Abstract

In contrast to the mechanism of interaction determined by the Kerr nolinearity, the electrostrictive interaction between picosecond pulses in optical fibers can occur when the temporal interval between them is much greater than their duration. The width of the interval is determined by the lifetime of the sound wave in the fiber core region, i.e., ~1 nsec. It follows from our calculations that for long propagation distances (L > 1000 km) the relative temporal separation of the interacting pulses can reach hundreds of picoseconds at the temporal interval between them of ~1 nsec.

© 1990 Optical Society of America

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References

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  1. A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
    [Crossref]
  2. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  3. L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
    [Crossref] [PubMed]
  4. V. I. Karpman, V. V. Solov’ev, Physica 3D, 487 (1981).
  5. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [Crossref] [PubMed]
  6. F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 12, 355 (1987).
    [Crossref] [PubMed]
  7. Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
    [Crossref] [PubMed]
  8. L. F. Mollenauer, K. Smith, in Digest of Meeting on Nonlinear Guided-Wave Phenomena: Physics and Applications (Optical Society of America, Washington, D.C., 1989), paper ThB2; Opt. Lett. 14, 1284 (1989).
    [PubMed]
  9. D. Heiman, D. S. Hamilton, R. W. Hellwarth, Phys. Rev. B 19, 6583 (1979).
    [Crossref]
  10. R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
    [Crossref]

1988 (1)

1987 (2)

1985 (1)

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[Crossref]

1983 (1)

1981 (2)

V. I. Karpman, V. V. Solov’ev, Physica 3D, 487 (1981).

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[Crossref]

1980 (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

1979 (1)

D. Heiman, D. S. Hamilton, R. W. Hellwarth, Phys. Rev. B 19, 6583 (1979).
[Crossref]

Bayer, P. W.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[Crossref]

Gordon, J. P.

J. P. Gordon, Opt. Lett. 8, 596 (1983).
[Crossref] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Hamilton, D. S.

D. Heiman, D. S. Hamilton, R. W. Hellwarth, Phys. Rev. B 19, 6583 (1979).
[Crossref]

Hasegawa, A.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[Crossref]

Heiman, D.

D. Heiman, D. S. Hamilton, R. W. Hellwarth, Phys. Rev. B 19, 6583 (1979).
[Crossref]

Hellwarth, R. W.

D. Heiman, D. S. Hamilton, R. W. Hellwarth, Phys. Rev. B 19, 6583 (1979).
[Crossref]

Karpman, V. I.

V. I. Karpman, V. V. Solov’ev, Physica 3D, 487 (1981).

Kodama, Y.

Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
[Crossref] [PubMed]

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[Crossref]

Levenson, M. D.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[Crossref]

Mitschke, F. M.

Mollenauer, L. F.

L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
[Crossref] [PubMed]

F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 12, 355 (1987).
[Crossref] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

L. F. Mollenauer, K. Smith, in Digest of Meeting on Nonlinear Guided-Wave Phenomena: Physics and Applications (Optical Society of America, Washington, D.C., 1989), paper ThB2; Opt. Lett. 14, 1284 (1989).
[PubMed]

Nozaki, K.

Shelby, R. M.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[Crossref]

Smith, K.

L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988).
[Crossref] [PubMed]

L. F. Mollenauer, K. Smith, in Digest of Meeting on Nonlinear Guided-Wave Phenomena: Physics and Applications (Optical Society of America, Washington, D.C., 1989), paper ThB2; Opt. Lett. 14, 1284 (1989).
[PubMed]

Solov’ev, V. V.

V. I. Karpman, V. V. Solov’ev, Physica 3D, 487 (1981).

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Opt. Lett. (4)

Phys. Rev. B (2)

D. Heiman, D. S. Hamilton, R. W. Hellwarth, Phys. Rev. B 19, 6583 (1979).
[Crossref]

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[Crossref]

Phys. Rev. Lett. (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Physica (1)

V. I. Karpman, V. V. Solov’ev, Physica 3D, 487 (1981).

Proc. IEEE (1)

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[Crossref]

Other (1)

L. F. Mollenauer, K. Smith, in Digest of Meeting on Nonlinear Guided-Wave Phenomena: Physics and Applications (Optical Society of America, Washington, D.C., 1989), paper ThB2; Opt. Lett. 14, 1284 (1989).
[PubMed]

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Figures (2)

Fig. 1
Fig. 1

Normalized response function F(t) of the electro-strictive pulse interaction for a = 3 μm and ν = 5.9 × 105 cm/sec.

Fig. 2
Fig. 2

Calculated [Eqs. (6) and (9)] dependence of the temporal delay τ on the temporal interval between the pulses at L = 1000 km (curve 1) and L = 3000 km (curve 2). The dashed curve is the same as curve 2 but with the temporal pulse separation change during the propagation taken into account. ρ0(∂/∂ρ) = 1.2, D = 17 psec/(nm-km), λ = 1.6 μm, PL = 16 mW, and τL = 55 psec.

Equations (10)

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E = e E 0 b ( t ) f ( r ) exp [ i ( ω t β z ) ] ,
2 ρ t 2 ν 2 Δ ρ 2 A Δ ρ t = 1 16 π ( ρ 0 ρ ) Δ | E | 2 ,
ρ ˜ ( Ω , k x , k y ) = 1 ( 2 π ) 3 ρ ( t , x , y ) × exp [ i ( Ω t k x x k y y ) ] d t d x d y .
ρ ˜ ( Ω , k x , k y ) = ρ 0 ρ 64 π 2 | E 0 | 2 a 2 exp ( q 2 a 2 / 4 ) B ( Ω ) q 2 Ω 2 ν 2 q 2 2 i A Ω q 2 ,
Δ β ( t ) = 1 2 β ω 2 c 2 ρ ρ ( t , r ) f 2 ( r ) d 2 r f 2 ( r ) d 2 r .
Δ β ( t ) = | E 0 | 2 F ( Ω ) B ( Ω ) exp ( i Ω t ) d Ω ,
F ( Ω ) = 1 64 π ( ρ 0 ρ ) 2 ω 2 a 2 β ρ 0 c 2 0 q 3 exp ( q 2 a 2 / 2 ) Ω 2 ν 2 q 2 2 i A Ω q 2 d q ,
δ τ = Δ β ( t ) δ L ω D Δ λ δ L ,
δ τ = Δ β ( t ) δ L ω D λ ω Δ β ( t ) t L δ L .
τ = 0 L [ Δ β ( t ) ω D λ ω Δ β ( t ) t L ] d L .

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