Abstract

We investigate theoretically the gain spectrum of a Brillouin fiber amplifier in the saturated region. When the amplifier is operated in the saturated region a hole is burned in the single-pass Brillouin gain spectrum, and peaks appear at frequencies determined mainly from the round-trip time of the amplifier, causing modulation instability in the amplified signal. This type of modulation instability originates intrinsically from signal amplification by the counterpropagating pump beam, which is depleted by the strong signal beam.

© 1995 Optical Society of America

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  1. D. Cotter, J. Opt. Commun. 4, 1 (1983).
    [CrossRef]
  2. R. W. Boyd, K. Rzazewski, Phys. Rev. A 42, 5514 (1990).
    [CrossRef] [PubMed]
  3. A. L. Gaeta, R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
    [CrossRef] [PubMed]
  4. K. Baumgärten, U. Motschmann, K. Sauer, Opt. Commun. 51, 53 (1984).
    [CrossRef]
  5. I. Bar-Joseph, A. A. Friesem, E. Lichtman, R. G. Waarts, J. Opt. Soc. Am. B 2, 10 (1985).
    [CrossRef]
  6. E. M. Dianov, A. Y. Karasik, A. V Lutchnikov, A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
    [CrossRef]
  7. A. Johnstone, Weiping Lu, J. S. Uppal, R. G. Harrison, Opt. Commun. 81, 222 (1991).
    [CrossRef]
  8. Weiping Lu, A. Johnstone, R. G Harrison, Phys. Rev. A 46, 4114 (1992).
    [CrossRef] [PubMed]
  9. M. Dämming, G. Zinner, F. Mitshke, H. Welling, Phys. Rev. A 48, 3301 (1993).
    [CrossRef]

1993 (1)

M. Dämming, G. Zinner, F. Mitshke, H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

1992 (1)

Weiping Lu, A. Johnstone, R. G Harrison, Phys. Rev. A 46, 4114 (1992).
[CrossRef] [PubMed]

1991 (2)

A. Johnstone, Weiping Lu, J. S. Uppal, R. G. Harrison, Opt. Commun. 81, 222 (1991).
[CrossRef]

A. L. Gaeta, R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

1990 (1)

R. W. Boyd, K. Rzazewski, Phys. Rev. A 42, 5514 (1990).
[CrossRef] [PubMed]

1989 (1)

E. M. Dianov, A. Y. Karasik, A. V Lutchnikov, A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

1985 (1)

I. Bar-Joseph, A. A. Friesem, E. Lichtman, R. G. Waarts, J. Opt. Soc. Am. B 2, 10 (1985).
[CrossRef]

1984 (1)

K. Baumgärten, U. Motschmann, K. Sauer, Opt. Commun. 51, 53 (1984).
[CrossRef]

1983 (1)

D. Cotter, J. Opt. Commun. 4, 1 (1983).
[CrossRef]

Bar-Joseph, I.

I. Bar-Joseph, A. A. Friesem, E. Lichtman, R. G. Waarts, J. Opt. Soc. Am. B 2, 10 (1985).
[CrossRef]

Baumgärten, K.

K. Baumgärten, U. Motschmann, K. Sauer, Opt. Commun. 51, 53 (1984).
[CrossRef]

Boyd, R. W.

A. L. Gaeta, R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

R. W. Boyd, K. Rzazewski, Phys. Rev. A 42, 5514 (1990).
[CrossRef] [PubMed]

Cotter, D.

D. Cotter, J. Opt. Commun. 4, 1 (1983).
[CrossRef]

Dämming, M.

M. Dämming, G. Zinner, F. Mitshke, H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

Dianov, E. M.

E. M. Dianov, A. Y. Karasik, A. V Lutchnikov, A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

Friesem, A. A.

I. Bar-Joseph, A. A. Friesem, E. Lichtman, R. G. Waarts, J. Opt. Soc. Am. B 2, 10 (1985).
[CrossRef]

Gaeta, A. L.

A. L. Gaeta, R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Harrison, R. G

Weiping Lu, A. Johnstone, R. G Harrison, Phys. Rev. A 46, 4114 (1992).
[CrossRef] [PubMed]

Harrison, R. G.

A. Johnstone, Weiping Lu, J. S. Uppal, R. G. Harrison, Opt. Commun. 81, 222 (1991).
[CrossRef]

Johnstone, A.

Weiping Lu, A. Johnstone, R. G Harrison, Phys. Rev. A 46, 4114 (1992).
[CrossRef] [PubMed]

A. Johnstone, Weiping Lu, J. S. Uppal, R. G. Harrison, Opt. Commun. 81, 222 (1991).
[CrossRef]

Karasik, A. Y.

E. M. Dianov, A. Y. Karasik, A. V Lutchnikov, A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

Lichtman, E.

I. Bar-Joseph, A. A. Friesem, E. Lichtman, R. G. Waarts, J. Opt. Soc. Am. B 2, 10 (1985).
[CrossRef]

Lu, Weiping

Weiping Lu, A. Johnstone, R. G Harrison, Phys. Rev. A 46, 4114 (1992).
[CrossRef] [PubMed]

A. Johnstone, Weiping Lu, J. S. Uppal, R. G. Harrison, Opt. Commun. 81, 222 (1991).
[CrossRef]

Lutchnikov, A. V

E. M. Dianov, A. Y. Karasik, A. V Lutchnikov, A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

Mitshke, F.

M. Dämming, G. Zinner, F. Mitshke, H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

Motschmann, U.

K. Baumgärten, U. Motschmann, K. Sauer, Opt. Commun. 51, 53 (1984).
[CrossRef]

Pilipetskii, A. N.

E. M. Dianov, A. Y. Karasik, A. V Lutchnikov, A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

Rzazewski, K.

R. W. Boyd, K. Rzazewski, Phys. Rev. A 42, 5514 (1990).
[CrossRef] [PubMed]

Sauer, K.

K. Baumgärten, U. Motschmann, K. Sauer, Opt. Commun. 51, 53 (1984).
[CrossRef]

Uppal, J. S.

A. Johnstone, Weiping Lu, J. S. Uppal, R. G. Harrison, Opt. Commun. 81, 222 (1991).
[CrossRef]

Waarts, R. G.

I. Bar-Joseph, A. A. Friesem, E. Lichtman, R. G. Waarts, J. Opt. Soc. Am. B 2, 10 (1985).
[CrossRef]

Welling, H.

M. Dämming, G. Zinner, F. Mitshke, H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

Zinner, G.

M. Dämming, G. Zinner, F. Mitshke, H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

J. Opt. Commun. (1)

D. Cotter, J. Opt. Commun. 4, 1 (1983).
[CrossRef]

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

I. Bar-Joseph, A. A. Friesem, E. Lichtman, R. G. Waarts, J. Opt. Soc. Am. B 2, 10 (1985).
[CrossRef]

Opt. Commun. (2)

A. Johnstone, Weiping Lu, J. S. Uppal, R. G. Harrison, Opt. Commun. 81, 222 (1991).
[CrossRef]

K. Baumgärten, U. Motschmann, K. Sauer, Opt. Commun. 51, 53 (1984).
[CrossRef]

Opt. Quantum Electron. (1)

E. M. Dianov, A. Y. Karasik, A. V Lutchnikov, A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

Phys. Rev. A (4)

R. W. Boyd, K. Rzazewski, Phys. Rev. A 42, 5514 (1990).
[CrossRef] [PubMed]

A. L. Gaeta, R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Weiping Lu, A. Johnstone, R. G Harrison, Phys. Rev. A 46, 4114 (1992).
[CrossRef] [PubMed]

M. Dämming, G. Zinner, F. Mitshke, H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Configuration of the Brillouin fiber amplifier and (b) spectra of the pump, signal, and probe beams.

Fig. 2
Fig. 2

Saturation properties of the Brillouin fiber amplifier. The Brillouin gain at the Stokes frequency is calculated as a function of the normalized signal intensity. The amplifier length L = 60 m.

Fig. 3
Fig. 3

Gain spectrum Grω) for the probe beam when the amplifier is saturated by the signal power. We assume that L = 60 m, Γ/2π = 20 MHz, and ln Gu(0) = 19.

Equations (9)

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z E p + ( n / c ) t E p = - α E p + i K 1 ρ E s ,
z E s - ( n / c ) t E s = α E s + i K 1 ρ * E s ,
t ρ + ( Γ / 2 ) ρ = i K 2 E p E s * ,
E s ( z , t ) = E s 0 ( z ) { 1 + s + ( z ) exp [ i ( - Δ ω t - Δ k z ) ] + s - ( z ) exp [ i ( Δ ω t + Δ k z ) ] } .
E p ( z , t ) = E p 0 ( z ) { 1 + p + ( z ) exp [ i ( - Δ ω t + Δ k z ) ] + p - ( z ) exp [ i ( Δ ω t - Δ k z ) ] } .
z p + = - η E s 0 ( z ) 2 { s + exp ( - 2 i Δ k z ) + ξ * [ ( 2 i Δ ω / Γ ) p + + s + * exp ( - 2 i Δ k z ) ] } ,
z p - = - η E s 0 ( z ) 2 { s - exp ( 2 i Δ k z ) + ξ [ ( - 2 i Δ ω / Γ ) p - + s + * exp ( 2 i Δ k z ) ] } ,
z s + = - η E p 0 ( z ) 2 { p - exp ( 2 i Δ k z ) + ξ * [ ( 2 i Δ ω / Γ ) s + + p - * exp ( 2 i Δ k z ) ] } ,
z s - = - η E p 0 ( z ) 2 { p - exp ( 2 i Δ k z ) + ξ [ ( - 2 i Δ ω / Γ ) s - + p + * exp ( - 2 i Δ k z ) ] } ,

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