Abstract

We derive an analytic expression describing the intensity and field frequency dependence of photorefractive gain in two-beam coupling under an alternating square-wave electric field. We determine the frequency and intensity ranges over which the gain is maximum and time independent. Experimental results for Bi12GeO20 crystals are presented.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. I. Stepanov, M. P. Petrov, Opt. Acta 31, 1335 (1984).
    [CrossRef]
  2. J. P. Huignard, G. Roosen, in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986), p. 128.
    [CrossRef]
  3. G. Pauliat, J. P. Herriau, A. Delboulbé, G. Roosen, J. P. Huignard, J. Opt. Soc. Am. B 3, 306 (1986).
    [CrossRef]
  4. A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, Opt. Eng. 24, 124 (1985).
  5. S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
    [CrossRef]
  6. J. Kumar, G. Albanese, W. H. Steier, J. Opt. Soc. Am. B 4, 1079 (1987).
    [CrossRef]
  7. R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
    [CrossRef]
  8. X. Gan, S. Ye, Y. Sun, Opt. Commun. 66, 155 (1988).
    [CrossRef]
  9. C. Besson, J. M. C. Jonathan, A. Villing, G. Roosen, Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 183 (1988).
  10. N. V. Kukhtarev, V. G. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 961 (1979).
    [CrossRef]
  11. F. P. Strohkendl, J. M. C. Jonathan, R. W. Hell-warth, Opt. Lett. 11, 312 (1986).
    [CrossRef] [PubMed]
  12. G. C. Valley, J. Appl. Phys. 59, 3363 (1986).
    [CrossRef]
  13. J. M. C. Jonathan, R. W. Hellwarth, G. Roosen, IEEE J. Quantum Electron. QE-22, 1936 (1986).
    [CrossRef]
  14. G. Pauliat, J. M. C. Jonathan, M. Allain, J. C. Launay, G. Roosen, Opt. Commun. 59, 266 (1986);Opt. Commun. 61, 321 (1987).
    [CrossRef]
  15. P. V. Lenzo, E. G. Spencer, A. A. Ballman, Appl. Opt. 5, 1688 (1966).
    [CrossRef] [PubMed]
  16. G. Pauliat, C. Besson, G. Roosen, IEEE J. Quantum Electron. 25, 1736 (1989).
    [CrossRef]

1989

G. Pauliat, C. Besson, G. Roosen, IEEE J. Quantum Electron. 25, 1736 (1989).
[CrossRef]

1988

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

X. Gan, S. Ye, Y. Sun, Opt. Commun. 66, 155 (1988).
[CrossRef]

C. Besson, J. M. C. Jonathan, A. Villing, G. Roosen, Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 183 (1988).

1987

1986

F. P. Strohkendl, J. M. C. Jonathan, R. W. Hell-warth, Opt. Lett. 11, 312 (1986).
[CrossRef] [PubMed]

G. Pauliat, J. P. Herriau, A. Delboulbé, G. Roosen, J. P. Huignard, J. Opt. Soc. Am. B 3, 306 (1986).
[CrossRef]

G. C. Valley, J. Appl. Phys. 59, 3363 (1986).
[CrossRef]

J. M. C. Jonathan, R. W. Hellwarth, G. Roosen, IEEE J. Quantum Electron. QE-22, 1936 (1986).
[CrossRef]

G. Pauliat, J. M. C. Jonathan, M. Allain, J. C. Launay, G. Roosen, Opt. Commun. 59, 266 (1986);Opt. Commun. 61, 321 (1987).
[CrossRef]

1985

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, Opt. Eng. 24, 124 (1985).

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

1984

S. I. Stepanov, M. P. Petrov, Opt. Acta 31, 1335 (1984).
[CrossRef]

1979

N. V. Kukhtarev, V. G. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

1966

Albanese, G.

Allain, M.

G. Pauliat, J. M. C. Jonathan, M. Allain, J. C. Launay, G. Roosen, Opt. Commun. 59, 266 (1986);Opt. Commun. 61, 321 (1987).
[CrossRef]

Ballman, A. A.

Besson, C.

G. Pauliat, C. Besson, G. Roosen, IEEE J. Quantum Electron. 25, 1736 (1989).
[CrossRef]

C. Besson, J. M. C. Jonathan, A. Villing, G. Roosen, Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 183 (1988).

Bylsma, R. B.

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

Delboulbé, A.

Gan, X.

X. Gan, S. Ye, Y. Sun, Opt. Commun. 66, 155 (1988).
[CrossRef]

Glass, A. M.

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

Hellwarth, R. W.

J. M. C. Jonathan, R. W. Hellwarth, G. Roosen, IEEE J. Quantum Electron. QE-22, 1936 (1986).
[CrossRef]

Hell-warth, R. W.

Herriau, J. P.

Huignard, J. P.

G. Pauliat, J. P. Herriau, A. Delboulbé, G. Roosen, J. P. Huignard, J. Opt. Soc. Am. B 3, 306 (1986).
[CrossRef]

J. P. Huignard, G. Roosen, in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986), p. 128.
[CrossRef]

Jonathan, J. M. C.

C. Besson, J. M. C. Jonathan, A. Villing, G. Roosen, Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 183 (1988).

J. M. C. Jonathan, R. W. Hellwarth, G. Roosen, IEEE J. Quantum Electron. QE-22, 1936 (1986).
[CrossRef]

F. P. Strohkendl, J. M. C. Jonathan, R. W. Hell-warth, Opt. Lett. 11, 312 (1986).
[CrossRef] [PubMed]

G. Pauliat, J. M. C. Jonathan, M. Allain, J. C. Launay, G. Roosen, Opt. Commun. 59, 266 (1986);Opt. Commun. 61, 321 (1987).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. G. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

Kumar, J.

Launay, J. C.

G. Pauliat, J. M. C. Jonathan, M. Allain, J. C. Launay, G. Roosen, Opt. Commun. 59, 266 (1986);Opt. Commun. 61, 321 (1987).
[CrossRef]

Lenzo, P. V.

Markov, V. G.

N. V. Kukhtarev, V. G. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

Marrakchi, A.

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, Opt. Eng. 24, 124 (1985).

Odulov, S. G.

N. V. Kukhtarev, V. G. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

Olson, D. H.

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

Pauliat, G.

G. Pauliat, C. Besson, G. Roosen, IEEE J. Quantum Electron. 25, 1736 (1989).
[CrossRef]

G. Pauliat, J. M. C. Jonathan, M. Allain, J. C. Launay, G. Roosen, Opt. Commun. 59, 266 (1986);Opt. Commun. 61, 321 (1987).
[CrossRef]

G. Pauliat, J. P. Herriau, A. Delboulbé, G. Roosen, J. P. Huignard, J. Opt. Soc. Am. B 3, 306 (1986).
[CrossRef]

Petrov, M. P.

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

S. I. Stepanov, M. P. Petrov, Opt. Acta 31, 1335 (1984).
[CrossRef]

Psaltis, D.

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, Opt. Eng. 24, 124 (1985).

Roosen, G.

G. Pauliat, C. Besson, G. Roosen, IEEE J. Quantum Electron. 25, 1736 (1989).
[CrossRef]

C. Besson, J. M. C. Jonathan, A. Villing, G. Roosen, Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 183 (1988).

J. M. C. Jonathan, R. W. Hellwarth, G. Roosen, IEEE J. Quantum Electron. QE-22, 1936 (1986).
[CrossRef]

G. Pauliat, J. P. Herriau, A. Delboulbé, G. Roosen, J. P. Huignard, J. Opt. Soc. Am. B 3, 306 (1986).
[CrossRef]

G. Pauliat, J. M. C. Jonathan, M. Allain, J. C. Launay, G. Roosen, Opt. Commun. 59, 266 (1986);Opt. Commun. 61, 321 (1987).
[CrossRef]

J. P. Huignard, G. Roosen, in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986), p. 128.
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. G. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

Spencer, E. G.

Steier, W. H.

Stepanov, S. I.

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

S. I. Stepanov, M. P. Petrov, Opt. Acta 31, 1335 (1984).
[CrossRef]

Strohkendl, F. P.

Sun, Y.

X. Gan, S. Ye, Y. Sun, Opt. Commun. 66, 155 (1988).
[CrossRef]

Tanguay, A. R.

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, Opt. Eng. 24, 124 (1985).

Valley, G. C.

G. C. Valley, J. Appl. Phys. 59, 3363 (1986).
[CrossRef]

Villing, A.

C. Besson, J. M. C. Jonathan, A. Villing, G. Roosen, Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 183 (1988).

Vinetskii, V. L.

N. V. Kukhtarev, V. G. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

Ye, S.

X. Gan, S. Ye, Y. Sun, Opt. Commun. 66, 155 (1988).
[CrossRef]

Yu, J.

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, Opt. Eng. 24, 124 (1985).

Appl. Opt.

Electron. Lett.

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

Ferroelectrics

N. V. Kukhtarev, V. G. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

IEEE J. Quantum Electron.

J. M. C. Jonathan, R. W. Hellwarth, G. Roosen, IEEE J. Quantum Electron. QE-22, 1936 (1986).
[CrossRef]

G. Pauliat, C. Besson, G. Roosen, IEEE J. Quantum Electron. 25, 1736 (1989).
[CrossRef]

J. Appl. Phys.

G. C. Valley, J. Appl. Phys. 59, 3363 (1986).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Acta

S. I. Stepanov, M. P. Petrov, Opt. Acta 31, 1335 (1984).
[CrossRef]

Opt. Commun.

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

X. Gan, S. Ye, Y. Sun, Opt. Commun. 66, 155 (1988).
[CrossRef]

G. Pauliat, J. M. C. Jonathan, M. Allain, J. C. Launay, G. Roosen, Opt. Commun. 59, 266 (1986);Opt. Commun. 61, 321 (1987).
[CrossRef]

Opt. Eng.

A. Marrakchi, A. R. Tanguay, J. Yu, D. Psaltis, Opt. Eng. 24, 124 (1985).

Opt. Lett.

Proc. Soc. Photo-Opt. Instrum. Eng.

C. Besson, J. M. C. Jonathan, A. Villing, G. Roosen, Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 183 (1988).

Other

J. P. Huignard, G. Roosen, in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986), p. 128.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Coupling gain versus applied field frequency for an undoped Bi12GeO20 sample with I0 = 200 μW/cm2 [curves (a)] and I0 = 3.6 mW/cm2 [curves (b)]. On the experimental (dashed) curves, the dotted vertical bars show the amplitude of the temporal oscillations of the gain. The points represent the temporal average values; the solid vertical bars with the points are the estimated experimental errors. Two theoretical (solid) curves are plotted for comparison with the theoretical values of Re|1/τ| and Im(1/τ). They correspond to a space-charge field calculated at the beginning of each half-period. The fringe spacing is Λ = 30 μm, and the applied field E0 = ±1.6 kV/cm.

Fig. 2
Fig. 2

Real and imaginary parts of the space-charge field versus the applied field frequency for our Bi12GeO20 sample. The experimental conditions are the same as for curves (b) in Fig. 1.

Fig. 3
Fig. 3

Periodic behavior of transmitted intensity in relative units [(transmitted intensity with pump beam)/(transmitted intensity without pump beam)] for three different applied field frequencies. The upper curves represent the intensity and correspond to the left axis, while the lower curves represent the applied electric field and correspond to the right axis. The experimental conditions are the same as for curves (b) in Fig. 1.

Equations (7)

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

E 1 t = 1 τ ( E 1 E sc ) ,
E 1 st + = 1 1 exp [ T 2 ( 1 τ + 1 τ * ) ] × { E * sc [ 1 exp ( T / 2 τ * ) ] + E sc exp ( T / 2 τ * ) × [ 1 exp ( T / 2 τ ) ] } .
τ ( E 0 ) = τ * ( E 0 ) and E sc ( E 0 ) = E sc * ( E 0 ) ,
E 1 st = E 1 st + * .
E 1 + ( t ) = Im ( E 1 st + ) Re ( E 1 st + ) × 1 + exp ( T 2 τ ) 2 exp ( t τ ) 1 exp ( T 2 τ ) ,
Im [ E 1 + ( t ) ] = Im [ E 1 ( t ) ] = Im ( E 1 st + ) Re ( E 1 st + ) × Im [ 1 + exp ( T 2 τ ) 2 exp ( t τ ) 1 exp ( T 2 τ ) ] .
E 1 + ( t ) = E 1 ( t ) = Im ( E sc / τ ) Re ( 1 / τ ) .

Metrics