Abstract

Continuous-wave phase conjugation of an image-bearing beam is demonstrated using a single-domain crystal of BaTiO3 and nothing else. The device operates by four-wave mixing using the photorefractive effect but without any external pumping beams or external mirrors. The customary pumping beams are derived from the incident beam and are internally reflected inside the crystal adjacent to an edge. The device is self-starting and has a phase-conjugate reflectivity of 30%. Imaging applications are discussed.

© 1982 Optical Society of America

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References

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  1. A recent review of optical phase conjugation is found in Opt. Eng.21 (March–April1982).
  2. J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in photorefractive crystals,” Appl. Phys. Lett. 40, 450 (1982).
    [CrossRef]
  3. J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. Am. 72, 46 (1982).
    [CrossRef]
  4. M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, “Exact solution of a nonlinear model of four-wave mixing and phase conjugation”, Opt. Lett. 7, 313 (1982).
    [CrossRef] [PubMed]
  5. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “A passive (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” submitted to Appl. Phys. Lett.
  6. K. R. MacDonald, J. Feinberg, submitted to J. Opt. Soc. Am.
  7. J. Feinberg, D. H. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297 (1980); J. Appl. Phys. 52, 537 (1981).
    [CrossRef]
  8. J. Feinberg, R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519 (1980); Opt. Lett. 6, 257 (1981).
    [CrossRef] [PubMed]
  9. M. D. Levenson, “High-resolution imaging by wave-front conjugation,” Opt. Lett. 5, 182 (1980).
    [CrossRef] [PubMed]

1982 (3)

1980 (3)

J. Feinberg, D. H. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297 (1980); J. Appl. Phys. 52, 537 (1981).
[CrossRef]

J. Feinberg, R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519 (1980); Opt. Lett. 6, 257 (1981).
[CrossRef] [PubMed]

M. D. Levenson, “High-resolution imaging by wave-front conjugation,” Opt. Lett. 5, 182 (1980).
[CrossRef] [PubMed]

Cronin-Golomb, M.

J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in photorefractive crystals,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, “Exact solution of a nonlinear model of four-wave mixing and phase conjugation”, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “A passive (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” submitted to Appl. Phys. Lett.

Feinberg, J.

J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. Am. 72, 46 (1982).
[CrossRef]

J. Feinberg, D. H. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297 (1980); J. Appl. Phys. 52, 537 (1981).
[CrossRef]

J. Feinberg, R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519 (1980); Opt. Lett. 6, 257 (1981).
[CrossRef] [PubMed]

K. R. MacDonald, J. Feinberg, submitted to J. Opt. Soc. Am.

Fischer, B.

J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in photorefractive crystals,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, “Exact solution of a nonlinear model of four-wave mixing and phase conjugation”, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “A passive (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” submitted to Appl. Phys. Lett.

Heiman, D. H.

J. Feinberg, D. H. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297 (1980); J. Appl. Phys. 52, 537 (1981).
[CrossRef]

Hellwarth, R. W.

J. Feinberg, R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519 (1980); Opt. Lett. 6, 257 (1981).
[CrossRef] [PubMed]

J. Feinberg, D. H. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297 (1980); J. Appl. Phys. 52, 537 (1981).
[CrossRef]

Levenson, M. D.

MacDonald, K. R.

K. R. MacDonald, J. Feinberg, submitted to J. Opt. Soc. Am.

Tanguay, A. R.

J. Feinberg, D. H. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297 (1980); J. Appl. Phys. 52, 537 (1981).
[CrossRef]

White, J.

J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in photorefractive crystals,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

White, J. O.

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, “Exact solution of a nonlinear model of four-wave mixing and phase conjugation”, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “A passive (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” submitted to Appl. Phys. Lett.

Yariv, A.

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, “Exact solution of a nonlinear model of four-wave mixing and phase conjugation”, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in photorefractive crystals,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “A passive (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” submitted to Appl. Phys. Lett.

Appl. Phys. Lett. (1)

J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in photorefractive crystals,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

J. Appl. Phys. (1)

J. Feinberg, D. H. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297 (1980); J. Appl. Phys. 52, 537 (1981).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (3)

Other (3)

A recent review of optical phase conjugation is found in Opt. Eng.21 (March–April1982).

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “A passive (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” submitted to Appl. Phys. Lett.

K. R. MacDonald, J. Feinberg, submitted to J. Opt. Soc. Am.

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Figures (4)

Fig. 1
Fig. 1

Three photomicrographs of the BaTiO3 crystal. In all the photographs, the incident beam enters the left face of the crystal. The dark horizontal line across the top of the crystal is light scattering from one of the crystal faces damaged during poling. The c axis of the crystral is directed from top to bottom. (a) The incident Gaussian beam is an ordinary ray. No loop forms, and no phase-conjugate wave is generated. (b) The incident Gaussian beam is polarized in the plane of the paper (extraordinary ray). A loop is seen between the incident beam and the lower-right-hand edge of the crystal. (c) The incident beam contains the image of a cat, and many loops have formed. In the top two photographs, the incident beam is from a cw dye laser (25 mW at 620 nm), and the crystal is in methanol. The apparent curvature of the crystal edges is caused by photographing through the methanol miniscus. In the bottom photograph, the crystal is in air, and the incident beam is from an argon-ion laser (5 mW at 514.5 nm).

Fig. 2
Fig. 2

The incident beam (1) enters the crystal from top left. Beam 2 splits off and is internally reflected twice near the crystal edge and becomes beam 3′, which then intersects beam 1 slightly upstream. Beam 2′ has also split off from beam 1 and travels around the loop in the opposite direction. Beams 1–3 generate beam 4 by four-wave mixing in the interaction region circled on the right, as do beams 1, 2′, and 3′ in the interaction region circled on the left. Beam 4 is the phase-conjugate replica of beam 1, and it leaves the crystal exactly back along the direction of the incident beam.

Fig. 3
Fig. 3

Plot of the computed coupling constant γ versus the angle α2 of the loop beam and for various angles α1 of the incident beam for a BaTiO3 crystal with a number density of charges N = 3 × 1016 cm−3 and for extraordinary rays. The data point corresponds to the angles made by the incident beam and the self-generated loop shown in Fig. 1(b). In general, the loop will form whenever γl ≥ 2.34 and will slide to the angle α2 that produces the largest coupling.

Fig. 4
Fig. 4

Image of a common household member using the self-pumped conjugator and also using an ordinary mirror. The myriad of loops present in the crystal during phase-conjugation of this image is shown in Fig. 1(c). These images were formed with a cw argon-ion laser and photographed through a ground-glass screen. The phase-conjugator corrects for aberration caused by the distorter; the ordinary mirror does not.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

γ = ω 2 n c E r eff cos ( α 1 α 2 2 ) .
E = k B T q k 1 + ( k / k 0 ) 2 ,
k 0 = ( N q 2 / ( 0 k B T ) ) 1 / 2 .
r eff = n 0 4 r 13 sin ( α 1 + α 2 2 )
r eff = [ n 0 4 r 13 cos α 1 cos α 2 + 2 n e 2 n 0 2 r 42 × cos 2 ( α 1 + α 2 2 ) + n e 4 r 33 sin α 1 sin α 2 ] × sin ( α 1 + α 2 2 ) .

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