Abstract

Modulational instability in doped glass fibers is analyzed theoretically in a steady-state regime, taking into account a saturable nonlinearity. The results have shown that the critical modulation frequency and modulation gain increase with input power, reaching a maximum value at the saturation power. This leads to a unique value of the critical modulation frequency for two different input powers so that two solutions will experience a maximum gain at the same frequency.

© 1993 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 1st ed. (Academic, Boston, Mass., 1989), Chap. 5, p. 104.
  2. A. Hasegawa, Opt. Lett. 9, 288 (1984).
    [CrossRef] [PubMed]
  3. K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
    [CrossRef]
  4. A. S. Gouveia-Neto, “Modulational instability and soliton-Raman generation in P2O5-doped silica fiber,”IEEE J. Lightwave Technol. (to be published).
  5. D. Anderson, M. Lisak, Opt. Lett. 9, 468 (1984).
    [CrossRef] [PubMed]
  6. J. L. Coutaz, M. Kull, J. Opt. Soc. Am. B 8, 95 (1991).
    [CrossRef]
  7. P. Roussignol, D. Ricard, J. Lukasik, C. Flytzanis, J. Opt. Soc. Am. B 4, 5 (1987).
    [CrossRef]
  8. R. K. Jain, R. C. Lind, J. Opt. Soc. Am. 73, 647 (1983).
    [CrossRef]
  9. L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
    [CrossRef]
  10. L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, C. B. de Araujo, Appl. Phys. Lett. 56, 2279 (1990).
    [CrossRef]
  11. D. Cotter, C. N. Ironside, B. J. Ainslie, H. P. Girdlestone, Opt. Lett. 14, 317 (1989).
    [CrossRef] [PubMed]
  12. N. Finlayson, W. C. Banayi, C. T. Seaton, G. I. Stegeman, M. O’Neill, T. J. Cullen, C. N. Ironside, Opt. Lett. 14, 532 (1989).
    [CrossRef] [PubMed]
  13. J. Herrmann, J. Opt. Soc. Am. B 8, 1507 (1991).
    [CrossRef]
  14. S. Gatz, J. Herrmann, J. Opt. Soc. Am. B 8, 2296 (1991).
    [CrossRef]
  15. M. J. Potasek, Opt. Lett. 12, 921 (1987).
    [CrossRef] [PubMed]
  16. S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
    [CrossRef] [PubMed]

1991 (4)

1990 (1)

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, C. B. de Araujo, Appl. Phys. Lett. 56, 2279 (1990).
[CrossRef]

1989 (2)

1988 (1)

L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

1987 (2)

1986 (1)

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

1984 (2)

1983 (1)

Acioli, L. H.

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, C. B. de Araujo, Appl. Phys. Lett. 56, 2279 (1990).
[CrossRef]

L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 1st ed. (Academic, Boston, Mass., 1989), Chap. 5, p. 104.

Ainslie, B. J.

Anderson, D.

Banayi, W. C.

Cavalcanti, S. B.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef] [PubMed]

Cotter, D.

Coutaz, J. L.

Cressoni, J. C.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef] [PubMed]

Cullen, T. J.

da Cruz, H. R.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef] [PubMed]

de Araujo, C. B.

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, C. B. de Araujo, Appl. Phys. Lett. 56, 2279 (1990).
[CrossRef]

Finlayson, N.

Flytzanis, C.

Gatz, S.

Girdlestone, H. P.

Gomes, A. S. L.

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, C. B. de Araujo, Appl. Phys. Lett. 56, 2279 (1990).
[CrossRef]

L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

Gouveia-Neto, A. S.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef] [PubMed]

A. S. Gouveia-Neto, “Modulational instability and soliton-Raman generation in P2O5-doped silica fiber,”IEEE J. Lightwave Technol. (to be published).

Hasegawa, A.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

A. Hasegawa, Opt. Lett. 9, 288 (1984).
[CrossRef] [PubMed]

Herrmann, J.

Hickmann, J. M.

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, C. B. de Araujo, Appl. Phys. Lett. 56, 2279 (1990).
[CrossRef]

Ironside, C. N.

Jain, R. K.

Jewell, J. L.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Kull, M.

Lind, R. C.

Lisak, M.

Lukasik, J.

O’Neill, M.

Potasek, M. J.

Ricard, D.

Rios Leite, J. R.

L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

Roussignol, P.

Seaton, C. T.

Stegeman, G. I.

Tai, K.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Tomita, A.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Appl. Phys. Lett. (3)

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, C. B. de Araujo, Appl. Phys. Lett. 56, 2279 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (4)

Opt. Lett. (5)

Phys. Rev. A (1)

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef] [PubMed]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 1st ed. (Academic, Boston, Mass., 1989), Chap. 5, p. 104.

A. S. Gouveia-Neto, “Modulational instability and soliton-Raman generation in P2O5-doped silica fiber,”IEEE J. Lightwave Technol. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Critical modulational frequency against input power for an unsaturated Kerr nonlinearity [curve (a)] and a saturated nonlinearity [curve (b)]. Parameters are |β2| = 60 ps2/km and Isat (=Psat/Aeff) = 108 W/cm2.

Fig. 2
Fig. 2

Three-dimensional plot of the normalized gain (G/Gmax) versus input power and frequency shift. The parameters are the same as in Fig. 1.

Fig. 3
Fig. 3

Critical modulation frequency versus input power for an unsaturated Kerr nonlinearity [curve (a)] and a saturated nonlinearity [curve (b)] in the region of minimum group-velocity dispersion. The parameters are |β2| = 0, |β4| = 7 × 10−4 ps4/km, and Isat = 108 W/cm2.

Fig. 4
Fig. 4

Three-dimensional plot of the normalized gain against input peak power and frequency shift in the region of minimum group-velocity dispersion. The parameters are the same as in Fig. 3.

Equations (11)

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i A z = β 2 2 2 A T 2 γ | A | 2 1 + Γ | A | 2 A ,
A ¯ = P 0 exp ( i ϕ NL ) , ϕ NL = γ P 0 z 1 + Γ P 0 ,
K = 1 2 | β 2 | Ω [ Ω 2 + sgn ( β 2 n 2 ) Ω cs 2 ] 1 / 2 ,
Ω cs = ± [ 4 | γ | P 0 | β 2 | 1 ( 1 + Γ P 0 ) 2 ] 1 / 2 ,
G ( Ω ) = 2 Im ( K ) = | β 2 | | Ω | Ω cs 2 Ω 2 ,
G max = | γ | 2 Γ .
i A ( z , T ) z = β 2 2 2 A T 2 + i β 3 6 3 A T 3 β 4 24 4 A T 4 γ | A | 2 1 + Γ | A | 2 A .
K D 2 = β 4 2 Ω D 8 ( 24 ) 2 + Ω D 6 ( β 2 β 4 24 β 3 2 36 ) + Ω 6 4 [ β 2 2 4 + β 4 γ S ( 1 Γ S ) 12 ] + K β 3 3 Ω D 3 + γ S β 2 ( 1 Γ S ) Ω D 2 ,
K D = β 3 Ω D 3 6 ± Ω D 2 | β 4 | 24 [ Ω D 4 + sgn ( β 4 ) Ω DC 4 ] 1 / 2 ,
Ω DC 4 = 48 | γ | P 0 | β 4 | ( 1 + Γ P 0 ) 2 .
G D ( Ω D ) = | β 4 | Ω D 2 12 Ω DC 4 Ω D 4 ,

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