Abstract

We have characterized the photorefractive performance of a special 45°-cut crystal of BaTiO3 and compared it with the conventional 0°-cut material. An increased peak gain coefficient of 26 cm−1 was measured using near normal beam incidence. Response times measured were ∼1 order of magnitude faster than similar 0° -cut crystals. The effects of an externally applied electric field parallel to the grating wave vector on the gain and response time were investigated. As an application example, the crystal was used to produce efficient and stable self-pumped image phase conjugation.

© 1989 Optical Society of America

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  1. Y. Fainman, E. Klancnik, S. H. Lee, “Optimal Coherent Image Amplification by Two-Wave Coupling in Photorefractive BaTiO3,” J. Opt. Soc. Am. A 1, 1229A (1984);Opt. Eng. 25, 228–234 (1986).
  2. M. Cronin-Golomb, A. M. Biernacki, C. Lin, H. Kong, “Photorefractive Time Differentiation of Coherent Optical Images,” Opt. Lett. 12, 1029–1031 (1987).
    [CrossRef] [PubMed]
  3. J. Feinberg, “Self-Pumped, Continuous-Wave Phase Conjugator Using Internal Reflection,” Opt. Lett. 7, 486–488 (1982).
    [CrossRef] [PubMed]
  4. Y. Fainman, C. C. Guest, S. H. Lee, “Optical Digital Operations by Two-Beam Coupling in Photorefractive Material,” Appl. Opt. 25, 1598–1603 (1986).
    [CrossRef] [PubMed]
  5. Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
    [CrossRef]
  6. S. Ducharme, J. Feinberg, “Speed of the Photorefractive Effect in a BaTiO3 Single Crystal,” J. Appl. Phys. 56, 839–842 (1984).
    [CrossRef]
  7. S. Ducharme, J. Feinberg, “Altering the Photorefractive Properties of BaTiO3 by Reduction and Oxidation at 650°C,” J. Opt. Soc. Am. B 3, 283–292 (1986).
    [CrossRef]
  8. M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, “Photorefractive Properties of Strontium-Barium Niobate,” J. Appl. Phys. 62, 374–380 (1987).
    [CrossRef]
  9. K. R. MacDonald, J. Feinberg, “Theory of a Self-Pumped Phase Conjugator with Two Coupled Interaction Regions,” J. Opt. Soc. Am. 73, 548–553 (1983).
    [CrossRef]
  10. G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” Opt. Eng. 22, 704–711 (1983).
    [CrossRef]
  11. F. Micheron, G. Bismuth, “Electric Control of Fixation and Erasure of Holographic Patterns in Ferroelectric Materials,” Appl. Phys. Lett. 20, 79–81 (1972).
    [CrossRef]
  12. D. M. Pepper, “Hybrid Phase Conjugator/Modulators Using Self-Pumped 0°-Cut and 45°-Cut BaTiO3 Crystals,” Appl. Phys. Lett. 49, 1001–1003 (1986).
    [CrossRef]
  13. P. G. Schunemann, T. M. Pollak, Y. Yang, Y.-Y. Teng, C. Wong, “Effects of Feed Material and Annealing Temperature on the Properties of Photorefractive Barium Titanate Crystals,” J. Opt. Soc. Am. B 5, 1702–1710 (1988).
    [CrossRef]
  14. R. A. Rupp, F. W. Drees, “Light-Induced Scattering in Photorefractive Crystals,” Appl. Phys. B 39, 223–229 (1986).
    [CrossRef]
  15. G. C. Valley, “Short-Pulse Grating Formation in Photorefractive Materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
    [CrossRef]
  16. M. B. Klein, “Physics of the Photorefractive Effect in BaTiO3,” in Photorefractive Materials and Applications, P. Gunter, J. P. Huignard, Eds. (Springer-Verlag, New York, 1986), Chap. 7.
  17. A. V. Nowak, T. R. Moore, R. A. Fisher, “Observations of Internal Beam Production in Barium Titanate Phase Conjugators,” J. Opt. Soc. Am. B 5, 1864–1878 (1988).
    [CrossRef]
  18. J. E. Ford, Y. Fainman, S. H. Lee, “Time Integrating Interferometry Using Photorefractive Fanout,” Opt. Lett. 13, 856–858 (1988).
    [CrossRef] [PubMed]

1988 (3)

1987 (2)

M. Cronin-Golomb, A. M. Biernacki, C. Lin, H. Kong, “Photorefractive Time Differentiation of Coherent Optical Images,” Opt. Lett. 12, 1029–1031 (1987).
[CrossRef] [PubMed]

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, “Photorefractive Properties of Strontium-Barium Niobate,” J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

1986 (4)

Y. Fainman, C. C. Guest, S. H. Lee, “Optical Digital Operations by Two-Beam Coupling in Photorefractive Material,” Appl. Opt. 25, 1598–1603 (1986).
[CrossRef] [PubMed]

D. M. Pepper, “Hybrid Phase Conjugator/Modulators Using Self-Pumped 0°-Cut and 45°-Cut BaTiO3 Crystals,” Appl. Phys. Lett. 49, 1001–1003 (1986).
[CrossRef]

R. A. Rupp, F. W. Drees, “Light-Induced Scattering in Photorefractive Crystals,” Appl. Phys. B 39, 223–229 (1986).
[CrossRef]

S. Ducharme, J. Feinberg, “Altering the Photorefractive Properties of BaTiO3 by Reduction and Oxidation at 650°C,” J. Opt. Soc. Am. B 3, 283–292 (1986).
[CrossRef]

1985 (1)

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

1984 (2)

S. Ducharme, J. Feinberg, “Speed of the Photorefractive Effect in a BaTiO3 Single Crystal,” J. Appl. Phys. 56, 839–842 (1984).
[CrossRef]

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal Coherent Image Amplification by Two-Wave Coupling in Photorefractive BaTiO3,” J. Opt. Soc. Am. A 1, 1229A (1984);Opt. Eng. 25, 228–234 (1986).

1983 (3)

G. C. Valley, “Short-Pulse Grating Formation in Photorefractive Materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

K. R. MacDonald, J. Feinberg, “Theory of a Self-Pumped Phase Conjugator with Two Coupled Interaction Regions,” J. Opt. Soc. Am. 73, 548–553 (1983).
[CrossRef]

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” Opt. Eng. 22, 704–711 (1983).
[CrossRef]

1982 (1)

1972 (1)

F. Micheron, G. Bismuth, “Electric Control of Fixation and Erasure of Holographic Patterns in Ferroelectric Materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

Biernacki, A. M.

Bismuth, G.

F. Micheron, G. Bismuth, “Electric Control of Fixation and Erasure of Holographic Patterns in Ferroelectric Materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

Cory, W. K.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, “Photorefractive Properties of Strontium-Barium Niobate,” J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

Cronin-Golomb, M.

Drees, F. W.

R. A. Rupp, F. W. Drees, “Light-Induced Scattering in Photorefractive Crystals,” Appl. Phys. B 39, 223–229 (1986).
[CrossRef]

Ducharme, S.

S. Ducharme, J. Feinberg, “Altering the Photorefractive Properties of BaTiO3 by Reduction and Oxidation at 650°C,” J. Opt. Soc. Am. B 3, 283–292 (1986).
[CrossRef]

S. Ducharme, J. Feinberg, “Speed of the Photorefractive Effect in a BaTiO3 Single Crystal,” J. Appl. Phys. 56, 839–842 (1984).
[CrossRef]

Ewbank, M. D.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, “Photorefractive Properties of Strontium-Barium Niobate,” J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

Fainman, Y.

Feinberg, J.

Fisher, R. A.

Ford, J. E.

Guest, C. C.

Huignard, J. P.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Klancnik, E.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal Coherent Image Amplification by Two-Wave Coupling in Photorefractive BaTiO3,” J. Opt. Soc. Am. A 1, 1229A (1984);Opt. Eng. 25, 228–234 (1986).

Klein, M. B.

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” Opt. Eng. 22, 704–711 (1983).
[CrossRef]

M. B. Klein, “Physics of the Photorefractive Effect in BaTiO3,” in Photorefractive Materials and Applications, P. Gunter, J. P. Huignard, Eds. (Springer-Verlag, New York, 1986), Chap. 7.

Kong, H.

Lee, S. H.

Lin, C.

MacDonald, K. R.

Micheron, F.

F. Micheron, G. Bismuth, “Electric Control of Fixation and Erasure of Holographic Patterns in Ferroelectric Materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

Moore, T. R.

Neurgaonkar, R. R.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, “Photorefractive Properties of Strontium-Barium Niobate,” J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

Nowak, A. V.

Pepper, D. M.

D. M. Pepper, “Hybrid Phase Conjugator/Modulators Using Self-Pumped 0°-Cut and 45°-Cut BaTiO3 Crystals,” Appl. Phys. Lett. 49, 1001–1003 (1986).
[CrossRef]

Pollak, T. M.

Rajbenbach, H.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Refregier, Ph.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Rupp, R. A.

R. A. Rupp, F. W. Drees, “Light-Induced Scattering in Photorefractive Crystals,” Appl. Phys. B 39, 223–229 (1986).
[CrossRef]

Schunemann, P. G.

Solymar, L.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Teng, Y.-Y.

Valley, G. C.

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” Opt. Eng. 22, 704–711 (1983).
[CrossRef]

G. C. Valley, “Short-Pulse Grating Formation in Photorefractive Materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

Wong, C.

Yang, Y.

Appl. Opt. (1)

Appl. Phys. B (1)

R. A. Rupp, F. W. Drees, “Light-Induced Scattering in Photorefractive Crystals,” Appl. Phys. B 39, 223–229 (1986).
[CrossRef]

Appl. Phys. Lett. (2)

F. Micheron, G. Bismuth, “Electric Control of Fixation and Erasure of Holographic Patterns in Ferroelectric Materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

D. M. Pepper, “Hybrid Phase Conjugator/Modulators Using Self-Pumped 0°-Cut and 45°-Cut BaTiO3 Crystals,” Appl. Phys. Lett. 49, 1001–1003 (1986).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. C. Valley, “Short-Pulse Grating Formation in Photorefractive Materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

J. Appl. Phys. (3)

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

S. Ducharme, J. Feinberg, “Speed of the Photorefractive Effect in a BaTiO3 Single Crystal,” J. Appl. Phys. 56, 839–842 (1984).
[CrossRef]

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, “Photorefractive Properties of Strontium-Barium Niobate,” J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal Coherent Image Amplification by Two-Wave Coupling in Photorefractive BaTiO3,” J. Opt. Soc. Am. A 1, 1229A (1984);Opt. Eng. 25, 228–234 (1986).

J. Opt. Soc. Am. B (3)

Opt. Eng. (1)

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” Opt. Eng. 22, 704–711 (1983).
[CrossRef]

Opt. Lett. (3)

Other (1)

M. B. Klein, “Physics of the Photorefractive Effect in BaTiO3,” in Photorefractive Materials and Applications, P. Gunter, J. P. Huignard, Eds. (Springer-Verlag, New York, 1986), Chap. 7.

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Figures (9)

Fig. 1
Fig. 1

Geometric configuration for two-wave mixing in BaTiO3. k ̂ 1 and k ̂ 2 are the vectors of the horizontally (extraordinarily) polarized pump and signal waves, respectively; k ̂ g is the wave vector of the induced index grating; ê1 and ê2 are the pump and signal beam electric field vectors. 2θ is the interior angle between k ̂ 1 and k ̂ 2, and β is the interior angle between k ̂ g and Ĉ, the crystal's optic axis. The particular case shown is that of a 0° -cut crystal with Ĉ parallel to the input face.

Fig. 2
Fig. 2

Exponential gain coefficient Γ for two-wave mixing in BaTiO3 as a function of externally controlled angles θ and β (measured inside the crystal). Experimental points shown were taken with a conventional 0°-cut crystal.

Fig. 3
Fig. 3

Orientation of the 45° -cut BaTiO3 crystal [with faces on the (100), (001), ( 01 1 ¯ ) and crystallographic planes] relative to the 0°-cut crystal.

Fig. 4
Fig. 4

Γ vs θ for both the conventional (crystal A; 4.5 mm thick, β = 15°) and the 45°-cut (crystal E; 2.5 mm thick, β = 45°) BaTiO3. Pump intensity of 20 mW/cm2 was 2 × 104 that of the probe.

Fig. 5
Fig. 5

Equal Γ contours in BaTiO3 grating phase space. The three heavy curves show the possible noise gratings which can form from input beams propagating in three different directions relative to Ĉ. The smaller diagrams at right illustrate the three directions by showing the incident angles on, from top to bottom, the (010) face of a 0°-cut crystal (β ≈ 15°), the (011) face of a 45°-cut crystal (β ≈ 45°), and the (001) face of a 0°-cut crystal (β ≈ 75°). Note that only the line corresponding to β ≈ 45° passes over the peak of the Γ contour.

Fig. 6
Fig. 6

Γ vs applied field for the 45°-cut 2.5-mm thick BaTiO3 crystal D. The pump intensity Ip was 20 mW/cm2, r = 2 × 20−4, θ = 2° (grating period, 3 μm), and β = 45°.

Fig. 7
Fig. 7

Γ vs β for both the conventional (crystal A) and the 45°-cut (crystal C) BaTiO3 4.5-mm thick samples. Both crystals were 4.5 mm thick. Operating conditions were identical for both crystals with θ = 4°, Ip = 20 mW/cm2, and r = 2 × 10−4. Strong fanout in the 45°-cut crystal reduced the Γ measured.

Fig. 8
Fig. 8

Experimental schematic for self-pumped image phase conjugation in 45°-cut BaTiO3 (crystal C). The input transparency was imaged telecentrically onto the face of the crystal. The focal length of lens 1 F1 was 750 mm and F2 was 80 mm, resulting in a demagnification factor of 9.375. The exterior angle between the input and crystal face ϕ was ≈40°. This angle produced the highest phase conjugate reflectivity and the fastest formation time. The apparent beam path inside the crystal is indicated by dotted lines.

Fig. 9
Fig. 9

(a) When a conventional dielectric mirror is used to reflect the input through the aberrating optical system, the result is a unrecognizable blur. (b) When the conventional mirror is replaced by a 45° -cut BaTiO3 self-pumped phase conjugate reflector, the aberration has little effect on the output resolution.

Tables (1)

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Table I Relative Response Times for Three Grating Orientation Angles in BaTiO3 from Our Approximate Calculation Compared with Those Measured Experimentally

Equations (6)

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G = I out I in = ( 1 + r ) exp ( Γ L ) 1 + r exp ( Γ L ) ,
Γ = ω n e c E r eff cos θ ,
r eff = ½ [ n o 4 r 13 ( cos 2 θ cos 2 β ) + 4 n e 2 n o 2 r 42 sin 2 β + n e 4 r 33 ( cos 2 β + cos 2 θ ) ] cos β ,
E = k B T q k g ( 1 + k g 2 k 0 2 ) 1 / 2 e ̂ 1 e ̂ 2 * ,
k 0 = ( N q 2 0 k B T ) 1 / 2 ,
τ di = ( μ s ) [ γ R N A 4 π e ( N A N D ) ] 1 I 0 ,

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