Abstract

We present analytic expressions for time-dependent space charge field and two wave mixing gain under the external applied field accompanying the grating translation. The variations of complex space charge field are analyzed in a complex plane, and the explicit expressions for the resonance and optimum frequencies (or moving grating velocities), which maximize the magnitude and imaginary part of space charge field, respectively, are also obtained. In addition, two wave mixing experiment was conducted with a grating translation technique without the external applied field in a BaTiO3 crystal and the transient behaviors of measured gain look like damped harmonic oscillations, showing excellent agreement with the theory for the entire time range.

© 2008 Optical Society of America

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  1. M. Z. Zha, P. Amrhein, and P. Günter, "Measurement of phase shift of photorefractive gratings by a novel method," IEEE Quantum Electron. 26, 788-792 (1990).
    [CrossRef]
  2. K. Sutter and P. Günter, "Photorefractive gratings in the organic crystal 2-cyclooctylamino-5-nitropyridine doped with 7,7,8,8-tetracyanoquinodimethane," J. Opt. Soc. Am. B 7, 2274-2278 (1990).
    [CrossRef]
  3. R. S. Cudney, G. D. Bacher, R. M. Pierce, and J. Feinberg, "Measurement of the photorefractive phase shift," Opt. Lett. 17, 67-69 (1992).
    [CrossRef]
  4. R. Hofmeister, A. Yariv, A. Kewitsch, and S. Yagi, "Simple methods of measuring the net photorefractive phase shift and coupling constant," Opt. Lett. 18, 488-490 (1993).
    [CrossRef]
  5. D. G. Gray, M. G. Moharam, and T. M. Ayres, "Heterodyne technique for the direct measurement of the amplitude and phase of photorefractive space-charge field," J. Opt. Soc. Am. B 11, 470-475 (1994).
    [CrossRef]
  6. C. H. Kwak and S. J. Lee, "Approximate analytic solution of photochromic and photorefractive gratings in photorefractive materials," Opt. Commun. 183, 547-554 (2000).
    [CrossRef]
  7. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals. I. Steady state," Ferroelectrics 22, 949-960 (1979), and idem, ibid22, 961-964 (1979).
  8. Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45-57 (1985).
    [CrossRef]
  9. S. I. Stepanov and M. P. Petrov, in Photorefractive materials and their applications I, P. Günter and J. P. Huignard, eds., (Springer, Berlin, 1988) Chap. 9.
  10. P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484-519 (1989).
    [CrossRef]
  11. C. H. Kwak, S. Y. Park, and E. H. Lee, "Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal," Opt. Commun. 115, 315-322 (1995).
    [CrossRef]
  12. G. C. Valley and M. B. Klein, "Optimal properties of photorefractive materials for optical data processing," Opt. Eng. 22, 704-711 (1983).
  13. C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, and E. H. Lee, "An analytical solution for large modulation effects in photorefractive two-wave couplings," Opt. Commun. 105, 353-358 (1994).
    [CrossRef]
  14. J. P. Huignard and A. Marrakchi, "Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals," Opt. Commun. 38, 249-254 (1981).
    [CrossRef]
  15. I. McMichael and P. Yeh, "Phase shift of photorefractive gratings and phase-conjugate waves," Opt. Lett. 12, 48-50 (1987).
    [CrossRef]
  16. K. H. Kim, E. J. Kim, S. J. Lee, J. H. Lee, C. H. Kwak, and J. E. Kim, "Effects of applied electric field on orientational photorefraction in porphyrin:Zn-doped nematic liquid crystals," Appl. Phys. Lett. 85, 366-368 (2004).
    [CrossRef]
  17. E. J. Kim, H. R. Yang, S. J. Lee, G. Y. Kim, and C. H. Kwak, "Orientational photorefractive holograms in porphyrin:Zn-doped nematic liquid crystals," Opt. Express 16, 17329-17341 (2008).
    [CrossRef]

2008 (1)

2004 (1)

K. H. Kim, E. J. Kim, S. J. Lee, J. H. Lee, C. H. Kwak, and J. E. Kim, "Effects of applied electric field on orientational photorefraction in porphyrin:Zn-doped nematic liquid crystals," Appl. Phys. Lett. 85, 366-368 (2004).
[CrossRef]

2000 (1)

C. H. Kwak and S. J. Lee, "Approximate analytic solution of photochromic and photorefractive gratings in photorefractive materials," Opt. Commun. 183, 547-554 (2000).
[CrossRef]

1995 (1)

C. H. Kwak, S. Y. Park, and E. H. Lee, "Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal," Opt. Commun. 115, 315-322 (1995).
[CrossRef]

1994 (2)

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, and E. H. Lee, "An analytical solution for large modulation effects in photorefractive two-wave couplings," Opt. Commun. 105, 353-358 (1994).
[CrossRef]

D. G. Gray, M. G. Moharam, and T. M. Ayres, "Heterodyne technique for the direct measurement of the amplitude and phase of photorefractive space-charge field," J. Opt. Soc. Am. B 11, 470-475 (1994).
[CrossRef]

1993 (1)

1992 (1)

1990 (2)

K. Sutter and P. Günter, "Photorefractive gratings in the organic crystal 2-cyclooctylamino-5-nitropyridine doped with 7,7,8,8-tetracyanoquinodimethane," J. Opt. Soc. Am. B 7, 2274-2278 (1990).
[CrossRef]

M. Z. Zha, P. Amrhein, and P. Günter, "Measurement of phase shift of photorefractive gratings by a novel method," IEEE Quantum Electron. 26, 788-792 (1990).
[CrossRef]

1989 (1)

P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484-519 (1989).
[CrossRef]

1987 (1)

1985 (1)

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45-57 (1985).
[CrossRef]

1983 (1)

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive materials for optical data processing," Opt. Eng. 22, 704-711 (1983).

1981 (1)

J. P. Huignard and A. Marrakchi, "Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals," Opt. Commun. 38, 249-254 (1981).
[CrossRef]

Amrhein, P.

M. Z. Zha, P. Amrhein, and P. Günter, "Measurement of phase shift of photorefractive gratings by a novel method," IEEE Quantum Electron. 26, 788-792 (1990).
[CrossRef]

Ayres, T. M.

Bacher, G. D.

Cudney, R. S.

Feinberg, J.

Gray, D. G.

Günter, P.

M. Z. Zha, P. Amrhein, and P. Günter, "Measurement of phase shift of photorefractive gratings by a novel method," IEEE Quantum Electron. 26, 788-792 (1990).
[CrossRef]

K. Sutter and P. Günter, "Photorefractive gratings in the organic crystal 2-cyclooctylamino-5-nitropyridine doped with 7,7,8,8-tetracyanoquinodimethane," J. Opt. Soc. Am. B 7, 2274-2278 (1990).
[CrossRef]

Hofmeister, R.

Huignard, J. P.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45-57 (1985).
[CrossRef]

J. P. Huignard and A. Marrakchi, "Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals," Opt. Commun. 38, 249-254 (1981).
[CrossRef]

Jeong, J. S.

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, and E. H. Lee, "An analytical solution for large modulation effects in photorefractive two-wave couplings," Opt. Commun. 105, 353-358 (1994).
[CrossRef]

Kewitsch, A.

Kim, E. J.

E. J. Kim, H. R. Yang, S. J. Lee, G. Y. Kim, and C. H. Kwak, "Orientational photorefractive holograms in porphyrin:Zn-doped nematic liquid crystals," Opt. Express 16, 17329-17341 (2008).
[CrossRef]

K. H. Kim, E. J. Kim, S. J. Lee, J. H. Lee, C. H. Kwak, and J. E. Kim, "Effects of applied electric field on orientational photorefraction in porphyrin:Zn-doped nematic liquid crystals," Appl. Phys. Lett. 85, 366-368 (2004).
[CrossRef]

Kim, G. Y.

Kim, J. E.

K. H. Kim, E. J. Kim, S. J. Lee, J. H. Lee, C. H. Kwak, and J. E. Kim, "Effects of applied electric field on orientational photorefraction in porphyrin:Zn-doped nematic liquid crystals," Appl. Phys. Lett. 85, 366-368 (2004).
[CrossRef]

Kim, K. H.

K. H. Kim, E. J. Kim, S. J. Lee, J. H. Lee, C. H. Kwak, and J. E. Kim, "Effects of applied electric field on orientational photorefraction in porphyrin:Zn-doped nematic liquid crystals," Appl. Phys. Lett. 85, 366-368 (2004).
[CrossRef]

Klein, M. B.

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive materials for optical data processing," Opt. Eng. 22, 704-711 (1983).

Kwak, C. H.

E. J. Kim, H. R. Yang, S. J. Lee, G. Y. Kim, and C. H. Kwak, "Orientational photorefractive holograms in porphyrin:Zn-doped nematic liquid crystals," Opt. Express 16, 17329-17341 (2008).
[CrossRef]

K. H. Kim, E. J. Kim, S. J. Lee, J. H. Lee, C. H. Kwak, and J. E. Kim, "Effects of applied electric field on orientational photorefraction in porphyrin:Zn-doped nematic liquid crystals," Appl. Phys. Lett. 85, 366-368 (2004).
[CrossRef]

C. H. Kwak and S. J. Lee, "Approximate analytic solution of photochromic and photorefractive gratings in photorefractive materials," Opt. Commun. 183, 547-554 (2000).
[CrossRef]

C. H. Kwak, S. Y. Park, and E. H. Lee, "Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal," Opt. Commun. 115, 315-322 (1995).
[CrossRef]

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, and E. H. Lee, "An analytical solution for large modulation effects in photorefractive two-wave couplings," Opt. Commun. 105, 353-358 (1994).
[CrossRef]

Lee, E. H.

C. H. Kwak, S. Y. Park, and E. H. Lee, "Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal," Opt. Commun. 115, 315-322 (1995).
[CrossRef]

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, and E. H. Lee, "An analytical solution for large modulation effects in photorefractive two-wave couplings," Opt. Commun. 105, 353-358 (1994).
[CrossRef]

Lee, J. H.

K. H. Kim, E. J. Kim, S. J. Lee, J. H. Lee, C. H. Kwak, and J. E. Kim, "Effects of applied electric field on orientational photorefraction in porphyrin:Zn-doped nematic liquid crystals," Appl. Phys. Lett. 85, 366-368 (2004).
[CrossRef]

Lee, S. J.

E. J. Kim, H. R. Yang, S. J. Lee, G. Y. Kim, and C. H. Kwak, "Orientational photorefractive holograms in porphyrin:Zn-doped nematic liquid crystals," Opt. Express 16, 17329-17341 (2008).
[CrossRef]

K. H. Kim, E. J. Kim, S. J. Lee, J. H. Lee, C. H. Kwak, and J. E. Kim, "Effects of applied electric field on orientational photorefraction in porphyrin:Zn-doped nematic liquid crystals," Appl. Phys. Lett. 85, 366-368 (2004).
[CrossRef]

C. H. Kwak and S. J. Lee, "Approximate analytic solution of photochromic and photorefractive gratings in photorefractive materials," Opt. Commun. 183, 547-554 (2000).
[CrossRef]

Marrakchi, A.

J. P. Huignard and A. Marrakchi, "Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals," Opt. Commun. 38, 249-254 (1981).
[CrossRef]

McMichael, I.

Moharam, M. G.

Park, S. Y.

C. H. Kwak, S. Y. Park, and E. H. Lee, "Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal," Opt. Commun. 115, 315-322 (1995).
[CrossRef]

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, and E. H. Lee, "An analytical solution for large modulation effects in photorefractive two-wave couplings," Opt. Commun. 105, 353-358 (1994).
[CrossRef]

Pierce, R. M.

Rajbenbach, H.

Ph. Refregier, L. Solymar, H. Rajbenbach, and 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, and J. P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45-57 (1985).
[CrossRef]

Solymar, L.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45-57 (1985).
[CrossRef]

Suh, H. H.

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, and E. H. Lee, "An analytical solution for large modulation effects in photorefractive two-wave couplings," Opt. Commun. 105, 353-358 (1994).
[CrossRef]

Sutter, K.

Valley, G. C.

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive materials for optical data processing," Opt. Eng. 22, 704-711 (1983).

Yagi, S.

Yang, H. R.

Yariv, A.

Yeh, P.

Zha, M. Z.

M. Z. Zha, P. Amrhein, and P. Günter, "Measurement of phase shift of photorefractive gratings by a novel method," IEEE Quantum Electron. 26, 788-792 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

K. H. Kim, E. J. Kim, S. J. Lee, J. H. Lee, C. H. Kwak, and J. E. Kim, "Effects of applied electric field on orientational photorefraction in porphyrin:Zn-doped nematic liquid crystals," Appl. Phys. Lett. 85, 366-368 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484-519 (1989).
[CrossRef]

IEEE Quantum Electron. (1)

M. Z. Zha, P. Amrhein, and P. Günter, "Measurement of phase shift of photorefractive gratings by a novel method," IEEE Quantum Electron. 26, 788-792 (1990).
[CrossRef]

J. Appl. Phys. (1)

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45-57 (1985).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (4)

C. H. Kwak and S. J. Lee, "Approximate analytic solution of photochromic and photorefractive gratings in photorefractive materials," Opt. Commun. 183, 547-554 (2000).
[CrossRef]

C. H. Kwak, S. Y. Park, and E. H. Lee, "Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal," Opt. Commun. 115, 315-322 (1995).
[CrossRef]

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, and E. H. Lee, "An analytical solution for large modulation effects in photorefractive two-wave couplings," Opt. Commun. 105, 353-358 (1994).
[CrossRef]

J. P. Huignard and A. Marrakchi, "Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals," Opt. Commun. 38, 249-254 (1981).
[CrossRef]

Opt. Eng. (1)

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive materials for optical data processing," Opt. Eng. 22, 704-711 (1983).

Opt. Express (1)

Opt. Lett. (3)

Other (2)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals. I. Steady state," Ferroelectrics 22, 949-960 (1979), and idem, ibid22, 961-964 (1979).

S. I. Stepanov and M. P. Petrov, in Photorefractive materials and their applications I, P. Günter and J. P. Huignard, eds., (Springer, Berlin, 1988) Chap. 9.

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