Abstract

A theoretical analysis is presented of spontaneous pattern formation in a system consisting of a photorefractive medium and a feedback mirror. A threshold condition for the pattern formation is derived from a new set of coupling equations with the assumption that reflection gratings are dominant. It is shown that the pattern formation can occur with only energy coupling. The direction of the sideband beams is calculated as a function of the mirror position, and the result is compared with that of an experiment with a KNbO3 crystal.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Pender, L. HesselinkJ. Opt. Soc. Am. B 7, 1361 (1990).
    [CrossRef]
  2. A. Petrossian, M. Pinard, A. Maître, J.-Y. Courtois, G. GrynbergEurophys. Lett. 18, 689 (1992).
    [CrossRef]
  3. R. Macdonald, H. J. EichlerOpt. Commun. 89, 289 (1992).
    [CrossRef]
  4. M. Tamburrini, M. Bonavita, S. Wabnitz, E. SantamatoOpt. Lett. 18, 855 (1993).
    [CrossRef] [PubMed]
  5. B. Thüring, R. Neubecker, T. TschudiOpt. Commun. 102, 111 (1993).
    [CrossRef]
  6. J. Glückstad, M. SaffmanOpt. Lett. 20, 551 (1995).
    [CrossRef] [PubMed]
  7. T. HondaOpt. Lett. 18, 598 (1993).
    [CrossRef] [PubMed]
  8. P. P. Banerjee, H.-L. Yu, D. A. Gregory, N. Kukhtarev, H. J. CaulfieldOpt. Lett. 20, 10 (1995).
    [CrossRef] [PubMed]
  9. T. HondaOpt. Lett. 20, 851 (1995).
    [CrossRef] [PubMed]
  10. T. Honda, H. MatsumotoOpt. Lett. 20, 1755 (1995).
    [CrossRef] [PubMed]
  11. N. V. Kukhtarev, T. Kukhtareva, H. J. Caulfield, P. P. Banerjee, H.-L. Yu, L. HesselinkOpt. Eng. 34, 2261 (1995).
    [CrossRef]
  12. M. Saffman, A. A. Zozulya, D. Z. AndersonJ. Opt. Soc. Am. B 11, 1409 (1994).
    [CrossRef]
  13. B. Sturman, A. ChernykhJ. Opt. Soc. Am. B 12, 1384 (1995).
    [CrossRef]
  14. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. VinetskiiFerroelectrics 22, 949 (1979).
    [CrossRef]
  15. M. Cronin-Golomb, B. Fisher, J. O. White, A. YarivIEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  16. K. Ratnam, P. P. BanerjeeOpt. Commun. 107, 522 (1994).
    [CrossRef]

1995 (6)

1994 (2)

1993 (3)

1992 (2)

A. Petrossian, M. Pinard, A. Maître, J.-Y. Courtois, G. GrynbergEurophys. Lett. 18, 689 (1992).
[CrossRef]

R. Macdonald, H. J. EichlerOpt. Commun. 89, 289 (1992).
[CrossRef]

1990 (1)

1984 (1)

M. Cronin-Golomb, B. Fisher, J. O. White, A. YarivIEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. VinetskiiFerroelectrics 22, 949 (1979).
[CrossRef]

Anderson, D. Z.

Banerjee, P. P.

N. V. Kukhtarev, T. Kukhtareva, H. J. Caulfield, P. P. Banerjee, H.-L. Yu, L. HesselinkOpt. Eng. 34, 2261 (1995).
[CrossRef]

P. P. Banerjee, H.-L. Yu, D. A. Gregory, N. Kukhtarev, H. J. CaulfieldOpt. Lett. 20, 10 (1995).
[CrossRef] [PubMed]

K. Ratnam, P. P. BanerjeeOpt. Commun. 107, 522 (1994).
[CrossRef]

Bonavita, M.

Caulfield, H. J.

N. V. Kukhtarev, T. Kukhtareva, H. J. Caulfield, P. P. Banerjee, H.-L. Yu, L. HesselinkOpt. Eng. 34, 2261 (1995).
[CrossRef]

P. P. Banerjee, H.-L. Yu, D. A. Gregory, N. Kukhtarev, H. J. CaulfieldOpt. Lett. 20, 10 (1995).
[CrossRef] [PubMed]

Chernykh, A.

Courtois, J.-Y.

A. Petrossian, M. Pinard, A. Maître, J.-Y. Courtois, G. GrynbergEurophys. Lett. 18, 689 (1992).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fisher, J. O. White, A. YarivIEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Eichler, H. J.

R. Macdonald, H. J. EichlerOpt. Commun. 89, 289 (1992).
[CrossRef]

Fisher, B.

M. Cronin-Golomb, B. Fisher, J. O. White, A. YarivIEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Glückstad, J.

Gregory, D. A.

Grynberg, G.

A. Petrossian, M. Pinard, A. Maître, J.-Y. Courtois, G. GrynbergEurophys. Lett. 18, 689 (1992).
[CrossRef]

Hesselink, L.

N. V. Kukhtarev, T. Kukhtareva, H. J. Caulfield, P. P. Banerjee, H.-L. Yu, L. HesselinkOpt. Eng. 34, 2261 (1995).
[CrossRef]

J. Pender, L. HesselinkJ. Opt. Soc. Am. B 7, 1361 (1990).
[CrossRef]

Honda, T.

Kukhtarev, N.

Kukhtarev, N. V.

N. V. Kukhtarev, T. Kukhtareva, H. J. Caulfield, P. P. Banerjee, H.-L. Yu, L. HesselinkOpt. Eng. 34, 2261 (1995).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. VinetskiiFerroelectrics 22, 949 (1979).
[CrossRef]

Kukhtareva, T.

N. V. Kukhtarev, T. Kukhtareva, H. J. Caulfield, P. P. Banerjee, H.-L. Yu, L. HesselinkOpt. Eng. 34, 2261 (1995).
[CrossRef]

Macdonald, R.

R. Macdonald, H. J. EichlerOpt. Commun. 89, 289 (1992).
[CrossRef]

Maître, A.

A. Petrossian, M. Pinard, A. Maître, J.-Y. Courtois, G. GrynbergEurophys. Lett. 18, 689 (1992).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. VinetskiiFerroelectrics 22, 949 (1979).
[CrossRef]

Matsumoto, H.

Neubecker, R.

B. Thüring, R. Neubecker, T. TschudiOpt. Commun. 102, 111 (1993).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. VinetskiiFerroelectrics 22, 949 (1979).
[CrossRef]

Pender, J.

Petrossian, A.

A. Petrossian, M. Pinard, A. Maître, J.-Y. Courtois, G. GrynbergEurophys. Lett. 18, 689 (1992).
[CrossRef]

Pinard, M.

A. Petrossian, M. Pinard, A. Maître, J.-Y. Courtois, G. GrynbergEurophys. Lett. 18, 689 (1992).
[CrossRef]

Ratnam, K.

K. Ratnam, P. P. BanerjeeOpt. Commun. 107, 522 (1994).
[CrossRef]

Saffman, M.

Santamato, E.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. VinetskiiFerroelectrics 22, 949 (1979).
[CrossRef]

Sturman, B.

Tamburrini, M.

Thüring, B.

B. Thüring, R. Neubecker, T. TschudiOpt. Commun. 102, 111 (1993).
[CrossRef]

Tschudi, T.

B. Thüring, R. Neubecker, T. TschudiOpt. Commun. 102, 111 (1993).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. VinetskiiFerroelectrics 22, 949 (1979).
[CrossRef]

Wabnitz, S.

White, J. O.

M. Cronin-Golomb, B. Fisher, J. O. White, A. YarivIEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fisher, J. O. White, A. YarivIEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Yu, H.-L.

N. V. Kukhtarev, T. Kukhtareva, H. J. Caulfield, P. P. Banerjee, H.-L. Yu, L. HesselinkOpt. Eng. 34, 2261 (1995).
[CrossRef]

P. P. Banerjee, H.-L. Yu, D. A. Gregory, N. Kukhtarev, H. J. CaulfieldOpt. Lett. 20, 10 (1995).
[CrossRef] [PubMed]

Zozulya, A. A.

Europhys. Lett. (1)

A. Petrossian, M. Pinard, A. Maître, J.-Y. Courtois, G. GrynbergEurophys. Lett. 18, 689 (1992).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. VinetskiiFerroelectrics 22, 949 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fisher, J. O. White, A. YarivIEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

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

Opt. Commun. (3)

K. Ratnam, P. P. BanerjeeOpt. Commun. 107, 522 (1994).
[CrossRef]

R. Macdonald, H. J. EichlerOpt. Commun. 89, 289 (1992).
[CrossRef]

B. Thüring, R. Neubecker, T. TschudiOpt. Commun. 102, 111 (1993).
[CrossRef]

Opt. Eng. (1)

N. V. Kukhtarev, T. Kukhtareva, H. J. Caulfield, P. P. Banerjee, H.-L. Yu, L. HesselinkOpt. Eng. 34, 2261 (1995).
[CrossRef]

Opt. Lett. (6)

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

Threshold condition for purely imaginary coupling (γR = 0) and for mirror feedback at the crystal’s back surface (L = 0).

Fig. 2
Fig. 2

Experimental configuration.

Fig. 3
Fig. 3

Angle θ between the carrier and the sideband as a function of the distance L between the crystal and the feedback mirror. Solid curve, theoretical curve; circles, experimental results.

Equations (8)

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

F z i 2 k 0 n 0 2 F = i γ | B | 2 | F | 2 + | B | 2 F ,
B z + i 2 k 0 n 0 2 B = i γ * | F | 2 | F | 2 + | B | 2 B ,
F ( r ) = F 0 ( z ) [ 1 + F + 1 ( z ) exp ( i k r ) + F 1 ( z ) exp ( i k r ) ] ,
B ( r ) = B 0 ( z ) [ 1 + B + 1 ( z ) exp ( i k r ) + B 1 ( z ) exp ( i k r ) ] ,
( / z + i k d ) F + 1 = i A γ ( F + 1 + F 1 * B + 1 B 1 * ) , ( / z i k d ) F 1 * = i A γ * ( F + 1 + F 1 * B + 1 B 1 * ) , ( / z i k d ) B + 1 = i A γ * ( F + 1 + F 1 * B + 1 B 1 * ) , ( / z + i k d ) B 1 * = i A γ ( F + 1 + F 1 * B + 1 B 1 * ) ,
F + 1 ( 0 ) = F 1 * ( 0 ) = 0 ,
B + 1 ( l ) = exp ( 2 i k d n 0 L ) F + 1 ( l ) , B 1 * ( l ) = exp ( 2 i k d n 0 L ) F 1 * ( l ) ,
cos w l cos k d l + ( γ I / 2 w ) sin w l cos k d ( l + 2 n 0 L ) + [ ( γ R + 2 k d ) / 2 w ] sin w l sin k d l ( γ R / 2 w ) sin w l sin k d ( l + 2 n 0 L ) = 0 ,

Metrics