Abstract

We show that the temporal distortion and spectral broadening of a pulse generated by the combined effects of group-velocity dispersion and self-phase modulation is removed by reflection of a cw-pumped, broadband, unity-reflecting Kerr-like optical phase conjugator followed by retraversal of the nonlinear medium. We also examine numerically the effects of finite linear loss in the material, of nonunity conjugate reflectivity, and of finite conjugator thickness.

© 1983 Optical Society of America

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References

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  1. See, for example, R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
  2. B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizulalov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 15, 160 (1972) [Sov. Phys. JETP 15, 109 (1972)].
  3. O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizullov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617 (1972) [Sov. Phys. JETP 16, 435 (1972)].
  4. A. Yariv, Opt. Commun. 21, 49 (1977).
    [CrossRef]
  5. D. M. Pepper, A. Yariv, Opt. Lett. 5, 59 (1980).
    [CrossRef] [PubMed]
  6. A. Yariv, D. Fekete, D. M. Pepper, Opt. Lett. 4, 52 (1978).
    [CrossRef]
  7. R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
    [CrossRef]
  8. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1983), Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  9. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983).
    [CrossRef] [PubMed]
  10. H. Nakatsuka, D. Grischkowsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981); C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982); B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1 (1983).
    [CrossRef]
  11. R. A. Fisher, B. R. Suydam, B. J. Feldman, Phys. Rev. A 23, 3071 (1981). For a related approach, see J.-C. Diels, W. C. Wang, H. Winful, Appl. Phys. B26, 105 (1981).
    [CrossRef]
  12. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974); K. Lonnegren, A. Scott, eds., Solitons in Action (Academic, New York, 1978).
  13. M. Lutzky, J. S. Toll, Phys. Rev. 133, 1649 (1959); F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
    [CrossRef]
  14. See, for example, A. E. Siegman, P. Belanger, A. Hardy, Ref. 1, Chap. 13.
  15. R. Eckardt, C. H. Lee, J. N. Bradford, Opto-Electron.6, 67 (1974).
    [CrossRef]

1983 (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1983), Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

1981 (2)

H. Nakatsuka, D. Grischkowsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981); C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982); B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1 (1983).
[CrossRef]

R. A. Fisher, B. R. Suydam, B. J. Feldman, Phys. Rev. A 23, 3071 (1981). For a related approach, see J.-C. Diels, W. C. Wang, H. Winful, Appl. Phys. B26, 105 (1981).
[CrossRef]

1980 (2)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983).
[CrossRef] [PubMed]

D. M. Pepper, A. Yariv, Opt. Lett. 5, 59 (1980).
[CrossRef] [PubMed]

1978 (1)

A. Yariv, D. Fekete, D. M. Pepper, Opt. Lett. 4, 52 (1978).
[CrossRef]

1977 (1)

A. Yariv, Opt. Commun. 21, 49 (1977).
[CrossRef]

1975 (1)

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[CrossRef]

1972 (2)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizulalov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 15, 160 (1972) [Sov. Phys. JETP 15, 109 (1972)].

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizullov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617 (1972) [Sov. Phys. JETP 16, 435 (1972)].

1959 (1)

M. Lutzky, J. S. Toll, Phys. Rev. 133, 1649 (1959); F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Balant, A. C.

H. Nakatsuka, D. Grischkowsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981); C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982); B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1 (1983).
[CrossRef]

Belanger, P.

See, for example, A. E. Siegman, P. Belanger, A. Hardy, Ref. 1, Chap. 13.

Bischel, W. K.

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[CrossRef]

Bradford, J. N.

R. Eckardt, C. H. Lee, J. N. Bradford, Opto-Electron.6, 67 (1974).
[CrossRef]

Eckardt, R.

R. Eckardt, C. H. Lee, J. N. Bradford, Opto-Electron.6, 67 (1974).
[CrossRef]

Faizulalov, F. S.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizulalov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 15, 160 (1972) [Sov. Phys. JETP 15, 109 (1972)].

Faizullov, F. S.

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizullov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617 (1972) [Sov. Phys. JETP 16, 435 (1972)].

Fekete, D.

A. Yariv, D. Fekete, D. M. Pepper, Opt. Lett. 4, 52 (1978).
[CrossRef]

Feldman, B. J.

R. A. Fisher, B. R. Suydam, B. J. Feldman, Phys. Rev. A 23, 3071 (1981). For a related approach, see J.-C. Diels, W. C. Wang, H. Winful, Appl. Phys. B26, 105 (1981).
[CrossRef]

Fisher, R. A.

R. A. Fisher, B. R. Suydam, B. J. Feldman, Phys. Rev. A 23, 3071 (1981). For a related approach, see J.-C. Diels, W. C. Wang, H. Winful, Appl. Phys. B26, 105 (1981).
[CrossRef]

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983).
[CrossRef] [PubMed]

Grischkowsky, D.

H. Nakatsuka, D. Grischkowsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981); C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982); B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1 (1983).
[CrossRef]

Hardy, A.

See, for example, A. E. Siegman, P. Belanger, A. Hardy, Ref. 1, Chap. 13.

Hasegawa, A.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1983), Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Lee, C. H.

R. Eckardt, C. H. Lee, J. N. Bradford, Opto-Electron.6, 67 (1974).
[CrossRef]

Lutzky, M.

M. Lutzky, J. S. Toll, Phys. Rev. 133, 1649 (1959); F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983).
[CrossRef] [PubMed]

Nakatsuka, H.

H. Nakatsuka, D. Grischkowsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981); C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982); B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1 (1983).
[CrossRef]

Pepper, D. M.

D. M. Pepper, A. Yariv, Opt. Lett. 5, 59 (1980).
[CrossRef] [PubMed]

A. Yariv, D. Fekete, D. M. Pepper, Opt. Lett. 4, 52 (1978).
[CrossRef]

Popovichev, V. I.

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizullov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617 (1972) [Sov. Phys. JETP 16, 435 (1972)].

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizulalov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 15, 160 (1972) [Sov. Phys. JETP 15, 109 (1972)].

Ragul’skiy, V. V.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizulalov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 15, 160 (1972) [Sov. Phys. JETP 15, 109 (1972)].

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizullov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617 (1972) [Sov. Phys. JETP 16, 435 (1972)].

Siegman, A. E.

See, for example, A. E. Siegman, P. Belanger, A. Hardy, Ref. 1, Chap. 13.

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983).
[CrossRef] [PubMed]

Suydam, B. R.

R. A. Fisher, B. R. Suydam, B. J. Feldman, Phys. Rev. A 23, 3071 (1981). For a related approach, see J.-C. Diels, W. C. Wang, H. Winful, Appl. Phys. B26, 105 (1981).
[CrossRef]

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1983), Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Toll, J. S.

M. Lutzky, J. S. Toll, Phys. Rev. 133, 1649 (1959); F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Whitham, G. B.

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974); K. Lonnegren, A. Scott, eds., Solitons in Action (Academic, New York, 1978).

Ya. Zel’dovich, B.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizulalov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 15, 160 (1972) [Sov. Phys. JETP 15, 109 (1972)].

Yariv, A.

D. M. Pepper, A. Yariv, Opt. Lett. 5, 59 (1980).
[CrossRef] [PubMed]

A. Yariv, D. Fekete, D. M. Pepper, Opt. Lett. 4, 52 (1978).
[CrossRef]

A. Yariv, Opt. Commun. 21, 49 (1977).
[CrossRef]

Yu. Nosach, O.

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizullov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617 (1972) [Sov. Phys. JETP 16, 435 (1972)].

Appl. Phys. Lett. (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1983), Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

J. Appl. Phys. (1)

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[CrossRef]

Opt. Commun. (1)

A. Yariv, Opt. Commun. 21, 49 (1977).
[CrossRef]

Opt. Lett. (2)

D. M. Pepper, A. Yariv, Opt. Lett. 5, 59 (1980).
[CrossRef] [PubMed]

A. Yariv, D. Fekete, D. M. Pepper, Opt. Lett. 4, 52 (1978).
[CrossRef]

Phys. Rev. (1)

M. Lutzky, J. S. Toll, Phys. Rev. 133, 1649 (1959); F. DeMartini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Phys. Rev. A (1)

R. A. Fisher, B. R. Suydam, B. J. Feldman, Phys. Rev. A 23, 3071 (1981). For a related approach, see J.-C. Diels, W. C. Wang, H. Winful, Appl. Phys. B26, 105 (1981).
[CrossRef]

Phys. Rev. Lett. (2)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983).
[CrossRef] [PubMed]

H. Nakatsuka, D. Grischkowsky, A. C. Balant, Phys. Rev. Lett. 47, 910 (1981); C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982); B. Nikolaus, D. Grischkowsky, Appl. Phys. Lett. 42, 1 (1983).
[CrossRef]

Zh. Eksp. Teor. Fiz. Pis’ma Red. (2)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizulalov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 15, 160 (1972) [Sov. Phys. JETP 15, 109 (1972)].

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skiy, F. S. Faizullov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617 (1972) [Sov. Phys. JETP 16, 435 (1972)].

Other (4)

See, for example, R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974); K. Lonnegren, A. Scott, eds., Solitons in Action (Academic, New York, 1978).

See, for example, A. E. Siegman, P. Belanger, A. Hardy, Ref. 1, Chap. 13.

R. Eckardt, C. H. Lee, J. N. Bradford, Opto-Electron.6, 67 (1974).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Numerical simulation of time-domain undoing. In this ideal case a 5-psec pulse, shown in (a), passes through 12 cm of CS2 having both Kerr nonlinearity and group-velocity dispersion. The resultant pulse, shown in (b), is then reflected from a thin, instantaneously responding, Kerr-like phase conjugator of unit reflectivity to produce the pulse of (c) and is subsequently returned through the CS2. The resultant pulse (d) has regained its initial shape, and all the spectral broadening has been removed. For clarity, the spectral intensities in (b) and (c) have both been multiplied by a factor of 12.

Fig. 2
Fig. 2

Numerical results showing imperfect pulse restoration resulting from linear losses in the CS2, from nonunity conjugate reflectivity, and from finite conjugator thickness. The return-pulse spectral intensity distributions shown here are shown on an expanded frequency scale, a, Presents the ideal-case output pulse of Fig. 1(d); this curve cannot be distinguished from the input pulse spectrum, b, Departs from the ideal case only in that incorporates linear loss in the CS2, reducing the one-way transmission to 90%, whereas c departs from the ideal case only in that the conjugate reflectivity is reduced to 90%. In d, we show that the deleterious role of the 90% transmission in the DSPM medium can be partially compensated for by increasing the conjugate reflectivity to 112%. e, Shows how ideal restoration is compromised when the conjugator thickness is increased by a factor of 10.

Equations (6)

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c ( t ) = 1 2 π h ( i Ω ) [ ˆ p ( Ω ) ] * e i Ω t d Ω .
h ( i Ω ) = i κ sin β l β cos β l i ( Ω / υ ) sin β l ,
β = ( κ 2 + Ω 2 / υ 2 ) 1 / 2 ,
i z = 1 2 k 2 2 ( t ) 2 + k 0 δ n
τ δ n t + δ n = 1 2 n 2 | | 2 .
i * z = 1 2 k 2 2 * ( t ) 2 + k 0 δ n * ,

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