Abstract

A method of polarization (vector) wavefront reversal by four-wave mixing in a photoanisotropic material is described. Jones matrices, describing the dynamic holographic gratings recorded in the material at arbitrary polarization of the signal wave, are derived. They are employed to define the conditions for generating a wave that is fully conjugate (by polarization as well) to the signal wave. The way to achieving these conditions by optically controlling the anisotropy of the nonlinear medium is demonstrated experimentally.

© 1988 Optical Society of America

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References

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  1. N. G. Bassov, V. F. Efimkov, I. G. Zubarev, A. U. Kotov, S. I. Mikhailov, M. G. Smirnov, “Phase conjugation of a depolarized wave by means of SMBD method,” JETP Lett. 4, 4, 1978).
  2. V. N. Blashchuk, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkunov, “A Complete Wavefront Reversal Under Degenerate Four-Photon Interaction”. (Theory and Experiment), Sov. J. Quantum Electron. 7, 627 (1980).
  3. G. Martin, L. K. Lam, R. W. Hellwarth, “Generation of a Time-Reversed Replica of a Nonuniformly Polarized Image-Bearing Optical Beam,” Opt. Lett. 5, 185 (1980).
    [CrossRef] [PubMed]
  4. I. C. McMichael, M. Khoshnevisan, P. A. Yeh, “Polarization-Preserving Phase Conjugator,” Opt. Lett. 11, 525 (1986).
    [CrossRef] [PubMed]
  5. E. Ya. Korchemskaya, M. S. Soskin, V. B. Taranenko, “The Space-Polarizational Phase Conjugation Under Four-Wave Mixing in Biochrome Films,” Sov. J. Quantum Electron. 14, 714 (1987).
  6. L. Nikolova, K. Stoyanova, T. Todorov, V. B. Taranenko, “Polarization wavefront Conjugation by means of Transient Holograms in Rigid Dye Solutions,” Opt. Commun. 64, 75 (1987).
    [CrossRef]
  7. D. Casasent, F. Caimi, “Photodichroic Crystals for Coherent Optical Data Processing,” Opt. Laser Technol. 9, 63 (1977).
    [CrossRef]
  8. L. Nikolova, T. Todorov, “Diffraction Efficiency and Selectivity of Polarization Holographic Recording,” Opt. Acta 31, 579 (1984).
    [CrossRef]

1987 (2)

E. Ya. Korchemskaya, M. S. Soskin, V. B. Taranenko, “The Space-Polarizational Phase Conjugation Under Four-Wave Mixing in Biochrome Films,” Sov. J. Quantum Electron. 14, 714 (1987).

L. Nikolova, K. Stoyanova, T. Todorov, V. B. Taranenko, “Polarization wavefront Conjugation by means of Transient Holograms in Rigid Dye Solutions,” Opt. Commun. 64, 75 (1987).
[CrossRef]

1986 (1)

1984 (1)

L. Nikolova, T. Todorov, “Diffraction Efficiency and Selectivity of Polarization Holographic Recording,” Opt. Acta 31, 579 (1984).
[CrossRef]

1980 (2)

V. N. Blashchuk, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkunov, “A Complete Wavefront Reversal Under Degenerate Four-Photon Interaction”. (Theory and Experiment), Sov. J. Quantum Electron. 7, 627 (1980).

G. Martin, L. K. Lam, R. W. Hellwarth, “Generation of a Time-Reversed Replica of a Nonuniformly Polarized Image-Bearing Optical Beam,” Opt. Lett. 5, 185 (1980).
[CrossRef] [PubMed]

1978 (1)

N. G. Bassov, V. F. Efimkov, I. G. Zubarev, A. U. Kotov, S. I. Mikhailov, M. G. Smirnov, “Phase conjugation of a depolarized wave by means of SMBD method,” JETP Lett. 4, 4, 1978).

1977 (1)

D. Casasent, F. Caimi, “Photodichroic Crystals for Coherent Optical Data Processing,” Opt. Laser Technol. 9, 63 (1977).
[CrossRef]

Bassov, N. G.

N. G. Bassov, V. F. Efimkov, I. G. Zubarev, A. U. Kotov, S. I. Mikhailov, M. G. Smirnov, “Phase conjugation of a depolarized wave by means of SMBD method,” JETP Lett. 4, 4, 1978).

Blashchuk, V. N.

V. N. Blashchuk, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkunov, “A Complete Wavefront Reversal Under Degenerate Four-Photon Interaction”. (Theory and Experiment), Sov. J. Quantum Electron. 7, 627 (1980).

Caimi, F.

D. Casasent, F. Caimi, “Photodichroic Crystals for Coherent Optical Data Processing,” Opt. Laser Technol. 9, 63 (1977).
[CrossRef]

Casasent, D.

D. Casasent, F. Caimi, “Photodichroic Crystals for Coherent Optical Data Processing,” Opt. Laser Technol. 9, 63 (1977).
[CrossRef]

Efimkov, V. F.

N. G. Bassov, V. F. Efimkov, I. G. Zubarev, A. U. Kotov, S. I. Mikhailov, M. G. Smirnov, “Phase conjugation of a depolarized wave by means of SMBD method,” JETP Lett. 4, 4, 1978).

Hellwarth, R. W.

Khoshnevisan, M.

Korchemskaya, E. Ya.

E. Ya. Korchemskaya, M. S. Soskin, V. B. Taranenko, “The Space-Polarizational Phase Conjugation Under Four-Wave Mixing in Biochrome Films,” Sov. J. Quantum Electron. 14, 714 (1987).

Kotov, A. U.

N. G. Bassov, V. F. Efimkov, I. G. Zubarev, A. U. Kotov, S. I. Mikhailov, M. G. Smirnov, “Phase conjugation of a depolarized wave by means of SMBD method,” JETP Lett. 4, 4, 1978).

Lam, L. K.

Mamaev, A. V.

V. N. Blashchuk, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkunov, “A Complete Wavefront Reversal Under Degenerate Four-Photon Interaction”. (Theory and Experiment), Sov. J. Quantum Electron. 7, 627 (1980).

Martin, G.

McMichael, I. C.

Mikhailov, S. I.

N. G. Bassov, V. F. Efimkov, I. G. Zubarev, A. U. Kotov, S. I. Mikhailov, M. G. Smirnov, “Phase conjugation of a depolarized wave by means of SMBD method,” JETP Lett. 4, 4, 1978).

Nikolova, L.

L. Nikolova, K. Stoyanova, T. Todorov, V. B. Taranenko, “Polarization wavefront Conjugation by means of Transient Holograms in Rigid Dye Solutions,” Opt. Commun. 64, 75 (1987).
[CrossRef]

L. Nikolova, T. Todorov, “Diffraction Efficiency and Selectivity of Polarization Holographic Recording,” Opt. Acta 31, 579 (1984).
[CrossRef]

Pilipetskii, N. F.

V. N. Blashchuk, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkunov, “A Complete Wavefront Reversal Under Degenerate Four-Photon Interaction”. (Theory and Experiment), Sov. J. Quantum Electron. 7, 627 (1980).

Shkunov, V. V.

V. N. Blashchuk, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkunov, “A Complete Wavefront Reversal Under Degenerate Four-Photon Interaction”. (Theory and Experiment), Sov. J. Quantum Electron. 7, 627 (1980).

Smirnov, M. G.

N. G. Bassov, V. F. Efimkov, I. G. Zubarev, A. U. Kotov, S. I. Mikhailov, M. G. Smirnov, “Phase conjugation of a depolarized wave by means of SMBD method,” JETP Lett. 4, 4, 1978).

Soskin, M. S.

E. Ya. Korchemskaya, M. S. Soskin, V. B. Taranenko, “The Space-Polarizational Phase Conjugation Under Four-Wave Mixing in Biochrome Films,” Sov. J. Quantum Electron. 14, 714 (1987).

Stoyanova, K.

L. Nikolova, K. Stoyanova, T. Todorov, V. B. Taranenko, “Polarization wavefront Conjugation by means of Transient Holograms in Rigid Dye Solutions,” Opt. Commun. 64, 75 (1987).
[CrossRef]

Taranenko, V. B.

L. Nikolova, K. Stoyanova, T. Todorov, V. B. Taranenko, “Polarization wavefront Conjugation by means of Transient Holograms in Rigid Dye Solutions,” Opt. Commun. 64, 75 (1987).
[CrossRef]

E. Ya. Korchemskaya, M. S. Soskin, V. B. Taranenko, “The Space-Polarizational Phase Conjugation Under Four-Wave Mixing in Biochrome Films,” Sov. J. Quantum Electron. 14, 714 (1987).

Todorov, T.

L. Nikolova, K. Stoyanova, T. Todorov, V. B. Taranenko, “Polarization wavefront Conjugation by means of Transient Holograms in Rigid Dye Solutions,” Opt. Commun. 64, 75 (1987).
[CrossRef]

L. Nikolova, T. Todorov, “Diffraction Efficiency and Selectivity of Polarization Holographic Recording,” Opt. Acta 31, 579 (1984).
[CrossRef]

Yeh, P. A.

Zel’dovich, B. Ya.

V. N. Blashchuk, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkunov, “A Complete Wavefront Reversal Under Degenerate Four-Photon Interaction”. (Theory and Experiment), Sov. J. Quantum Electron. 7, 627 (1980).

Zubarev, I. G.

N. G. Bassov, V. F. Efimkov, I. G. Zubarev, A. U. Kotov, S. I. Mikhailov, M. G. Smirnov, “Phase conjugation of a depolarized wave by means of SMBD method,” JETP Lett. 4, 4, 1978).

JETP Lett. (1)

N. G. Bassov, V. F. Efimkov, I. G. Zubarev, A. U. Kotov, S. I. Mikhailov, M. G. Smirnov, “Phase conjugation of a depolarized wave by means of SMBD method,” JETP Lett. 4, 4, 1978).

Opt. Acta (1)

L. Nikolova, T. Todorov, “Diffraction Efficiency and Selectivity of Polarization Holographic Recording,” Opt. Acta 31, 579 (1984).
[CrossRef]

Opt. Commun. (1)

L. Nikolova, K. Stoyanova, T. Todorov, V. B. Taranenko, “Polarization wavefront Conjugation by means of Transient Holograms in Rigid Dye Solutions,” Opt. Commun. 64, 75 (1987).
[CrossRef]

Opt. Laser Technol. (1)

D. Casasent, F. Caimi, “Photodichroic Crystals for Coherent Optical Data Processing,” Opt. Laser Technol. 9, 63 (1977).
[CrossRef]

Opt. Lett. (2)

Sov. J. Quantum Electron. (2)

E. Ya. Korchemskaya, M. S. Soskin, V. B. Taranenko, “The Space-Polarizational Phase Conjugation Under Four-Wave Mixing in Biochrome Films,” Sov. J. Quantum Electron. 14, 714 (1987).

V. N. Blashchuk, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkunov, “A Complete Wavefront Reversal Under Degenerate Four-Photon Interaction”. (Theory and Experiment), Sov. J. Quantum Electron. 7, 627 (1980).

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Figures (4)

Fig. 1
Fig. 1

Basic arrangement for wavefront reversal by four-wave mixing: 1 and 2, pump waves; 3, signal wave; 4, phase-conjugate wave; M, mirror; H, dynamic recording material.

Fig. 2
Fig. 2

Dependence of the photoanisotropic ratio k/k on the intensity of reference wave 1 for a sample of methyl red/PMMA.

Fig. 3
Fig. 3

Formation and decay of reversed wave 4 for a circularly polarized wave 1 when the signal wave has the same circular polarization as wave 1 (solid line) or the orthogonal circular polarization (dotted line). The intensity of wave 3 is 1 mW · cm−2 and the total intensity of waves 1 and 2 is: (a) 100 mW · cm−2; (b) 48 mW · cm−2; (c) 70 mW · cm−2.

Fig. 4
Fig. 4

Dependence of the photoanisotropic ratio k/k on the intensity of reference wave 1 for a sample of Sudan IV/PMMA.

Equations (26)

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E 1 = | R x R y | exp ( i δ ) ; E 3 = | S x S y | exp ( + i δ )
E = | E x E y | = | R x exp ( i δ ) + S x exp ( i δ ) R y exp ( i δ ) + S y exp ( i δ ) | .
α x = α 0 + Δ α x = α 0 + k α a 2 + k α b 2 , α y = α 0 + Δ α y = α 0 + k α a 2 + k α b 2 , n x = n 0 + Δ n x = n 0 + k n a 2 + k n b 2 , n y = n 0 + Δ n y = n 0 + k n a 2 + k n b 2 ,
T ˆ = T ˆ 0 + Δ T ˆ ,
Δ T ˆ = C | k a 2 + k b 2 0 0 k b 2 + k a 2 | ,
Δ T x x = C ( k J x x + k J y y ) ,
Δ T x y = Δ T y x = C ( k k ) ( J x y + J y x ) / 2 ,
Δ T y y = C ( k J x x + k J y y ) ,
E 1 = | R 0 | exp ( i δ ) ; E 3 = | S x S y exp ( i Δ ) | exp ( i δ ) .
Δ T x x = C [ ( R 2 + S x 2 ) k + k S y 2 + 2 R S x k cos 2 δ ] , Δ T x y = Δ T y x = C [ ( k k ) R S y cos ( 2 δ + Δ ) + S x S y cos Δ ] , Δ T y y = C [ ( R 2 + S x 2 ) k + k S y 2 + 2 k R S x cos 2 δ ] .
Δ T 1 = | 2 R k S x cos 2 δ R ( k k ) S Y cos ( 2 δ + Δ ) R ( k k ) S Y cos ( 2 δ + Δ ) 2 R k S x cos 2 δ | .
Δ T 1 = C | 2 R S x k cos 2 δ 0 0 2 R S x k cos 2 δ | ,
Δ T 1 = C | 0 ( k k ) R S y cos ( 2 δ + Δ ) ( k k ) R S y cos ( 2 δ + Δ ) 0 | .
E 2 = | r 0 | exp ( + i δ ) .
E 4 x = C r R 2 k S x , E 4 y = C r R ( k k ) S y exp ( i Δ ) .
2 k = k k or k = k ,
E 1 = | R i R | exp ( i δ ) ; E 3 = | S x S y exp ( i Δ ) | exp ( i δ ) ,
2 k R S x cos 2 δ + 2 k R S y sin ( 2 δ + Δ ) Δ T ˆ = C ( k k ) ( R S x sin 2 δ + R S y cos ( 2 δ + Δ ) . ( k k ) ( R S x sin 2 δ + R S y cos ( 2 δ + Δ ) 2 k R S y sin ( 2 δ + Δ ) + 2 k k S x cos 2 δ
k + k = 2 ( k k ) or k = 1 3 ( k ) .
E 1 = | A i B | exp ( i δ ) ,
E 3 = | A i B | exp ( + i δ ) .
Δ T ˆ = | 2 ( k A 2 + k B 2 ) cos 2 δ 0 0 2 ( k A 2 + k B 2 ) cos 2 δ | .
E 4 x E 4 y = A ( k A 2 + k B 2 ) i B ( k A 2 + k B 2 .
k ( n ¯ ) = k ( n ¯ )
k ( n ¯ ) = 1 3 k ( n ¯ )
k / k > 0 for layers of methyl red / PMMA , k / k < 0 for layers of sudan IV / PMMA .

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