Abstract

We have developed a model to study nonlinear pulse propagation in a fiber Bragg grating written in an erbium-doped fiber amplifier. The saturation effect in such amplifiers depends on the accumulated energy along the pulse rather than on the pulse instantaneous power. We have shown that the gain saturation effect cannot be neglected when Bragg solitons are amplified by erbium-doped fiber amplifiers. The slow saturation of the amplifier limits the output pulse power, and it tends to split the amplified pulse into several pulses. We have shown that when the propagation velocity of the amplified pulses decreases, the amplifier gain per unit length increases.

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  1. W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
    [CrossRef] [PubMed]
  2. J. E. Sipe and H. G. Winful, Opt. Lett. 13, 132 (1988).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
    [CrossRef]
  5. B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
    [CrossRef] [PubMed]
  6. J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
    [CrossRef]
  7. C. M. de Sterke and J. E. Sipe, Phys. Rev. A 43, 2467 (1991).
    [CrossRef]
  8. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 77, 056606 (2008).
    [CrossRef]
  9. C. R. Giles and E. Desurvire, J. Lightwave Technol. 9, 271 (1991).
    [CrossRef]
  10. K. Motoshima, L. M. Leba, D. N. Chen, M. M. Downs, T. Li, and E. Desurvire, IEEE Photon. Technol. Lett. 5, 1423 (1993).
    [CrossRef]
  11. A. Rosenthal and M. Horowitz, Opt. Lett. 31, 1334 (2006).
    [CrossRef] [PubMed]
  12. G. P. Agrawal, Phys. Rev. A 44, 7493 (1991).
    [CrossRef] [PubMed]
  13. R. L. Smith, Am. J. Phys. 38, 978 (1970).
    [CrossRef]

2008 (1)

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 77, 056606 (2008).
[CrossRef]

2006 (2)

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
[CrossRef]

A. Rosenthal and M. Horowitz, Opt. Lett. 31, 1334 (2006).
[CrossRef] [PubMed]

1996 (1)

B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

1993 (1)

K. Motoshima, L. M. Leba, D. N. Chen, M. M. Downs, T. Li, and E. Desurvire, IEEE Photon. Technol. Lett. 5, 1423 (1993).
[CrossRef]

1991 (3)

C. R. Giles and E. Desurvire, J. Lightwave Technol. 9, 271 (1991).
[CrossRef]

C. M. de Sterke and J. E. Sipe, Phys. Rev. A 43, 2467 (1991).
[CrossRef]

G. P. Agrawal, Phys. Rev. A 44, 7493 (1991).
[CrossRef] [PubMed]

1989 (2)

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

1988 (1)

1987 (1)

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

1970 (1)

R. L. Smith, Am. J. Phys. 38, 978 (1970).
[CrossRef]

Aceves, A. B.

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Phys. Rev. A 44, 7493 (1991).
[CrossRef] [PubMed]

Chen, D. N.

K. Motoshima, L. M. Leba, D. N. Chen, M. M. Downs, T. Li, and E. Desurvire, IEEE Photon. Technol. Lett. 5, 1423 (1993).
[CrossRef]

Chen, W.

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

Christodoulides, D. N.

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

de Sterke, C. M.

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
[CrossRef]

C. M. de Sterke and J. E. Sipe, Phys. Rev. A 43, 2467 (1991).
[CrossRef]

deSterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Desurvire, E.

K. Motoshima, L. M. Leba, D. N. Chen, M. M. Downs, T. Li, and E. Desurvire, IEEE Photon. Technol. Lett. 5, 1423 (1993).
[CrossRef]

C. R. Giles and E. Desurvire, J. Lightwave Technol. 9, 271 (1991).
[CrossRef]

Downs, M. M.

K. Motoshima, L. M. Leba, D. N. Chen, M. M. Downs, T. Li, and E. Desurvire, IEEE Photon. Technol. Lett. 5, 1423 (1993).
[CrossRef]

Eggleton, B. J.

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Giles, C. R.

C. R. Giles and E. Desurvire, J. Lightwave Technol. 9, 271 (1991).
[CrossRef]

Horowitz, M.

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Leba, L. M.

K. Motoshima, L. M. Leba, D. N. Chen, M. M. Downs, T. Li, and E. Desurvire, IEEE Photon. Technol. Lett. 5, 1423 (1993).
[CrossRef]

Li, T.

K. Motoshima, L. M. Leba, D. N. Chen, M. M. Downs, T. Li, and E. Desurvire, IEEE Photon. Technol. Lett. 5, 1423 (1993).
[CrossRef]

Littler, I. C. M.

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
[CrossRef]

Malomed, B. A.

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 77, 056606 (2008).
[CrossRef]

Mills, D. L.

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

Mok, J. T.

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
[CrossRef]

Motoshima, K.

K. Motoshima, L. M. Leba, D. N. Chen, M. M. Downs, T. Li, and E. Desurvire, IEEE Photon. Technol. Lett. 5, 1423 (1993).
[CrossRef]

Rosenthal, A.

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 77, 056606 (2008).
[CrossRef]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, Phys. Rev. A 43, 2467 (1991).
[CrossRef]

J. E. Sipe and H. G. Winful, Opt. Lett. 13, 132 (1988).
[CrossRef] [PubMed]

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Smith, R. L.

R. L. Smith, Am. J. Phys. 38, 978 (1970).
[CrossRef]

Wabnitz, S.

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

Winful, H. G.

Am. J. Phys. (1)

R. L. Smith, Am. J. Phys. 38, 978 (1970).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Motoshima, L. M. Leba, D. N. Chen, M. M. Downs, T. Li, and E. Desurvire, IEEE Photon. Technol. Lett. 5, 1423 (1993).
[CrossRef]

J. Lightwave Technol. (1)

C. R. Giles and E. Desurvire, J. Lightwave Technol. 9, 271 (1991).
[CrossRef]

Nat. Phys. (1)

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

Phys. Rev. A (2)

C. M. de Sterke and J. E. Sipe, Phys. Rev. A 43, 2467 (1991).
[CrossRef]

G. P. Agrawal, Phys. Rev. A 44, 7493 (1991).
[CrossRef] [PubMed]

Phys. Rev. E (1)

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 77, 056606 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Pulse power as a function of time after a propagation of L = 15 cm in BG-EDFA for input pulses with the same FWHM duration of 0.5 ns and with different carrier frequencies. The peak power P 0 , energy E 0 , velocity ν 0 , and detuning from the Bragg frequency f 0 of the input pulses are, as [ P 0 , E 0 , ν 0 , f 0 ] , (a) [43 W, 0.02 E sat , 0.3 V g , 1952 GHz], (b) [186 W, 0.1 E sat , 0.15 V g , 1883 GHz], (c) [423 W, 0.23 E sat , 0.1 V g , 1871 GHz], (d) [1.2 kW, 0.65 E sat , 0.06 V g , 1865 GHz]. The energy of the output pulses E L equals (a) 0.4 E sat , (b) 2.8 E sat , (c) 5.1 E sat , and (d) 11 E sat .

Fig. 2
Fig. 2

Pulse power at different locations along the amplifier as a function of the reduced time τ = t z ν 0 where ν 0 is the group velocity of the input pulse. The parameters of the input pulse are the same as used in Fig. 1c.

Fig. 3
Fig. 3

Pulse power P as a function of time when saturation effect is neglected after a propagation of (a) L = 6 cm and (b) L = 7 cm . The initial pulse parameters are identical to that used in Fig. 1c.

Equations (7)

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i z u + i V g 1 t u + [ σ ( z ) + σ g ( z , t ) ] u + κ ( z ) v + Γ ( | u | 2 + 2 | v | 2 ) u j 1 2 g ( z , t ) u = 0 ,
i z v + i V g 1 t v + [ σ ( z ) + σ g ( z , t ) ] v + κ ( z ) u + Γ ( | v | 2 + 2 | u | 2 ) v j 1 2 g ( z , t ) v = 0 ,
t N 2 ( z , t ) = t N 1 ( z , t ) = P p ( z , t ) P p , sat N 1 ( z , t ) τ + P s ( z , t ) P s , sat N 1 ( z , t ) η s N 2 ( z , t ) ( 1 + η s ) τ N 2 ( z , t ) τ ,
z P p ( z , t ) = α p N 1 ( z , t ) P p ( z , t ) ,
g ( z , t ) = g 0 ( z ) exp [ t P s ( z , s ) d s E sat ] ,
d d z [ ν e ( z ) E s ( z ) ] = g 0 ( z ) E sat { 1 exp [ E s ( z ) E sat ] } ,
ν e ( z ) = + { ν e ( z , τ ) [ | u ( z , τ ) | 2 + | v ( z , τ ) | 2 ] } d τ + [ | u ( z , τ ) | 2 + | v ( z , τ ) | 2 ] d τ ,

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