Abstract

It is shown that a subharmonic grating may have two different phase relationships relative to the fundamental grating, leading to the appearance of domains. The subharmonic beam is generated in a Bi12GiO20 crystal illuminated by two beams in the presence of an applied ac square-wave voltage. The domain structure and the relative phases of the gratings contained in them have been observed with the aid of an interferometric technique.

© 1993 Optical Society of America

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    [CrossRef]
  2. J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
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  4. H. Rajbenbach, J. P. Huignard, Ph. Refregier, Opt. Lett. 9, 558 (1984).
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  5. B. Mainguet, F. Le Guiner, G. Picoli, Opt. Lett. 15, 938 (1990).
    [CrossRef] [PubMed]
  6. S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
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  7. S. L. Sochava, S. I. Stepanov, M. P. Petrov, Sov. Tech. Phys. Lett. 13, 274 (1987).
  8. S. I. Stepanov, S. L. Sochava, Sov. Phys. Tech. Phys. 32, 1054 (1987).
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    [CrossRef] [PubMed]
  10. A. Grunnet-Jepsen, C. H. Kwak, I. Richter, L. Solymar, “Fundamental space-charge fields for applied alternating electric fields in photorefractive materials” J. Opt. Soc. Am. B (to be published).
  11. X. Gan, S. Ye, Y. Sun, Opt. Commun. 66, 155 (1988).
    [CrossRef]
  12. A. P. Gosh, D. Just, R. R. Dube, Opt. Commun. 72, 109 (1989).
    [CrossRef]
  13. S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5660 (1988).
    [CrossRef]
  14. J. Takacs, L. Solymar, Opt. Lett. 17, 247 (1992).
    [CrossRef] [PubMed]
  15. C. H. Kwak, M. Shamonin, J. Takacs, L. Solymar, Appl. Phys. Lett. 62, 328 (1993).
    [CrossRef]
  16. L. B. Au, L. Solymar, K. H. Ringhofer, in Technical Digest of Topical Meeting on Photorefractive Materials, Effects and Devices II (Société Française d'Optique, Aussois, France, 1990), paper B41.
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    [CrossRef]
  18. B. I. Sturman, K. Mann, K. H. Ringhofer, Opt. Lett. 17, 1629 (1992).
    [CrossRef]
  19. A. Grunnet-Jepsen, I. Richter, M. Shamonin, L. Solymar, “Subharmonic instabilities in photorefractive crystals for an applied alternating electric field: theoretical analysis,” J. Opt. Soc. Am. B (to be published).
  20. N. B. Baranova, I. V. Goosev, V. A. Krivoschekov, B. Ya Zel'dovich, Mol. Cryst. Liq. Cryst 210, 155 (1992).
    [CrossRef]

1993

C. H. Kwak, M. Shamonin, J. Takacs, L. Solymar, Appl. Phys. Lett. 62, 328 (1993).
[CrossRef]

1992

1990

1989

A. P. Gosh, D. Just, R. R. Dube, Opt. Commun. 72, 109 (1989).
[CrossRef]

1988

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5660 (1988).
[CrossRef]

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

1987

S. L. Sochava, S. I. Stepanov, M. P. Petrov, Sov. Tech. Phys. Lett. 13, 274 (1987).

S. I. Stepanov, S. L. Sochava, Sov. Phys. Tech. Phys. 32, 1054 (1987).

J. Kumar, G. Albanese, W. H. Steier, M. Ziari, Opt. Lett. 12, 120 (1987).
[CrossRef] [PubMed]

1985

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

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

1984

1981

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Albanese, G.

Au, L. B.

L. B. Au, L. Solymar, K. H. Ringhofer, in Technical Digest of Topical Meeting on Photorefractive Materials, Effects and Devices II (Société Française d'Optique, Aussois, France, 1990), paper B41.

Baranova, N. B.

N. B. Baranova, I. V. Goosev, V. A. Krivoschekov, B. Ya Zel'dovich, Mol. Cryst. Liq. Cryst 210, 155 (1992).
[CrossRef]

Bledowski, A.

Dube, R. R.

A. P. Gosh, D. Just, R. R. Dube, Opt. Commun. 72, 109 (1989).
[CrossRef]

Ducollet, H.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5660 (1988).
[CrossRef]

Gan, X.

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

Goosev, I. V.

N. B. Baranova, I. V. Goosev, V. A. Krivoschekov, B. Ya Zel'dovich, Mol. Cryst. Liq. Cryst 210, 155 (1992).
[CrossRef]

Gosh, A. P.

A. P. Gosh, D. Just, R. R. Dube, Opt. Commun. 72, 109 (1989).
[CrossRef]

Grunnet-Jepsen, A.

A. Grunnet-Jepsen, C. H. Kwak, I. Richter, L. Solymar, “Fundamental space-charge fields for applied alternating electric fields in photorefractive materials” J. Opt. Soc. Am. B (to be published).

A. Grunnet-Jepsen, I. Richter, M. Shamonin, L. Solymar, “Subharmonic instabilities in photorefractive crystals for an applied alternating electric field: theoretical analysis,” J. Opt. Soc. Am. B (to be published).

Herriau, J. P.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5660 (1988).
[CrossRef]

Huignard, J. P.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5660 (1988).
[CrossRef]

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

D. Rak, I. Ledoux, J. P. Huignard, Opt. Commun. 49, 302 (1984).
[CrossRef]

H. Rajbenbach, J. P. Huignard, Ph. Refregier, Opt. Lett. 9, 558 (1984).
[CrossRef] [PubMed]

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Imbert, B.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5660 (1988).
[CrossRef]

Just, D.

A. P. Gosh, D. Just, R. R. Dube, Opt. Commun. 72, 109 (1989).
[CrossRef]

Krivoschekov, V. A.

N. B. Baranova, I. V. Goosev, V. A. Krivoschekov, B. Ya Zel'dovich, Mol. Cryst. Liq. Cryst 210, 155 (1992).
[CrossRef]

Kumar, J.

Kwak, C. H.

C. H. Kwak, M. Shamonin, J. Takacs, L. Solymar, Appl. Phys. Lett. 62, 328 (1993).
[CrossRef]

A. Grunnet-Jepsen, C. H. Kwak, I. Richter, L. Solymar, “Fundamental space-charge fields for applied alternating electric fields in photorefractive materials” J. Opt. Soc. Am. B (to be published).

Le Guiner, F.

Ledoux, I.

D. Rak, I. Ledoux, J. P. Huignard, Opt. Commun. 49, 302 (1984).
[CrossRef]

Mainguet, B.

Mallick, S.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5660 (1988).
[CrossRef]

Mann, K.

Marrakchi, A.

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Otten, J.

Petrov, M. P.

S. L. Sochava, S. I. Stepanov, M. P. Petrov, Sov. Tech. Phys. Lett. 13, 274 (1987).

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

Picoli, G.

Rajbenbach, H.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

H. Rajbenbach, J. P. Huignard, Ph. Refregier, Opt. Lett. 9, 558 (1984).
[CrossRef] [PubMed]

Rak, D.

D. Rak, I. Ledoux, J. P. Huignard, Opt. Commun. 49, 302 (1984).
[CrossRef]

Refregier, Ph.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

H. Rajbenbach, J. P. Huignard, Ph. Refregier, Opt. Lett. 9, 558 (1984).
[CrossRef] [PubMed]

Richter, I.

A. Grunnet-Jepsen, C. H. Kwak, I. Richter, L. Solymar, “Fundamental space-charge fields for applied alternating electric fields in photorefractive materials” J. Opt. Soc. Am. B (to be published).

A. Grunnet-Jepsen, I. Richter, M. Shamonin, L. Solymar, “Subharmonic instabilities in photorefractive crystals for an applied alternating electric field: theoretical analysis,” J. Opt. Soc. Am. B (to be published).

Ringhofer, K. H.

B. I. Sturman, K. Mann, K. H. Ringhofer, Opt. Lett. 17, 1629 (1992).
[CrossRef]

B. Sturman, A. Bledowski, J. Otten, K. H. Ringhofer, J. Opt. Soc. Am. B 9, 672 (1992).
[CrossRef]

L. B. Au, L. Solymar, K. H. Ringhofer, in Technical Digest of Topical Meeting on Photorefractive Materials, Effects and Devices II (Société Française d'Optique, Aussois, France, 1990), paper B41.

Shamonin, M.

C. H. Kwak, M. Shamonin, J. Takacs, L. Solymar, Appl. Phys. Lett. 62, 328 (1993).
[CrossRef]

A. Grunnet-Jepsen, I. Richter, M. Shamonin, L. Solymar, “Subharmonic instabilities in photorefractive crystals for an applied alternating electric field: theoretical analysis,” J. Opt. Soc. Am. B (to be published).

Sochava, S. L.

S. I. Stepanov, S. L. Sochava, Sov. Phys. Tech. Phys. 32, 1054 (1987).

S. L. Sochava, S. I. Stepanov, M. P. Petrov, Sov. Tech. Phys. Lett. 13, 274 (1987).

Solymar, L.

C. H. Kwak, M. Shamonin, J. Takacs, L. Solymar, Appl. Phys. Lett. 62, 328 (1993).
[CrossRef]

J. Takacs, L. Solymar, Opt. Lett. 17, 247 (1992).
[CrossRef] [PubMed]

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

A. Grunnet-Jepsen, C. H. Kwak, I. Richter, L. Solymar, “Fundamental space-charge fields for applied alternating electric fields in photorefractive materials” J. Opt. Soc. Am. B (to be published).

L. B. Au, L. Solymar, K. H. Ringhofer, in Technical Digest of Topical Meeting on Photorefractive Materials, Effects and Devices II (Société Française d'Optique, Aussois, France, 1990), paper B41.

A. Grunnet-Jepsen, I. Richter, M. Shamonin, L. Solymar, “Subharmonic instabilities in photorefractive crystals for an applied alternating electric field: theoretical analysis,” J. Opt. Soc. Am. B (to be published).

Steier, W. H.

Stepanov, S. I.

S. I. Stepanov, S. L. Sochava, Sov. Phys. Tech. Phys. 32, 1054 (1987).

S. L. Sochava, S. I. Stepanov, M. P. Petrov, Sov. Tech. Phys. Lett. 13, 274 (1987).

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

Sturman, B.

Sturman, B. I.

Sun, Y.

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

Takacs, J.

C. H. Kwak, M. Shamonin, J. Takacs, L. Solymar, Appl. Phys. Lett. 62, 328 (1993).
[CrossRef]

J. Takacs, L. Solymar, Opt. Lett. 17, 247 (1992).
[CrossRef] [PubMed]

Ye, S.

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

Zel'dovich, B. Ya

N. B. Baranova, I. V. Goosev, V. A. Krivoschekov, B. Ya Zel'dovich, Mol. Cryst. Liq. Cryst 210, 155 (1992).
[CrossRef]

Ziari, M.

Appl. Phys. Lett.

C. H. Kwak, M. Shamonin, J. Takacs, L. Solymar, Appl. Phys. Lett. 62, 328 (1993).
[CrossRef]

J. Appl. Phys.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5660 (1988).
[CrossRef]

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

J. Opt. Soc. Am. B

Mol. Cryst. Liq. Cryst

N. B. Baranova, I. V. Goosev, V. A. Krivoschekov, B. Ya Zel'dovich, Mol. Cryst. Liq. Cryst 210, 155 (1992).
[CrossRef]

Opt. Commun.

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

A. P. Gosh, D. Just, R. R. Dube, Opt. Commun. 72, 109 (1989).
[CrossRef]

D. Rak, I. Ledoux, J. P. Huignard, Opt. Commun. 49, 302 (1984).
[CrossRef]

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

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

Opt. Lett.

Sov. Phys. Tech. Phys.

S. I. Stepanov, S. L. Sochava, Sov. Phys. Tech. Phys. 32, 1054 (1987).

Sov. Tech. Phys. Lett.

S. L. Sochava, S. I. Stepanov, M. P. Petrov, Sov. Tech. Phys. Lett. 13, 274 (1987).

Other

A. Grunnet-Jepsen, C. H. Kwak, I. Richter, L. Solymar, “Fundamental space-charge fields for applied alternating electric fields in photorefractive materials” J. Opt. Soc. Am. B (to be published).

A. Grunnet-Jepsen, I. Richter, M. Shamonin, L. Solymar, “Subharmonic instabilities in photorefractive crystals for an applied alternating electric field: theoretical analysis,” J. Opt. Soc. Am. B (to be published).

L. B. Au, L. Solymar, K. H. Ringhofer, in Technical Digest of Topical Meeting on Photorefractive Materials, Effects and Devices II (Société Française d'Optique, Aussois, France, 1990), paper B41.

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Figures (4)

Fig. 1
Fig. 1

(a) Subharmonic instability will give rise to a grating with wave vector K/2 in addition to the fundamental grating of wave vector K. (b) There exist two degenerate subharmonic states that differ only in that they are shifted a half period with respect to a fixed coordinate system. (c) Where two different subharmonic states meet there exists a region of competition that constitutes a domain wall.

Fig. 2
Fig. 2

Experimental arrangement for generating spatial subharmonic instability in a photorefractive Bi12GeO20 (BGO) crystal and for the observation of phase through interference with a reference plane wave. M's, mirrors; BS's, beam splitters.

Fig. 3
Fig. 3

Photograph of screen A showing the subharmonic beam (middle) and the two pump beams. The applied ac square-wave field has an amplitude of 6.67 kV/cm and a frequency of 144 Hz.

Fig. 4
Fig. 4

Intensity profile measured by a CCD camera on screen B. The measurement is taken along the straight (dashed) line shown in the inset, which illustrates schematically the interference between the subharmonic beam and a plane reference wave. The 180° shift of the interference pattern as it crosses a domain wall is evident.

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