Abstract

We derive a closed-form approximate analytical formula for the gain of a Brillouin fiber amplifier operating in the depleted pump regime. We take into account the material loss of the medium, which is a strong effect in optical fibers. We validate obtained results numerically and experimentally. The presented analysis can be used to accurately predict the performance of high-gain Brillouin fiber amplifiers.

© 2006 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), Chap. 9.
  2. X. S. Yao, IEEE Photon. Technol. Lett. 10, 138 (1998).
    [CrossRef]
  3. T. Tanemura, Y. Takushima, and K. Kikuchi, Opt. Lett. 27, 1552 (2002).
    [CrossRef]
  4. S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, Electron. Lett. 36, 944 (2000).
    [CrossRef]
  5. M. J. LaGasse, W. Charczenko, M. C. Hamilton, and S. Thaniyavarn, Electron. Lett. 30, 2157 (1994).
    [CrossRef]
  6. K. J. Williams and R. D. Esman, Electron. Lett. 30, 1965 (1994).
    [CrossRef]
  7. A. Wiberg and P. O. Hedekvist, in Proc. SPIE 5466, 148 (2004).
    [CrossRef]
  8. T. Schneider, M. Junker, and D. Hannover, Electron. Lett. 40, 1500 (2004).
    [CrossRef]
  9. K.T. V.Graffan and B.T.Meggitt, eds., Optical Fiber Sensor Technology, Vol. 4 (Kluwer, 1999).
  10. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003), Chap. 9.
  11. A. Kobyakov, S. Kumar, D. Chowdhury, A. B. Ruffin, M. Sauer, S. R. Bickham, and R. Mishra, Opt. Express 13, 5338 (2005).
    [CrossRef] [PubMed]
  12. M. Vasilyev and A. Kobyakov, in Conference on Lasers & Electro-Optics (CLEO), Vol. 88 of OSA Trends in Optics and Photonics (Optical Society of America, 2003), paper CWL3.
  13. L. Chen and X. Bao, Opt. Commun. 152, 65 (1998).
    [CrossRef]
  14. S. Le Floch and P. Cambon, J. Opt. Soc. Am. B 20, 1132 (2003).
    [CrossRef]
  15. A. Kobyakov, S. Darmanyan, and D. Chowdhury, Opt. Commun. 260, 46 (2006).
    [CrossRef]

2006 (1)

A. Kobyakov, S. Darmanyan, and D. Chowdhury, Opt. Commun. 260, 46 (2006).
[CrossRef]

2005 (1)

2004 (2)

A. Wiberg and P. O. Hedekvist, in Proc. SPIE 5466, 148 (2004).
[CrossRef]

T. Schneider, M. Junker, and D. Hannover, Electron. Lett. 40, 1500 (2004).
[CrossRef]

2003 (1)

S. Le Floch and P. Cambon, J. Opt. Soc. Am. B 20, 1132 (2003).
[CrossRef]

2002 (1)

2000 (1)

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, Electron. Lett. 36, 944 (2000).
[CrossRef]

1998 (2)

X. S. Yao, IEEE Photon. Technol. Lett. 10, 138 (1998).
[CrossRef]

L. Chen and X. Bao, Opt. Commun. 152, 65 (1998).
[CrossRef]

1994 (2)

M. J. LaGasse, W. Charczenko, M. C. Hamilton, and S. Thaniyavarn, Electron. Lett. 30, 2157 (1994).
[CrossRef]

K. J. Williams and R. D. Esman, Electron. Lett. 30, 1965 (1994).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), Chap. 9.

Bao, X.

L. Chen and X. Bao, Opt. Commun. 152, 65 (1998).
[CrossRef]

Bickham, S. R.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003), Chap. 9.

Cambon, P.

S. Le Floch and P. Cambon, J. Opt. Soc. Am. B 20, 1132 (2003).
[CrossRef]

Charczenko, W.

M. J. LaGasse, W. Charczenko, M. C. Hamilton, and S. Thaniyavarn, Electron. Lett. 30, 2157 (1994).
[CrossRef]

Charlet, G.

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, Electron. Lett. 36, 944 (2000).
[CrossRef]

Chazelas, J.

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, Electron. Lett. 36, 944 (2000).
[CrossRef]

Chen, L.

L. Chen and X. Bao, Opt. Commun. 152, 65 (1998).
[CrossRef]

Chowdhury, D.

Darmanyan, S.

A. Kobyakov, S. Darmanyan, and D. Chowdhury, Opt. Commun. 260, 46 (2006).
[CrossRef]

Dolfi, D.

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, Electron. Lett. 36, 944 (2000).
[CrossRef]

Esman, R. D.

K. J. Williams and R. D. Esman, Electron. Lett. 30, 1965 (1994).
[CrossRef]

Hamilton, M. C.

M. J. LaGasse, W. Charczenko, M. C. Hamilton, and S. Thaniyavarn, Electron. Lett. 30, 2157 (1994).
[CrossRef]

Hannover, D.

T. Schneider, M. Junker, and D. Hannover, Electron. Lett. 40, 1500 (2004).
[CrossRef]

Hedekvist, P. O.

A. Wiberg and P. O. Hedekvist, in Proc. SPIE 5466, 148 (2004).
[CrossRef]

Huignard, J.-P.

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, Electron. Lett. 36, 944 (2000).
[CrossRef]

Junker, M.

T. Schneider, M. Junker, and D. Hannover, Electron. Lett. 40, 1500 (2004).
[CrossRef]

Kikuchi, K.

Kobyakov, A.

A. Kobyakov, S. Darmanyan, and D. Chowdhury, Opt. Commun. 260, 46 (2006).
[CrossRef]

A. Kobyakov, S. Kumar, D. Chowdhury, A. B. Ruffin, M. Sauer, S. R. Bickham, and R. Mishra, Opt. Express 13, 5338 (2005).
[CrossRef] [PubMed]

M. Vasilyev and A. Kobyakov, in Conference on Lasers & Electro-Optics (CLEO), Vol. 88 of OSA Trends in Optics and Photonics (Optical Society of America, 2003), paper CWL3.

Kumar, S.

LaGasse, M. J.

M. J. LaGasse, W. Charczenko, M. C. Hamilton, and S. Thaniyavarn, Electron. Lett. 30, 2157 (1994).
[CrossRef]

Le Floch, S.

S. Le Floch and P. Cambon, J. Opt. Soc. Am. B 20, 1132 (2003).
[CrossRef]

Mishra, R.

Ruffin, A. B.

Sauer, M.

Schneider, T.

T. Schneider, M. Junker, and D. Hannover, Electron. Lett. 40, 1500 (2004).
[CrossRef]

Takushima, Y.

Tanemura, T.

Thaniyavarn, S.

M. J. LaGasse, W. Charczenko, M. C. Hamilton, and S. Thaniyavarn, Electron. Lett. 30, 2157 (1994).
[CrossRef]

Tonda-Goldstein, S.

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, Electron. Lett. 36, 944 (2000).
[CrossRef]

Vasilyev, M.

M. Vasilyev and A. Kobyakov, in Conference on Lasers & Electro-Optics (CLEO), Vol. 88 of OSA Trends in Optics and Photonics (Optical Society of America, 2003), paper CWL3.

Wiberg, A.

A. Wiberg and P. O. Hedekvist, in Proc. SPIE 5466, 148 (2004).
[CrossRef]

Williams, K. J.

K. J. Williams and R. D. Esman, Electron. Lett. 30, 1965 (1994).
[CrossRef]

Yao, X. S.

X. S. Yao, IEEE Photon. Technol. Lett. 10, 138 (1998).
[CrossRef]

Electron. Lett. (4)

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, Electron. Lett. 36, 944 (2000).
[CrossRef]

M. J. LaGasse, W. Charczenko, M. C. Hamilton, and S. Thaniyavarn, Electron. Lett. 30, 2157 (1994).
[CrossRef]

K. J. Williams and R. D. Esman, Electron. Lett. 30, 1965 (1994).
[CrossRef]

T. Schneider, M. Junker, and D. Hannover, Electron. Lett. 40, 1500 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

X. S. Yao, IEEE Photon. Technol. Lett. 10, 138 (1998).
[CrossRef]

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

S. Le Floch and P. Cambon, J. Opt. Soc. Am. B 20, 1132 (2003).
[CrossRef]

Opt. Commun. (2)

A. Kobyakov, S. Darmanyan, and D. Chowdhury, Opt. Commun. 260, 46 (2006).
[CrossRef]

L. Chen and X. Bao, Opt. Commun. 152, 65 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

A. Wiberg and P. O. Hedekvist, in Proc. SPIE 5466, 148 (2004).
[CrossRef]

Other (4)

K.T. V.Graffan and B.T.Meggitt, eds., Optical Fiber Sensor Technology, Vol. 4 (Kluwer, 1999).

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003), Chap. 9.

M. Vasilyev and A. Kobyakov, in Conference on Lasers & Electro-Optics (CLEO), Vol. 88 of OSA Trends in Optics and Photonics (Optical Society of America, 2003), paper CWL3.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), Chap. 9.

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Figures (2)

Fig. 1
Fig. 1

(a), (b) Normalized power of the Stokes wave u and (c), (d) of the pump w versus the dimensionless propagation distance ξ for two values of the nonlinear parameter: k = 14 [(a), (c)] and k = 70 [(b), (d)]. Thick solid curves, approximate analytical solution (11, 12); dashed curves, full numerical solution of Eq. (2); thin solid curves, UPA solution (14). ϵ = 10 3 , a = 0.46 .

Fig. 2
Fig. 2

(a) Transmitted pump power P p ( L ) and (b) BFA gain G BFA versus the input pump power P p ( 0 ) . Open circles, experimental data; thick solid curves, predictions of the analytical formula (15); thin solid curves, calculations based on UPA; dashed curves, numerical results. The power of the Stokes seed wave is P S ( L ) = 28 dBm and L = 10 km .

Equations (18)

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d P p d z = γ P p P S α P p ,
d P S d z = γ P p P S + α P S ,
w ξ = k u w a w , u ξ = k u w + a u ,
w ( ξ ) = A ( ξ ) [ 1 ρ ( ξ ) ] , u ( ξ ) = B ( ξ ) [ 1 μ ( ξ ) ] ,
A ξ = k A B , B ξ = k A B ,
A ( ξ ) = c 0 [ 1 ( 1 c 0 ) exp ( c 0 k ξ ) ] 1 ,
B ( ξ ) = c 0 ( 1 c 0 ) [ exp ( c 0 k ξ ) 1 + c 0 ] 1 ,
ρ ξ = ( k B μ + a ) ( 1 ρ ) ,
μ ξ = ( k A ρ + a ) ( 1 μ ) ,
μ ( ξ ) 1 e a ( ξ 1 ) .
ln [ 1 ρ ( ξ ) ] = k 0 ξ B ( ζ ) [ 1 e a ( ζ 1 ) ] d ζ a ξ k ( 1 e a ) 0 ξ B ( ζ ) d ζ a ξ .
1 ρ ( ξ ) = A ( ξ ) exp ( a ) 1 e a ξ .
w ( ξ ) A ( ξ ) exp ( a ) exp ( a ξ ) ,
u ( ξ ) B ( ξ ) exp [ a ( ξ 1 ) ] ,
c 0 1 k { Λ + ln [ Λ ( 1 Λ k ) ] } ,
w UPA ( ξ ) = e a ξ ,
u UPA ( ξ ) = ϵ exp [ a ( ξ 1 ) + k a ( e a ξ e a ) ] .
G BFA = P p ( 0 ) P S ( L ) { 1 Λ + ln [ Λ ( 1 Λ k ) ] k } e α L .

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