Abstract

We demonstrate optical-beam phase conjugation by the process of two-beam coupling in photorefractive barium titanate. The incident, image-bearing beam causes exponential gain for counterpropagating waves, which are fed by noise and emerge with a power of the order of 10% of the incident beam and phase conjugate to it. This is expected from the calculated plane-wave gain plus the analogy to the theory of phase conjugation of complex wave fronts by stimulated Brillouin backscattering. We conjugate beams at either 515 or 488 nm at between 10- and 50-mW power, and find, as expected, no frequency shift (<1 Hz) in the process.

© 1985 Optical Society of America

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  1. V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Mel’nikov, N. F. Pilipetskii, V. I. Popovichev, V. V. Ragul’skii, Sov. Tech. Phys. Lett. 3, 83 (1977).
  2. V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Sov. Tech. Phys. Lett. 8, 85 (1977).
  3. V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Radio-phys. Quantum Electron. 20, 544 (1977).
  4. R. Mays, R. J. Lysiak, Opt. Commun. 31, 89 (1979).
  5. R. Mays, R. J. Lysiak, Opt. Commun. 32, 334 (1980).
  6. V. G. Sidorovich, Sov. Phys. Tech. Phys. 21, 1270 (1976).
  7. R. W. Hellwarth, J. Opt. Soc. Am. 68, 1050 (1978).
  8. N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhailov, M. G. Smirnov, JETP Lett. 28, 197 (1978).
  9. V. N. Blashchuk, B. Ya. Zel’dovich, V. N. Krasheninnikov, N. A. Mel’nikov, N. F. Pilipetskii, V. V. Ragul’skii, V. V. Shkunov, Sov. Phys. Dokl. 23, 588 (1978).
  10. V. N. Blashchuk, V. N. Krasheninnikov, N. A. Melnikov, N. F. Pilipetsky, V. V. Ragulsky, V. V. Shkunov, B. Ya. Zel’dovich, Opt. Commun. 27, 137 (1978).
  11. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980); erratum 52, 537 (1981).
  12. A. R. Johnston, J. Appl. Phys. 42, 3501 (1971).
  13. J. Feinberg, Opt. Lett. 7, 486 (1982).

1982 (1)

1980 (2)

R. Mays, R. J. Lysiak, Opt. Commun. 32, 334 (1980).

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980); erratum 52, 537 (1981).

1979 (1)

R. Mays, R. J. Lysiak, Opt. Commun. 31, 89 (1979).

1978 (4)

R. W. Hellwarth, J. Opt. Soc. Am. 68, 1050 (1978).

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhailov, M. G. Smirnov, JETP Lett. 28, 197 (1978).

V. N. Blashchuk, B. Ya. Zel’dovich, V. N. Krasheninnikov, N. A. Mel’nikov, N. F. Pilipetskii, V. V. Ragul’skii, V. V. Shkunov, Sov. Phys. Dokl. 23, 588 (1978).

V. N. Blashchuk, V. N. Krasheninnikov, N. A. Melnikov, N. F. Pilipetsky, V. V. Ragulsky, V. V. Shkunov, B. Ya. Zel’dovich, Opt. Commun. 27, 137 (1978).

1977 (3)

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Mel’nikov, N. F. Pilipetskii, V. I. Popovichev, V. V. Ragul’skii, Sov. Tech. Phys. Lett. 3, 83 (1977).

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Sov. Tech. Phys. Lett. 8, 85 (1977).

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Radio-phys. Quantum Electron. 20, 544 (1977).

1976 (1)

V. G. Sidorovich, Sov. Phys. Tech. Phys. 21, 1270 (1976).

1971 (1)

A. R. Johnston, J. Appl. Phys. 42, 3501 (1971).

Basov, N. G.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhailov, M. G. Smirnov, JETP Lett. 28, 197 (1978).

Bespalov, V. I.

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Radio-phys. Quantum Electron. 20, 544 (1977).

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Sov. Tech. Phys. Lett. 8, 85 (1977).

Betin, A. A.

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Sov. Tech. Phys. Lett. 8, 85 (1977).

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Radio-phys. Quantum Electron. 20, 544 (1977).

Blashchuk, V. N.

V. N. Blashchuk, V. N. Krasheninnikov, N. A. Melnikov, N. F. Pilipetsky, V. V. Ragulsky, V. V. Shkunov, B. Ya. Zel’dovich, Opt. Commun. 27, 137 (1978).

V. N. Blashchuk, B. Ya. Zel’dovich, V. N. Krasheninnikov, N. A. Mel’nikov, N. F. Pilipetskii, V. V. Ragul’skii, V. V. Shkunov, Sov. Phys. Dokl. 23, 588 (1978).

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Mel’nikov, N. F. Pilipetskii, V. I. Popovichev, V. V. Ragul’skii, Sov. Tech. Phys. Lett. 3, 83 (1977).

Efimkov, V. F.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhailov, M. G. Smirnov, JETP Lett. 28, 197 (1978).

Feinberg, J.

J. Feinberg, Opt. Lett. 7, 486 (1982).

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980); erratum 52, 537 (1981).

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980); erratum 52, 537 (1981).

Hellwarth, R. W.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980); erratum 52, 537 (1981).

R. W. Hellwarth, J. Opt. Soc. Am. 68, 1050 (1978).

Johnston, A. R.

A. R. Johnston, J. Appl. Phys. 42, 3501 (1971).

Kotov, A. V.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhailov, M. G. Smirnov, JETP Lett. 28, 197 (1978).

Krasheninnikov, V. N.

V. N. Blashchuk, V. N. Krasheninnikov, N. A. Melnikov, N. F. Pilipetsky, V. V. Ragulsky, V. V. Shkunov, B. Ya. Zel’dovich, Opt. Commun. 27, 137 (1978).

V. N. Blashchuk, B. Ya. Zel’dovich, V. N. Krasheninnikov, N. A. Mel’nikov, N. F. Pilipetskii, V. V. Ragul’skii, V. V. Shkunov, Sov. Phys. Dokl. 23, 588 (1978).

Lysiak, R. J.

R. Mays, R. J. Lysiak, Opt. Commun. 32, 334 (1980).

R. Mays, R. J. Lysiak, Opt. Commun. 31, 89 (1979).

Mays, R.

R. Mays, R. J. Lysiak, Opt. Commun. 32, 334 (1980).

R. Mays, R. J. Lysiak, Opt. Commun. 31, 89 (1979).

Mel’nikov, N. A.

V. N. Blashchuk, B. Ya. Zel’dovich, V. N. Krasheninnikov, N. A. Mel’nikov, N. F. Pilipetskii, V. V. Ragul’skii, V. V. Shkunov, Sov. Phys. Dokl. 23, 588 (1978).

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Mel’nikov, N. F. Pilipetskii, V. I. Popovichev, V. V. Ragul’skii, Sov. Tech. Phys. Lett. 3, 83 (1977).

Melnikov, N. A.

V. N. Blashchuk, V. N. Krasheninnikov, N. A. Melnikov, N. F. Pilipetsky, V. V. Ragulsky, V. V. Shkunov, B. Ya. Zel’dovich, Opt. Commun. 27, 137 (1978).

Mikhailov, S. I.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhailov, M. G. Smirnov, JETP Lett. 28, 197 (1978).

Pasmanik, G. A.

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Radio-phys. Quantum Electron. 20, 544 (1977).

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Sov. Tech. Phys. Lett. 8, 85 (1977).

Pilipetskii, N. F.

V. N. Blashchuk, B. Ya. Zel’dovich, V. N. Krasheninnikov, N. A. Mel’nikov, N. F. Pilipetskii, V. V. Ragul’skii, V. V. Shkunov, Sov. Phys. Dokl. 23, 588 (1978).

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Mel’nikov, N. F. Pilipetskii, V. I. Popovichev, V. V. Ragul’skii, Sov. Tech. Phys. Lett. 3, 83 (1977).

Pilipetsky, N. F.

V. N. Blashchuk, V. N. Krasheninnikov, N. A. Melnikov, N. F. Pilipetsky, V. V. Ragulsky, V. V. Shkunov, B. Ya. Zel’dovich, Opt. Commun. 27, 137 (1978).

Popovichev, V. I.

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Mel’nikov, N. F. Pilipetskii, V. I. Popovichev, V. V. Ragul’skii, Sov. Tech. Phys. Lett. 3, 83 (1977).

Ragul’skii, V. V.

V. N. Blashchuk, B. Ya. Zel’dovich, V. N. Krasheninnikov, N. A. Mel’nikov, N. F. Pilipetskii, V. V. Ragul’skii, V. V. Shkunov, Sov. Phys. Dokl. 23, 588 (1978).

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Mel’nikov, N. F. Pilipetskii, V. I. Popovichev, V. V. Ragul’skii, Sov. Tech. Phys. Lett. 3, 83 (1977).

Ragulsky, V. V.

V. N. Blashchuk, V. N. Krasheninnikov, N. A. Melnikov, N. F. Pilipetsky, V. V. Ragulsky, V. V. Shkunov, B. Ya. Zel’dovich, Opt. Commun. 27, 137 (1978).

Shkunov, V. V.

V. N. Blashchuk, V. N. Krasheninnikov, N. A. Melnikov, N. F. Pilipetsky, V. V. Ragulsky, V. V. Shkunov, B. Ya. Zel’dovich, Opt. Commun. 27, 137 (1978).

V. N. Blashchuk, B. Ya. Zel’dovich, V. N. Krasheninnikov, N. A. Mel’nikov, N. F. Pilipetskii, V. V. Ragul’skii, V. V. Shkunov, Sov. Phys. Dokl. 23, 588 (1978).

Sidorovich, V. G.

V. G. Sidorovich, Sov. Phys. Tech. Phys. 21, 1270 (1976).

Smirnov, M. G.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhailov, M. G. Smirnov, JETP Lett. 28, 197 (1978).

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980); erratum 52, 537 (1981).

Zel’dovich, B. Ya.

V. N. Blashchuk, V. N. Krasheninnikov, N. A. Melnikov, N. F. Pilipetsky, V. V. Ragulsky, V. V. Shkunov, B. Ya. Zel’dovich, Opt. Commun. 27, 137 (1978).

V. N. Blashchuk, B. Ya. Zel’dovich, V. N. Krasheninnikov, N. A. Mel’nikov, N. F. Pilipetskii, V. V. Ragul’skii, V. V. Shkunov, Sov. Phys. Dokl. 23, 588 (1978).

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Mel’nikov, N. F. Pilipetskii, V. I. Popovichev, V. V. Ragul’skii, Sov. Tech. Phys. Lett. 3, 83 (1977).

Zubarev, I. G.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhailov, M. G. Smirnov, JETP Lett. 28, 197 (1978).

J. Appl. Phys. (2)

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980); erratum 52, 537 (1981).

A. R. Johnston, J. Appl. Phys. 42, 3501 (1971).

J. Opt. Soc. Am. (1)

JETP Lett. (1)

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhailov, M. G. Smirnov, JETP Lett. 28, 197 (1978).

Opt. Commun. (3)

V. N. Blashchuk, V. N. Krasheninnikov, N. A. Melnikov, N. F. Pilipetsky, V. V. Ragulsky, V. V. Shkunov, B. Ya. Zel’dovich, Opt. Commun. 27, 137 (1978).

R. Mays, R. J. Lysiak, Opt. Commun. 31, 89 (1979).

R. Mays, R. J. Lysiak, Opt. Commun. 32, 334 (1980).

Opt. Lett. (1)

Radio-phys. Quantum Electron. (1)

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Radio-phys. Quantum Electron. 20, 544 (1977).

Sov. Phys. Dokl. (1)

V. N. Blashchuk, B. Ya. Zel’dovich, V. N. Krasheninnikov, N. A. Mel’nikov, N. F. Pilipetskii, V. V. Ragul’skii, V. V. Shkunov, Sov. Phys. Dokl. 23, 588 (1978).

Sov. Phys. Tech. Phys. (1)

V. G. Sidorovich, Sov. Phys. Tech. Phys. 21, 1270 (1976).

Sov. Tech. Phys. Lett. (2)

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Mel’nikov, N. F. Pilipetskii, V. I. Popovichev, V. V. Ragul’skii, Sov. Tech. Phys. Lett. 3, 83 (1977).

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, Sov. Tech. Phys. Lett. 8, 85 (1977).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the experimental apparatus described in the text.

Fig. 2
Fig. 2

Top view of the barium titanate crystal immersed in the index-matching fluid when it is generating the backscattering. (a) Negative photograph of the crystal when it is phase conjugating; (b) important features of (a).

Fig. 3
Fig. 3

Backscattered images recorded (magnified) at plane B in Fig. 2, (a) when an ordinary mirror is used in place of the barium titanate crystal, and (b) when the barium titanate crystal is used. The smallest visible bars are spaced at 3 per millimeter. The slight deterioration of the image in the middle of (b) arises from our inability to collect all the scattered light from the distorters.

Fig. 4
Fig. 4

Top view of how the same crystal, when surrounded by air, utilizes another beam geometry to generate phase-conjugate backscattering. (a)–(c) are all negative photographs to emphasize the beam traces inside the crystal. Before the backscattering starts the crystal is flooded with light from beam fanning and total internal reflection as seen in (a). Then seconds later a phase-conjugation configuration forms as shown in (b), collapsing most of the fanned beam into this thin path. Presumably, this is the path that wins a competition for the highest total net gain for backscattered waves. At some entrance angles a multiple-path phase conjugator forms with beams as shown in (c). In (d) are labeled features discussed in the text of the single-path phase-conjugating geometry of (b). At some angles, (b) switched briefly to (c) and back to (b) periodically with period 0.03 to 1 sec, depending on angle and wavelength.

Equations (7)

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P NL = - i b E ( x ) F ( x ) 2
δ k 1 = i ω 1 k D 2 k B T n 1 3 r eff 2 c k q ( k 2 + i k · f k D 2 + k 2 + i k · f ) ,
k r eff n 1 4 ( e ^ 1 * · ω · [ R · k ] · ω · e ^ 2 ) ( e ^ 2 * · e ^ 1 ) .
k D 2 = N q 2 / 0 k B T ,
| | cos 2 θ + sin 2 θ ,
r eff ~ 2 r 42 cos θ sin 2 θ .
g ( θ ) = n 1 2 q r 42 N sin 2 θ cos θ 0 ( | | cos 2 θ + sin 2 θ ) .

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