Lightwave Technol. 4, 288–297 (1986).
    [CrossRef]
  14. H. M. Pask, P. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1, 2–13 (1995).
    [CrossRef]
  15. D. C. Hanna, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Efficient superfluorescent emission at 974 nm and 1040 nm from an Yb-doped fiber,” Opt. Commun. 72, 230–234 (1989).
    [CrossRef]

1998

A. A. Hardy and R. Oron, “Amplified spontaneous emission and Rayleigh backscattering in strongly pumped fiber amplifiers,” J. Lightwave Technol. 16, 1865–1873 (1998).
[CrossRef]

I. Kelson and A. A. Hardy, “Strongly pumped fiber lasers,” IEEE J. Quantum Electron. 34, 1570–1577 (1998).
[CrossRef]

R. Oron and A. Hardy, “Approximate analytical expressions for signal amplification in strongly pumped fiber amplifiers,” IEE Proc.: Optoelectron. 145, 138–140 (1998).

1997

A. Hardy and R. Oron, “Signal amplification in strongly pumped fiber amplifiers,” IEEE J. Quantum Electron. 33, 307–313 (1997).
[CrossRef]

B. Rossi, “Commercial fiber lasers take on industrial markets,” Laser Focus World 33(5), 143–149 (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]

1995

H. M. Pask, P. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1, 2–13 (1995).
[CrossRef]

M. N. Zervas and R. I. Laming, “Rayleigh scattering effect on the gain efficiency and noise of erbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 31, 468–471 (1995).
[CrossRef]

1989

D. C. Hanna, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Efficient superfluorescent emission at 974 nm and 1040 nm from an Yb-doped fiber,” Opt. Commun. 72, 230–234 (1989).
[CrossRef]

E. Desurvire and J. R. Simpson, “Amplification of spontaneous emission in erbium doped single mode fibers,” J. Lightwave Technol. 7, 835–845 (1989).
[CrossRef]

1988

R. Olshansky, “Noise figure for erbium doped optical fibre amplifiers,” Electron. Lett. 24, 1363–1365 (1988).
[CrossRef]

1986

C. H. Henry, “Theory of spontaneous emission noise and its application to lasers and optical amplifiers,” J. Lightwave Technol. 4, 288–297 (1986).
[CrossRef]

Barber, P. R.

H. M. Pask, P. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1, 2–13 (1995).
[CrossRef]

Carman, P. J.

H. M. Pask, P. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1, 2–13 (1995).
[CrossRef]

Dawes, J. M.

H. M. Pask, P. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1, 2–13 (1995).
[CrossRef]

Desurvire, E.

E. Desurvire and J. R. Simpson, “Amplification of spontaneous emission in erbium doped single mode fibers,” J. Lightwave Technol. 7, 835–845 (1989).
[CrossRef]

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]

H. M. Pask, P. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1, 2–13 (1995).
[CrossRef]

D. C. Hanna, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Efficient superfluorescent emission at 974 nm and 1040 nm from an Yb-doped fiber,” Opt. Commun. 72, 230–234 (1989).
[CrossRef]

Hardy, A.

R. Oron and A. Hardy, “Approximate analytical expressions for signal amplification in strongly pumped fiber amplifiers,” IEE Proc.: Optoelectron. 145, 138–140 (1998).

A. Hardy and R. Oron, “Signal amplification in strongly pumped fiber amplifiers,” IEEE J. Quantum Electron. 33, 307–313 (1997).
[CrossRef]

Hardy, A. A.

Henry, C. H.

C. H. Henry, “Theory of spontaneous emission noise and its application to lasers and optical amplifiers,” J. Lightwave Technol. 4, 288–297 (1986).
[CrossRef]

Kelson, I.

I. Kelson and A. A. Hardy, “Strongly pumped fiber lasers,” IEEE J. Quantum Electron. 34, 1570–1577 (1998).
[CrossRef]

Laming, R. I.

M. N. Zervas and R. I. Laming, “Rayleigh scattering effect on the gain efficiency and noise of erbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 31, 468–471 (1995).
[CrossRef]

Mackechnie, C. J.

H. M. Pask, P. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1, 2–13 (1995).
[CrossRef]

Nilsson, J.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997).
[CrossRef]

Olshansky, R.

R. Olshansky, “Noise figure for erbium doped optical fibre amplifiers,” Electron. Lett. 24, 1363–1365 (1988).
[CrossRef]

Oron, R.

A. A. Hardy and R. Oron, “Amplified spontaneous emission and Rayleigh backscattering in strongly pumped fiber amplifiers,” J. Lightwave Technol. 16, 1865–1873 (1998).
[CrossRef]

R. Oron and A. Hardy, “Approximate analytical expressions for signal amplification in strongly pumped fiber amplifiers,” IEE Proc.: Optoelectron. 145, 138–140 (1998).

A. Hardy and R. Oron, “Signal amplification in strongly pumped fiber amplifiers,” IEEE J. Quantum Electron. 33, 307–313 (1997).
[CrossRef]

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]

Pask, H. M.

H. M. Pask, P. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1, 2–13 (1995).
[CrossRef]

Perry, I. R.

D. C. Hanna, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Efficient superfluorescent emission at 974 nm and 1040 nm from an Yb-doped fiber,” Opt. Commun. 72, 230–234 (1989).
[CrossRef]

Rossi, B.

B. Rossi, “Commercial fiber lasers take on industrial markets,” Laser Focus World 33(5), 143–149 (1997).

Simpson, J. R.

E. Desurvire and J. R. Simpson, “Amplification of spontaneous emission in erbium doped single mode fibers,” J. Lightwave Technol. 7, 835–845 (1989).
[CrossRef]

Smart, R. G.

D. C. Hanna, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Efficient superfluorescent emission at 974 nm and 1040 nm from an Yb-doped fiber,” Opt. Commun. 72, 230–234 (1989).
[CrossRef]

Suni, P. J.

D. C. Hanna, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Efficient superfluorescent emission at 974 nm and 1040 nm from an Yb-doped fiber,” Opt. Commun. 72, 230–234 (1989).
[CrossRef]

Townsend, J. E.

D. C. Hanna, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Efficient superfluorescent emission at 974 nm and 1040 nm from an Yb-doped fiber,” Opt. Commun. 72, 230–234 (1989).
[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]

H. M. Pask, P. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1, 2–13 (1995).
[CrossRef]

D. C. Hanna, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Efficient superfluorescent emission at 974 nm and 1040 nm from an Yb-doped fiber,” Opt. Commun. 72, 230–234 (1989).
[CrossRef]

Zervas, M. N.

M. N. Zervas and R. I. Laming, “Rayleigh scattering effect on the gain efficiency and noise of erbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 31, 468–471 (1995).
[CrossRef]

Electron. Lett.

R. Olshansky, “Noise figure for erbium doped optical fibre amplifiers,” Electron. Lett. 24, 1363–1365 (1988).
[CrossRef]

IEE Proc.: Optoelectron.

R. Oron and A. Hardy, “Approximate analytical expressions for signal amplification in strongly pumped fiber amplifiers,” IEE Proc.: Optoelectron. 145, 138–140 (1998).

IEEE J. Quantum Electron.

I. Kelson and A. A. Hardy, “Strongly pumped fiber lasers,” IEEE J. Quantum Electron. 34, 1570–1577 (1998).
[CrossRef]

A. Hardy and R. Oron, “Signal amplification in strongly pumped fiber amplifiers,” IEEE J. Quantum Electron. 33, 307–313 (1997).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997).
[CrossRef]

M. N. Zervas and R. I. Laming, “Rayleigh scattering effect on the gain efficiency and noise of erbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 31, 468–471 (1995).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

H. M. Pask, P. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1, 2–13 (1995).
[CrossRef]

J. Lightwave Technol.

C. H. Henry, “Theory of spontaneous emission noise and its application to lasers and optical amplifiers,” J. Lightwave Technol. 4, 288–297 (1986).
[CrossRef]

A. A. Hardy and R. Oron, “Amplified spontaneous emission and Rayleigh backscattering in strongly pumped fiber amplifiers,” J. Lightwave Technol. 16, 1865–1873 (1998).
[CrossRef]

E. Desurvire and J. R. Simpson, “Amplification of spontaneous emission in erbium doped single mode fibers,” J. Lightwave Technol. 7, 835–845 (1989).
[CrossRef]

Laser Focus World

B. Rossi, “Commercial fiber lasers take on industrial markets,” Laser Focus World 33(5), 143–149 (1997).

Opt. Commun.

D. C. Hanna, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Efficient superfluorescent emission at 974 nm and 1040 nm from an Yb-doped fiber,” Opt. Commun. 72, 230–234 (1989).
[CrossRef]

Other

M. J. F. Digonnet, Rare Earth Doped Fiber Lasers and Amplifiers (Marcel Dekker, New York 1993).

E. G. Neumann, Single Mode Fibers Fundamentals (Springer-Verlag, New York, 1988), pp. 108–111.

A. Bjarklev, Optical Fiber Amplifiers: Design and System Applications (Artech House, Boston, Mass. 1993).

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Figures (8)

Fig. 1
Fig. 1

Energy-band diagram for a three-level system: (a) a general representation, (b) a representation reduced to the system of ytterbium-doped fibers.

Fig. 2
Fig. 2

Pump and signal powers along the fiber length for Pp(0)=20 W and Ps=0.1 W. Continuous curves, exact solutions; circles, approximate solutions for (a) forward and (b) backward pumping.

Fig. 3
Fig. 3

RBS power along the fiber length for forward and backward pumping. Solid curves, exact numerical solutions, circles, approximate solutions given by Eqs. (9) and (10); dashed curves, the artificial four-level system. Note that the RBS propagates in the direction opposite the signal.

Fig. 4
Fig. 4

RBS power at the fiber end as a function of the input signal. Solid curves, exact numerical solutions; circles and asterisks, approximate solutions of Eqs. (9) and (10) for forward and backward pumping, respectively.

Fig. 5
Fig. 5

ASE± powers along the fiber length. Solid curves, exact solutions; circles, approximate solutions; dashed curves, the artificial four-level system for (a) forward and (b) backward pumping.

Fig. 6
Fig. 6

ASE power at the fiber ends as a function of the input signal. Solid curves, exact numerical solutions; circles and asterisks, approximate solutions of Eqs. (11) and (12) for ASE+ and ASE-, respectively, in both (a) forward and (b) backward pumping schemes.

Fig. 7
Fig. 7

Amplifier noise figure at the fiber output end as a function of the injected signal power. Solid curves, exact solutions; circles and asterisks, approximate solutions obtained by plugging Eq. (11) or (12) into Eq. (16) or (17) for forward and backward pumping, respectively.

Fig. 8
Fig. 8

Output power and the amplifier noise figure at the fiber output end as a function of the fiber length for forward and backward pumping for an input signal power of 0.1 W.

Tables (1)

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Table 1 Parameters Used in the Computation

Equations (25)

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N2(z, t)t=λpΓpσaphcAPp(z, t)[N-N2(z, t)]-N2(z, t)τ-λpΓpσephcAPp(z, t)N2(z, t)-ΓshcAN2(z, t)σe(λ)[P+(z, t, λ)+P-(z, t, λ)]λdλ+ΓshcA[N-N2(z, t)]σa(λ)×[P+(z, t, λ)+P-(z, t, λ)]λdλ,
±dP±(z, t, λ)dz=Γs{σe(λ)N2(z, t)-σa(λ)[N-N2(z, t)]}P±(z, t, λ)+Γsσe(λ)N2(z, t)P0(λ)-α(λ)P±(z, t, λ)+SαRS(λ)P(z, λ),
±dPp±(z, t)dz=-Γp{σap[N-N2(z, t)]+[σ24(λp)-σep]N2(z, t)}Pp±(z, t)-α(λp)Pp±(z, t),
Ps+(z)=Ps+(0)ϕ(z)exp[Rz/(q-1)],
[ϕ(z)]1-q1-B3/B41-(B3/B4)[ϕ(z)]1-q1+B2B4/B3=exp[B4(1-q)z)]
Pp(z)=Pp(0)[Ps(z)/Ps(0)]q exp(-Rz);
Ps-(z)=Ps-(0)ϕˆ(L-z)exp[R(L-z)/(1+q)],
[ϕˆ(ζ)]1+q1-C3/C41-(C3/C4)[ϕˆ(ζ)]1+q1+C2C4/C3=exp[C4(1+q)ζ)],
PRBS-(z)=SαRS(λs)Ps+(z)zL[Ps+(z)]2dz,
PRBS+(z)=SαRS(λs)Ps-(z)0z[Ps-(z)]2dz,
P+(z, λ)=P+(0, λ)G(0, z, λ)+σe(λ)P0(λ)σe(λ)+σa(λ)[G(0, z, λ)-1]+[ΓsNσa(λ)+α(λ)]σe(λ)P0(λ)σe(λ)+σa(λ)×0zG(z, z, λ)dz,
P-(z, λ)=P-(L, λ)G(z, L, λ)+σe(λ)P0(λ)σe(λ)+σa(λ)[G(z, L, λ)-1]+[ΓsNσa(λ)+α(λ)]σe(λ)P0(λ)σe(λ)+σa(λ)×zLG(z, z, λ)dz,
G(z, z, λ)expzzgeff(ξ, λ)dξ
geff(ξ, λ)=Γs{[σe(λ)+σa(λ)]N2(ξ)-σa(λ)N}-α(λ).
N2(z)N=1+λsΓsσa(λs)Ps±(z)λpΓpσapPp(z)1+σepσap+hcAτλpΓpσapPp(z)+λsΓs[σe(λs)+σa(λs)]Ps±(z)λpΓpσapPp(z).
F0+(z)=1G(0, z, λs)2PASE+(z, λs)P0(λs)+1
F0-(z)=1G(z, L, λs)2PASE-(z, λs)P0(λs)+1
q=Γp[σap+σep-σ24(λp)]Γs[σe(λs)+σa(λs)],
R=ΓpσapN+α(λp)-[Γsσa(λs)N+α(λs)]q,
B2=Γsλs[σe(λs)+σa(λs)]ΓpλpσapPs+(0)Pp(0)11+(σep/σap),
B3=α(λs)-R1-qB2,
B4=Γsσe(λs)N1+(σep/σap)+R1-q-α(λs),
C2=Γsλs[σe(λs)+σa(λs)]ΓpλpσapPs-(L)Pp(L)11+(σep/σap),
C3=α(λs)+R1+qC2,
C4=Γsσe(λs)N1+(σep/σap)-R1+q-α(λs).

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