Abstract

We present data showing a nonlinear photorefractive response at high modulation depths in a Bi12TiO20 sample when applied ac fields are used. The data are interpreted by means of both a numerical finite-difference model and an analytic theory developed by Swinburne et al. [ IEEProceedings of the International Conference on Holographic Systems, Components and Applications ( Institution of Electrical Engineers, London, 1989), p. 175]. Both models provide physical insights into the performance of semiconductor and sillenite materials with ac field enhancements.

© 1992 Optical Society of America

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References

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  1. J.-P. Huignard, A. Marrakchi, “Coherent signal beam amplification in two wave mixing experiments with photorefractive Bi12SiO20crystals,” Opt. Commun. 38, 249 (1981).
    [CrossRef]
  2. G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
    [CrossRef]
  3. S. Stepanov, M. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292 (1985).
    [CrossRef]
  4. Ph. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
    [CrossRef]
  5. S. I. Stepanov, S. L. Sochava, “Effective energy transfer in a two-wave interaction in Bi12TiO20,” Sov. Phys. Tech. Phys. 32, 1054 (1987).
  6. B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, J.-P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals.” Opt. Lett. 13, 327 (1988).
    [CrossRef] [PubMed]
  7. P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I (Springer-Verlag, New York, 1988).
    [CrossRef]
  8. G. A. Swinburne, T. J. Hall, A. K. Powell, “Large modulation effects in photorefractive crystals,” IEE Proceedings of the International Conference on Holographic Systems, Components and Applications (Institution of Electrical Engineers, London, 1989), p. 175.
  9. E. Ochoa, F. Vachss, L. Hesselink, “Higher-order analysis of the photorefractive effect for large modulation depths,” J. Opt. Soc. Am. A 3, 181, (1986).
    [CrossRef]
  10. F. Vachss, L. Hesselink, “Nonlinear photorefractive response at high modulation depths,” J. Opt. Soc. Am. A 5, 690 (1988).
    [CrossRef]
  11. L. B. Au, L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554 (1990).
    [CrossRef]
  12. G. A. Brost, “Photorefractive grating formation at large modulation with alternating electric fields,” J. Opt. Soc. Am. B 9, 1454 (1992).
    [CrossRef]
  13. J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
    [CrossRef]
  14. D. Rytz, B. A. Wechsler, C. C. Nelson, K. W. Kirby, J. Cryst. Growth 99, 864 (1990).
    [CrossRef]

1992 (1)

1990 (3)

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

D. Rytz, B. A. Wechsler, C. C. Nelson, K. W. Kirby, J. Cryst. Growth 99, 864 (1990).
[CrossRef]

L. B. Au, L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554 (1990).
[CrossRef]

1989 (1)

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

1988 (2)

1987 (1)

S. I. Stepanov, S. L. Sochava, “Effective energy transfer in a two-wave interaction in Bi12TiO20,” Sov. Phys. Tech. Phys. 32, 1054 (1987).

1986 (1)

1985 (2)

S. Stepanov, M. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292 (1985).
[CrossRef]

Ph. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

1981 (1)

J.-P. Huignard, A. Marrakchi, “Coherent signal beam amplification in two wave mixing experiments with photorefractive Bi12SiO20crystals,” Opt. Commun. 38, 249 (1981).
[CrossRef]

Au, L. B.

Brost, G. A.

Gravey, P.

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

Günter, P.

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I (Springer-Verlag, New York, 1988).
[CrossRef]

Hall, T. J.

G. A. Swinburne, T. J. Hall, A. K. Powell, “Large modulation effects in photorefractive crystals,” IEE Proceedings of the International Conference on Holographic Systems, Components and Applications (Institution of Electrical Engineers, London, 1989), p. 175.

Herriau, J. P.

Hesselink, L.

Huignard, J.-P.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, J.-P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals.” Opt. Lett. 13, 327 (1988).
[CrossRef] [PubMed]

Ph. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

J.-P. Huignard, A. Marrakchi, “Coherent signal beam amplification in two wave mixing experiments with photorefractive Bi12SiO20crystals,” Opt. Commun. 38, 249 (1981).
[CrossRef]

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I (Springer-Verlag, New York, 1988).
[CrossRef]

Imbert, B.

Kirby, K. W.

D. Rytz, B. A. Wechsler, C. C. Nelson, K. W. Kirby, J. Cryst. Growth 99, 864 (1990).
[CrossRef]

Klein, M. B.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

Mallick, S.

Marrakchi, A.

J.-P. Huignard, A. Marrakchi, “Coherent signal beam amplification in two wave mixing experiments with photorefractive Bi12SiO20crystals,” Opt. Commun. 38, 249 (1981).
[CrossRef]

McCahon, S. W.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

Nelson, C. C.

D. Rytz, B. A. Wechsler, C. C. Nelson, K. W. Kirby, J. Cryst. Growth 99, 864 (1990).
[CrossRef]

Ochoa, E.

Ozkul, C.

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

Petrov, M.

S. Stepanov, M. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292 (1985).
[CrossRef]

Picoli, G.

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

Powell, A. K.

G. A. Swinburne, T. J. Hall, A. K. Powell, “Large modulation effects in photorefractive crystals,” IEE Proceedings of the International Conference on Holographic Systems, Components and Applications (Institution of Electrical Engineers, London, 1989), p. 175.

Rajbenbach, H.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, J.-P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals.” Opt. Lett. 13, 327 (1988).
[CrossRef] [PubMed]

Ph. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Refregier, Ph.

Ph. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Rytz, D.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

D. Rytz, B. A. Wechsler, C. C. Nelson, K. W. Kirby, J. Cryst. Growth 99, 864 (1990).
[CrossRef]

Sochava, S. L.

S. I. Stepanov, S. L. Sochava, “Effective energy transfer in a two-wave interaction in Bi12TiO20,” Sov. Phys. Tech. Phys. 32, 1054 (1987).

Solymar, L.

L. B. Au, L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554 (1990).
[CrossRef]

Ph. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Stepanov, S.

S. Stepanov, M. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292 (1985).
[CrossRef]

Stepanov, S. I.

S. I. Stepanov, S. L. Sochava, “Effective energy transfer in a two-wave interaction in Bi12TiO20,” Sov. Phys. Tech. Phys. 32, 1054 (1987).

Swinburne, G. A.

G. A. Swinburne, T. J. Hall, A. K. Powell, “Large modulation effects in photorefractive crystals,” IEE Proceedings of the International Conference on Holographic Systems, Components and Applications (Institution of Electrical Engineers, London, 1989), p. 175.

Vachss, F.

Vieux, V.

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

Wechsler, B. A.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

D. Rytz, B. A. Wechsler, C. C. Nelson, K. W. Kirby, J. Cryst. Growth 99, 864 (1990).
[CrossRef]

Wilde, J. P.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

J. Appl. Phys. (3)

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

Ph. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

J. Cryst. Growth (1)

D. Rytz, B. A. Wechsler, C. C. Nelson, K. W. Kirby, J. Cryst. Growth 99, 864 (1990).
[CrossRef]

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

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

Opt. Commun. (2)

S. Stepanov, M. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292 (1985).
[CrossRef]

J.-P. Huignard, A. Marrakchi, “Coherent signal beam amplification in two wave mixing experiments with photorefractive Bi12SiO20crystals,” Opt. Commun. 38, 249 (1981).
[CrossRef]

Opt. Lett. (1)

Sov. Phys. Tech. Phys. (1)

S. I. Stepanov, S. L. Sochava, “Effective energy transfer in a two-wave interaction in Bi12TiO20,” Sov. Phys. Tech. Phys. 32, 1054 (1987).

Other (2)

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I (Springer-Verlag, New York, 1988).
[CrossRef]

G. A. Swinburne, T. J. Hall, A. K. Powell, “Large modulation effects in photorefractive crystals,” IEE Proceedings of the International Conference on Holographic Systems, Components and Applications (Institution of Electrical Engineers, London, 1989), p. 175.

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Figures (8)

Fig. 1
Fig. 1

Gain coefficient versus grating spacing for two-wave mixing in BTO without an applied field: λ = 633 nm, α = 1 cm−1 Fitted with Ne = 3 × 1016 cm−3, reff = 5.3 pm/V.

Fig. 2
Fig. 2

Gain coefficient versus grating spacing for two-wave mixing in BTO with a 60-Hz ac square wave applied. Field values are zero to peak. Fitted with Ne = 3 × 1016 cm−3, reff = 5.3 pm/V, LD = 0.43 μm.

Fig. 3
Fig. 3

Two-wave mixing gain as a function of input pump-to-signal beam ratio β. L = 1.37 mm, Λ = 5.5 μm. Bold curves are the results of the numerical model; the thin curve is the standard pump-depletion theory for the 10-kV/cm case.

Fig. 4
Fig. 4

Two-wave mixing gain as a function of input beam ratio for several grating spacings and applied fields. Curves are from analytic theory with no free parameters.

Fig. 5
Fig. 5

Enhancement factor p as a function of grating spacing. Ea = 10 kV/cm, LEa = 6.8 μm. Curve, theory; filled circles, best fit of data.

Fig. 6
Fig. 6

Comparison of functional forms of f(m) for the different models. Values for af and p are best fit for Λ = 5.5-μm data.

Fig. 7
Fig. 7

Time response of the two-beam coupling process for two different beam ratios. Λ = 6.1 μm, total intensity is 100 mW/cm2. Fitted using γ = γ0[1 − exp(−t/τ)], where γ0 is the maximum gain.

Fig. 8
Fig. 8

Comparison of large-signal beam-coupling performance for the cases of sinusoidal and square waves. Λ = 3.5 μm.

Equations (8)

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

Γ = ln ( γ ) / L ,
E sc = i m E D 1 + E D / E q ,
Γ = 2 π n 0 3 r eff i m ( E sc ) λ ( cos θ ) m ,
E a c = i m E D 1 + K 2 L s 2 { 1 + ( K L E a E a ) / [ E D ( 1 + K 2 L D 2 ) ] 1 + ( K 2 L E a L e ) / [ ( 1 + K 2 L D 2 ) ( 1 + K 2 L s 2 ) ] } ,
E sc ( z ) = E a ( { 1 + 2 [ p m ( z ) ] 2 } 1 / 2 1 p m ( z ) ) ,
d A s / d z = ( 1 / 4 ) Γ ( m ) A p , d A p / d z = ( 1 / 4 ) Γ ( m ) A s ,
E sc ( m ) = E ac exp ( m ) a f m [ 1 exp ( a f m ) ] ,
a f = 2.19 E ac ( E a + E D ) m ·

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