Abstract

An exact solution of a nonlinear model of holographic four-wave mixing is derived. An expression for the reflectivity of a phase-conjugate mirror with depleted pumps is presented. We find that such a phase-conjugate mirror may exhibit bistability.

© 1982 Optical Society of America

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References

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  1. A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
    [Crossref] [PubMed]
  2. R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
    [Crossref]
  3. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [Crossref]
  4. V. T. Platonenko, R. V. Khoklov, Zh. Eksp. Teor. Fiz. 46, 555 (1964) [Sov. Phys. JETP 19, 378 (1964)].
  5. J. H. Marburger, J. F. Lam, Appl. Phys. Lett. 34, 389 (1979); Appl. Phys. Lett. 35, 249 (1979).
    [Crossref]
  6. J. Feinberg, R. W. Hellwarth, Opt. Lett. 5, 519 (1980).
    [Crossref] [PubMed]
  7. R. C. Lind, D. G. Steel, Opt. Lett. 6, 554 (1981).
    [Crossref] [PubMed]
  8. J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
    [Crossref]
  9. A. Yariv, Opt. Commun. 25, 23 (1978).
    [Crossref]
  10. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [Crossref] [PubMed]
  11. In photorefractive media, for example, γ depends on parameters such as crystal orientation, grating period, charge-carrier concentration, and the angle of incidence α.

1982 (1)

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

1981 (2)

1980 (1)

1979 (1)

J. H. Marburger, J. F. Lam, Appl. Phys. Lett. 34, 389 (1979); Appl. Phys. Lett. 35, 249 (1979).
[Crossref]

1978 (1)

A. Yariv, Opt. Commun. 25, 23 (1978).
[Crossref]

1977 (2)

1964 (1)

V. T. Platonenko, R. V. Khoklov, Zh. Eksp. Teor. Fiz. 46, 555 (1964) [Sov. Phys. JETP 19, 378 (1964)].

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Cronin-Golomb, M.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[Crossref] [PubMed]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Feinberg, J.

Fischer, B.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[Crossref] [PubMed]

Hellwarth, R. W.

Khoklov, R. V.

V. T. Platonenko, R. V. Khoklov, Zh. Eksp. Teor. Fiz. 46, 555 (1964) [Sov. Phys. JETP 19, 378 (1964)].

Lam, J. F.

J. H. Marburger, J. F. Lam, Appl. Phys. Lett. 34, 389 (1979); Appl. Phys. Lett. 35, 249 (1979).
[Crossref]

Lind, R. C.

Marburger, J. H.

J. H. Marburger, J. F. Lam, Appl. Phys. Lett. 34, 389 (1979); Appl. Phys. Lett. 35, 249 (1979).
[Crossref]

Pepper, D. M.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Platonenko, V. T.

V. T. Platonenko, R. V. Khoklov, Zh. Eksp. Teor. Fiz. 46, 555 (1964) [Sov. Phys. JETP 19, 378 (1964)].

Steel, D. G.

White, J. O.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[Crossref] [PubMed]

Yariv, A.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[Crossref] [PubMed]

A. Yariv, Opt. Commun. 25, 23 (1978).
[Crossref]

A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

J. H. Marburger, J. F. Lam, Appl. Phys. Lett. 34, 389 (1979); Appl. Phys. Lett. 35, 249 (1979).
[Crossref]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

A. Yariv, Opt. Commun. 25, 23 (1978).
[Crossref]

Opt. Lett. (4)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[Crossref]

Zh. Eksp. Teor. Fiz. (1)

V. T. Platonenko, R. V. Khoklov, Zh. Eksp. Teor. Fiz. 46, 555 (1964) [Sov. Phys. JETP 19, 378 (1964)].

Other (1)

In photorefractive media, for example, γ depends on parameters such as crystal orientation, grating period, charge-carrier concentration, and the angle of incidence α.

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Figures (2)

Fig. 1
Fig. 1

Scheme of the four beams involved in nonlinear interaction.

Fig. 2
Fig. 2

Reflectivity of a phase-conjugate mirror versus coupling strength |γl|. The incident pump beams are of equal intensity, the intensity of the incident probe beam is 20% of the total incident pumping intensity, and the phase shift between the index grating and interference fringes is 5°.

Equations (21)

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E j = A j ( r ) exp [ i ( k j · r ω ˜ t ) ] + c . c .
d A 1 d z = γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 4 ,
d A 2 * d z = γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 3 * ,
d A 3 d z = γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 2 ,
d A 4 * d z = γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 1 * ,
I 0 = I 1 + I 2 + I 3 + I 4 ,
A 1 A 2 + A 3 A 4 = c ,
I 1 + I 4 = d 1 ,
I 2 + I 3 = d 2 ,
d A 1 d z = γ I 0 [ A 1 d 1 A 1 ( I 1 + I 2 ) + A 2 * c ] ,
d A 2 * d z = γ I 0 [ A 1 c * A 2 * ( I 1 + I 2 ) + A 2 * d 2 ] ,
d A 3 d z = γ I 0 [ A 3 d 2 A 3 ( I 3 + I 4 ) + A 4 * c ] ,
d A 4 * d z = γ I 0 [ A 3 c * A 4 * ( I 3 + I 4 ) + A 4 * d 1 ] .
d d z ( A 1 A 2 * ) = γ I 0 [ c + ( d 1 d 2 ) ( A 1 A 2 * ) c * ( A 1 A 2 * ) 2 ] ,
d d z ( A 3 A 4 * ) = γ I 0 [ c + ( d 2 d 1 ) ( A 3 A 4 * ) c * ( A 3 A 4 * ) 2 ] .
A 1 A 2 * = { [ Δ ( Δ 2 + 4 | c | 2 ) 1 / 2 ] D e μ z [ Δ + ( Δ 2 + 4 | c | 2 ) 1 / 2 ] D 1 e μ z 2 c * ( D e μ z D 1 e μ z ) } ,
A 3 A 4 * = { [ Δ ( Δ 2 + 4 | c | 2 ) 1 / 2 ] E e μ z [ Δ + ( Δ 2 + 4 | c | 2 ) 1 / 2 ] E 1 e μ z 2 c * ( E e μ z E 1 e μ z ) } ,
μ = γ ( Δ 2 + 4 | c | 2 ) 1 / 2 2 I 0 ,
R = 4 | c | 2 | T | 2 | Δ T + ( Δ 2 + 4 | c | 2 ) 1 / 2 | 2 ,
[ | c | 2 I 1 ( 0 ) I 2 ( l ) ] | Δ T + ( Δ 2 + 4 | c | 2 ) 1 / 2 | 2 + 4 | c | 2 | T | 2 I 4 ( 0 ) I 2 ( l ) + 2 | c | 2 I 4 ( 0 ) ( Δ 2 + 4 | c | 2 ) 1 / 2 ( T + T * ) = 0 .
q = I 4 ( 0 ) I 1 ( 0 ) + I 2 ( l ) ,

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