Abstract

When a probe pulse copropagates with a pump pulse inside an optical fiber, the two can interact through cross-phase modulation. It is shown that an interplay between the effects of group-velocity dispersion and cross-phase modulation can lead to optical wave breaking that manifests as rapid oscillations near the leading or the trailing side of the probe pulse. Qualitative features of this new kind of optical wave breaking are discussed, as well as the conditions under which it can be observed experimentally. The probe pulse can be compressed significantly by optimizing the initial delay between the pump and probe pulses even when the two pulses experience normal dispersion in the fiber.

© 1989 Optical Society of America

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References

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  1. W. J. Tomlinson, R. H. Stolen, A. M. Johnson, Opt. Lett. 10, 457 (1985).
    [CrossRef] [PubMed]
  2. J. I. Gersten, R. R. Alfano, M. Belie, Phys. Rev. A 21, 1222 (1980).
    [CrossRef]
  3. A. A. Chraplyvy, J. Stone, Electron. Lett. 20, 996 (1984).
    [CrossRef]
  4. R. R. Alfano, Q. X. Li, T. Jimbo, J. T. Manassah, P. P. Ho, Opt. Lett. 11, 628 (1986).
    [CrossRef]
  5. D. Schadt, B. Jaskorzynska, U. Osterberg, J. Opt. Soc. Am. B 3, 1257 (1986).
    [CrossRef]
  6. M. N. Islam, L. F. Mollenauer, R. H. Stolen, J. R. Simpson, H. T. Shang, Opt. Lett. 12, 625 (1987).
    [CrossRef] [PubMed]
  7. G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
    [CrossRef] [PubMed]
  8. R. R. Alfano, P. L. Baldeck, F. Raccah, P. P. Ho, Appl. Opt. 26, 3491 (1987).
    [CrossRef] [PubMed]
  9. D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
    [CrossRef]
  10. P. L. Baldeck, R. R. Alfano, G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
    [CrossRef]
  11. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989), Chap. 2.
  12. J. T. Manassah, Opt. Lett. 13, 755 (1988).
    [CrossRef] [PubMed]

1988 (2)

P. L. Baldeck, R. R. Alfano, G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

J. T. Manassah, Opt. Lett. 13, 755 (1988).
[CrossRef] [PubMed]

1987 (4)

1986 (2)

R. R. Alfano, Q. X. Li, T. Jimbo, J. T. Manassah, P. P. Ho, Opt. Lett. 11, 628 (1986).
[CrossRef]

D. Schadt, B. Jaskorzynska, U. Osterberg, J. Opt. Soc. Am. B 3, 1257 (1986).
[CrossRef]

1985 (1)

1984 (1)

A. A. Chraplyvy, J. Stone, Electron. Lett. 20, 996 (1984).
[CrossRef]

1980 (1)

J. I. Gersten, R. R. Alfano, M. Belie, Phys. Rev. A 21, 1222 (1980).
[CrossRef]

Agrawal, G. P.

P. L. Baldeck, R. R. Alfano, G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989), Chap. 2.

Alfano, R. R.

P. L. Baldeck, R. R. Alfano, G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

R. R. Alfano, P. L. Baldeck, F. Raccah, P. P. Ho, Appl. Opt. 26, 3491 (1987).
[CrossRef] [PubMed]

R. R. Alfano, Q. X. Li, T. Jimbo, J. T. Manassah, P. P. Ho, Opt. Lett. 11, 628 (1986).
[CrossRef]

J. I. Gersten, R. R. Alfano, M. Belie, Phys. Rev. A 21, 1222 (1980).
[CrossRef]

Baldeck, P. L.

P. L. Baldeck, R. R. Alfano, G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

R. R. Alfano, P. L. Baldeck, F. Raccah, P. P. Ho, Appl. Opt. 26, 3491 (1987).
[CrossRef] [PubMed]

Belie, M.

J. I. Gersten, R. R. Alfano, M. Belie, Phys. Rev. A 21, 1222 (1980).
[CrossRef]

Chraplyvy, A. A.

A. A. Chraplyvy, J. Stone, Electron. Lett. 20, 996 (1984).
[CrossRef]

Gersten, J. I.

J. I. Gersten, R. R. Alfano, M. Belie, Phys. Rev. A 21, 1222 (1980).
[CrossRef]

Ho, P. P.

R. R. Alfano, P. L. Baldeck, F. Raccah, P. P. Ho, Appl. Opt. 26, 3491 (1987).
[CrossRef] [PubMed]

R. R. Alfano, Q. X. Li, T. Jimbo, J. T. Manassah, P. P. Ho, Opt. Lett. 11, 628 (1986).
[CrossRef]

Islam, M. N.

Jaskorzynska, B.

Jimbo, T.

R. R. Alfano, Q. X. Li, T. Jimbo, J. T. Manassah, P. P. Ho, Opt. Lett. 11, 628 (1986).
[CrossRef]

Johnson, A. M.

Li, Q. X.

R. R. Alfano, Q. X. Li, T. Jimbo, J. T. Manassah, P. P. Ho, Opt. Lett. 11, 628 (1986).
[CrossRef]

Manassah, J. T.

J. T. Manassah, Opt. Lett. 13, 755 (1988).
[CrossRef] [PubMed]

R. R. Alfano, Q. X. Li, T. Jimbo, J. T. Manassah, P. P. Ho, Opt. Lett. 11, 628 (1986).
[CrossRef]

Mollenauer, L. F.

Osterberg, U.

Raccah, F.

Schadt, D.

Shang, H. T.

Simpson, J. R.

Stolen, R. H.

Stone, J.

A. A. Chraplyvy, J. Stone, Electron. Lett. 20, 996 (1984).
[CrossRef]

Tomlinson, W. J.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. L. Baldeck, R. R. Alfano, G. P. Agrawal, Appl. Phys. Lett. 52, 1939 (1988).
[CrossRef]

Electron. Lett. (2)

D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
[CrossRef]

A. A. Chraplyvy, J. Stone, Electron. Lett. 20, 996 (1984).
[CrossRef]

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

Opt. Lett. (4)

Phys. Rev. A (1)

J. I. Gersten, R. R. Alfano, M. Belie, Phys. Rev. A 21, 1222 (1980).
[CrossRef]

Phys. Rev. Lett. (1)

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989), Chap. 2.

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Figures (3)

Fig. 1
Fig. 1

Shape and spectrum of the probe pulse (left-hand side) and the pump pulse (right-hand side) at z/LD = 0.4 when the two pulses copropagate in the normal-dispersion regime of a single-mode fiber. The parameters are N = 10, LW/LD = 0.1, λ1/λ2 = 1.2, and τd = 0. Oscillations near the trailing edge (τ > 0) of the probe pulse are due to XPM-induced optical wave breaking.

Fig. 2
Fig. 2

XPM-induced phase shift and frequency chirp for the probe pulse whose shape is shown is shown by the dashed curve

Fig. 3
Fig. 3

Evolution of the probe pulse for τd = −3. the other parameters are identical to those of Fig. 1.

Equations (10)

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A j z + 1 υ gj A j t + i 2 β j 2 A j t 2 + α j 2 A j = i γ j ( | A j | 2 + 2 | A 3 j | 2 ) A j ,
γ j = 2 π n 2 λ j A eff ,
ξ = z L D , τ = ( t z / υ g 1 ) T 0 , U j = A j P 1
U 1 ξ + i 2 sgn ( β 1 ) 2 U 1 τ 2 = i N 2 ( | U 1 | 2 + 2 | U 2 | 2 ) U 1 ,
U 2 ξ ± L D L W U 2 τ + i 2 β 2 | β 1 | 2 U 2 τ 2 = i N 2 λ 1 λ 2 ( | U 2 | 2 + 2 | U 1 | 2 ) U 2 ,
L D = T 0 2 | β 1 | , L W = υ g 1 υ g 2 T 0 | υ g 1 υ g 2 | ,
N 2 = γ 1 P 1 L D = γ 1 P 1 T 0 2 / | β 1 | .
U 1 ( 0 , τ ) = exp ( τ 2 / 2 ) , U 2 ( 0 , τ ) = ( P 2 / P 1 ) exp [ ( τ τ d ) 2 / 2 ] ,
Δ ν = Δ ν max { exp [ ( τ + τ d z / L W ) 2 ] exp [ ( τ + τ d ) 2 ] } ,
Δ ν max = γ 2 P 1 L W / ( π T 0 ) .

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