Abstract

The influence of beam coupling on photorefractive parametric oscillation generated in a Bi12SiO20 crystal is investigated experimentally by comparing two configurations with and without the presence of beam coupling. It is shown that beam coupling has a great influence; for example, the transversal split of the K/2 subharmonic grating is seen only in the beam-coupling geometry. A case that resembles K/4 subharmonic generation can, however, still be found in the absence of beam coupling.

© 1998 Optical Society of America

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  1. S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J. P. Huignard, “Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium,” J. Appl. Phys. 63, 5660–5663 (1988).
    [CrossRef]
  2. B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves in photorefractive crystals and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
    [CrossRef]
  3. See, for example, 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); Ph. Réfrégier, 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]
  4. H. C. Pedersen and P. M. Johansen, “Parametric oscillation in photorefractive media,” J. Opt. Soc. Am. B 12, 1065–1073 (1995).
    [CrossRef]
  5. J. Takacs and L. Solymar, “Observation of split subharmonics in a Bi12SiO20 crystal” (personal communication, 1991).
  6. H. C. Pedersen and P. M. Johansen, “Observation of angularly tilted subharmonic gratings in photorefractive bismuth silicon oxide,” Opt. Lett. 19, 1418–1420 (1994).
    [CrossRef] [PubMed]
  7. H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal parametric oscillation in photorefractive media,” Phys. Rev. Lett. 77, 3106–3109 (1996).
    [CrossRef] [PubMed]
  8. H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal photorefractive parametric oscillation: theory and experiment,” J. Opt. Soc. Am. B 14, 1418–1427 (1997).
    [CrossRef]
  9. C. H. Kwak, M. Shamonin, J. Takacs, and L. Solymar, “Spatial subharmonics in photorefractive Bi12SiO20 crystal with a square wave applied field,” Appl. Phys. Lett. 62, 328–330 (1993).
    [CrossRef]
  10. T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
    [CrossRef] [PubMed]
  11. L. B. Au, L. Solymar, and K. H. Ringhofer, “Subharmonics in BSO,” in Technical Digest on Photorefractive Materials, Effects and Devices II (Société Francais d’Optique, Aussois, France, 1990), pp. 87–91.
  12. O. P. Nestiorkin, “Instability of spatial subharmonics under hologram recording in a photorefractive crystal,” Opt. Commun. 81, 315–320 (1991).
    [CrossRef]
  13. B. I. Sturman, A. Bledowski, J. Otten, and K. H. Ringhofer, “Spatial subharmonics in photorefractive crystals,” J. Opt. Soc. Am. B 9, 672–681 (1992).
    [CrossRef]
  14. D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–388 (1990).
    [CrossRef]
  15. D. J. Webb, L. B. Au, D. C. Jones, and L. Solymar, “Onset of subharmonics generated by forward interactions in Bi12SiO20,” Appl. Phys. Lett. 57, 1602–1604 (1990).
    [CrossRef]
  16. J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
    [CrossRef]
  17. H. C. Pedersen, P. M. Johansen, and D. J. Webb, “Photorefractive subharmonics—a beam coupling effect?” J. Opt. Soc. Am. B 15, 1528–1532 (1998).
    [CrossRef]
  18. B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072 (1997).
    [CrossRef]
  19. E. V. Podivilov, H. C. Pedersen, P. M. Johansen, and B. I. Sturman, “Transversal parametric oscillation and it’s external stability in photorefractive sillenite crystals,” Phys. Rev. E 57, 6112–6126 (1998).
    [CrossRef]
  20. See, for example, A. Marrakchi, R. V. Johnson, and A. R. Tanguay, Jr., “Polarization properties of photorefractive diffraction in electrooptic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321–336 (1986); or P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
    [CrossRef]
  21. T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
    [CrossRef]
  22. T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
    [CrossRef]
  23. P. M. Johansen, “Enhanced four-wave mixing in photore-fractive BSO produced by temporal phase shifts,” J. Phys. D 22, 247–253 (1989).
    [CrossRef]
  24. P. E. Andersen, P. Buchhave, P. M. Petersen, and M. V. Vasnetsov, “Nonlinear combinations of gratings in Bi12SiO20: theory and experiment,” J. Opt. Soc. Am. B 12, 1422–1433 (1995).
    [CrossRef]

1998 (2)

E. V. Podivilov, H. C. Pedersen, P. M. Johansen, and B. I. Sturman, “Transversal parametric oscillation and it’s external stability in photorefractive sillenite crystals,” Phys. Rev. E 57, 6112–6126 (1998).
[CrossRef]

H. C. Pedersen, P. M. Johansen, and D. J. Webb, “Photorefractive subharmonics—a beam coupling effect?” J. Opt. Soc. Am. B 15, 1528–1532 (1998).
[CrossRef]

1997 (2)

H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal photorefractive parametric oscillation: theory and experiment,” J. Opt. Soc. Am. B 14, 1418–1427 (1997).
[CrossRef]

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072 (1997).
[CrossRef]

1996 (2)

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal parametric oscillation in photorefractive media,” Phys. Rev. Lett. 77, 3106–3109 (1996).
[CrossRef] [PubMed]

1995 (3)

1994 (2)

H. C. Pedersen and P. M. Johansen, “Observation of angularly tilted subharmonic gratings in photorefractive bismuth silicon oxide,” Opt. Lett. 19, 1418–1420 (1994).
[CrossRef] [PubMed]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

1993 (2)

C. H. Kwak, M. Shamonin, J. Takacs, and L. Solymar, “Spatial subharmonics in photorefractive Bi12SiO20 crystal with a square wave applied field,” Appl. Phys. Lett. 62, 328–330 (1993).
[CrossRef]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves in photorefractive crystals and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

1992 (2)

B. I. Sturman, A. Bledowski, J. Otten, and K. H. Ringhofer, “Spatial subharmonics in photorefractive crystals,” J. Opt. Soc. Am. B 9, 672–681 (1992).
[CrossRef]

J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
[CrossRef]

1991 (1)

O. P. Nestiorkin, “Instability of spatial subharmonics under hologram recording in a photorefractive crystal,” Opt. Commun. 81, 315–320 (1991).
[CrossRef]

1990 (2)

D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–388 (1990).
[CrossRef]

D. J. Webb, L. B. Au, D. C. Jones, and L. Solymar, “Onset of subharmonics generated by forward interactions in Bi12SiO20,” Appl. Phys. Lett. 57, 1602–1604 (1990).
[CrossRef]

1989 (1)

P. M. Johansen, “Enhanced four-wave mixing in photore-fractive BSO produced by temporal phase shifts,” J. Phys. D 22, 247–253 (1989).
[CrossRef]

1988 (1)

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J. P. Huignard, “Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium,” J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

Aguilar, M.

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072 (1997).
[CrossRef]

Agullo-Lopez, F.

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072 (1997).
[CrossRef]

Andersen, P. E.

Au, L. B.

D. J. Webb, L. B. Au, D. C. Jones, and L. Solymar, “Onset of subharmonics generated by forward interactions in Bi12SiO20,” Appl. Phys. Lett. 57, 1602–1604 (1990).
[CrossRef]

Bledowski, A.

Buchhave, P.

Ducollet, H.

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J. P. Huignard, “Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium,” J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

Herriau, J.-P.

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J. P. Huignard, “Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium,” J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

Huignard, J. P.

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J. P. Huignard, “Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium,” J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

Imbert, B.

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J. P. Huignard, “Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium,” J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

Johansen, P. M.

H. C. Pedersen, P. M. Johansen, and D. J. Webb, “Photorefractive subharmonics—a beam coupling effect?” J. Opt. Soc. Am. B 15, 1528–1532 (1998).
[CrossRef]

E. V. Podivilov, H. C. Pedersen, P. M. Johansen, and B. I. Sturman, “Transversal parametric oscillation and it’s external stability in photorefractive sillenite crystals,” Phys. Rev. E 57, 6112–6126 (1998).
[CrossRef]

H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal photorefractive parametric oscillation: theory and experiment,” J. Opt. Soc. Am. B 14, 1418–1427 (1997).
[CrossRef]

H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal parametric oscillation in photorefractive media,” Phys. Rev. Lett. 77, 3106–3109 (1996).
[CrossRef] [PubMed]

H. C. Pedersen and P. M. Johansen, “Parametric oscillation in photorefractive media,” J. Opt. Soc. Am. B 12, 1065–1073 (1995).
[CrossRef]

H. C. Pedersen and P. M. Johansen, “Observation of angularly tilted subharmonic gratings in photorefractive bismuth silicon oxide,” Opt. Lett. 19, 1418–1420 (1994).
[CrossRef] [PubMed]

P. M. Johansen, “Enhanced four-wave mixing in photore-fractive BSO produced by temporal phase shifts,” J. Phys. D 22, 247–253 (1989).
[CrossRef]

Jones, D. C.

D. J. Webb, L. B. Au, D. C. Jones, and L. Solymar, “Onset of subharmonics generated by forward interactions in Bi12SiO20,” Appl. Phys. Lett. 57, 1602–1604 (1990).
[CrossRef]

Kwak, C. H.

C. H. Kwak, M. Shamonin, J. Takacs, and L. Solymar, “Spatial subharmonics in photorefractive Bi12SiO20 crystal with a square wave applied field,” Appl. Phys. Lett. 62, 328–330 (1993).
[CrossRef]

Mallick, S.

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J. P. Huignard, “Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium,” J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

Mann, M.

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves in photorefractive crystals and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

McClelland, T. E.

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

Nestiorkin, O. P.

O. P. Nestiorkin, “Instability of spatial subharmonics under hologram recording in a photorefractive crystal,” Opt. Commun. 81, 315–320 (1991).
[CrossRef]

Otten, J.

Pedersen, H. C.

Petersen, P. M.

Podivilov, E. V.

E. V. Podivilov, H. C. Pedersen, P. M. Johansen, and B. I. Sturman, “Transversal parametric oscillation and it’s external stability in photorefractive sillenite crystals,” Phys. Rev. E 57, 6112–6126 (1998).
[CrossRef]

Ringhofer, K. H.

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072 (1997).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves in photorefractive crystals and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

B. I. Sturman, A. Bledowski, J. Otten, and K. H. Ringhofer, “Spatial subharmonics in photorefractive crystals,” J. Opt. Soc. Am. B 9, 672–681 (1992).
[CrossRef]

Schaub, M.

J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
[CrossRef]

Shamonin, M.

C. H. Kwak, M. Shamonin, J. Takacs, and L. Solymar, “Spatial subharmonics in photorefractive Bi12SiO20 crystal with a square wave applied field,” Appl. Phys. Lett. 62, 328–330 (1993).
[CrossRef]

Shamonina, E.

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

Solymar, L.

C. H. Kwak, M. Shamonin, J. Takacs, and L. Solymar, “Spatial subharmonics in photorefractive Bi12SiO20 crystal with a square wave applied field,” Appl. Phys. Lett. 62, 328–330 (1993).
[CrossRef]

J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
[CrossRef]

D. J. Webb, L. B. Au, D. C. Jones, and L. Solymar, “Onset of subharmonics generated by forward interactions in Bi12SiO20,” Appl. Phys. Lett. 57, 1602–1604 (1990).
[CrossRef]

D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–388 (1990).
[CrossRef]

Sturman, B. I.

E. V. Podivilov, H. C. Pedersen, P. M. Johansen, and B. I. Sturman, “Transversal parametric oscillation and it’s external stability in photorefractive sillenite crystals,” Phys. Rev. E 57, 6112–6126 (1998).
[CrossRef]

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072 (1997).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves in photorefractive crystals and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

B. I. Sturman, A. Bledowski, J. Otten, and K. H. Ringhofer, “Spatial subharmonics in photorefractive crystals,” J. Opt. Soc. Am. B 9, 672–681 (1992).
[CrossRef]

Takacs, J.

C. H. Kwak, M. Shamonin, J. Takacs, and L. Solymar, “Spatial subharmonics in photorefractive Bi12SiO20 crystal with a square wave applied field,” Appl. Phys. Lett. 62, 328–330 (1993).
[CrossRef]

J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
[CrossRef]

Vasnetsov, M. V.

Webb, D. J.

H. C. Pedersen, P. M. Johansen, and D. J. Webb, “Photorefractive subharmonics—a beam coupling effect?” J. Opt. Soc. Am. B 15, 1528–1532 (1998).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–388 (1990).
[CrossRef]

D. J. Webb, L. B. Au, D. C. Jones, and L. Solymar, “Onset of subharmonics generated by forward interactions in Bi12SiO20,” Appl. Phys. Lett. 57, 1602–1604 (1990).
[CrossRef]

Appl. Phys. Lett. (2)

C. H. Kwak, M. Shamonin, J. Takacs, and L. Solymar, “Spatial subharmonics in photorefractive Bi12SiO20 crystal with a square wave applied field,” Appl. Phys. Lett. 62, 328–330 (1993).
[CrossRef]

D. J. Webb, L. B. Au, D. C. Jones, and L. Solymar, “Onset of subharmonics generated by forward interactions in Bi12SiO20,” Appl. Phys. Lett. 57, 1602–1604 (1990).
[CrossRef]

J. Appl. Phys. (1)

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J. P. Huignard, “Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium,” J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

J. Opt. Soc. Am. B (6)

J. Phys. D (1)

P. M. Johansen, “Enhanced four-wave mixing in photore-fractive BSO produced by temporal phase shifts,” J. Phys. D 22, 247–253 (1989).
[CrossRef]

Opt. Commun. (5)

O. P. Nestiorkin, “Instability of spatial subharmonics under hologram recording in a photorefractive crystal,” Opt. Commun. 81, 315–320 (1991).
[CrossRef]

D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–388 (1990).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (2)

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072 (1997).
[CrossRef]

E. V. Podivilov, H. C. Pedersen, P. M. Johansen, and B. I. Sturman, “Transversal parametric oscillation and it’s external stability in photorefractive sillenite crystals,” Phys. Rev. E 57, 6112–6126 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal parametric oscillation in photorefractive media,” Phys. Rev. Lett. 77, 3106–3109 (1996).
[CrossRef] [PubMed]

Other (4)

L. B. Au, L. Solymar, and K. H. Ringhofer, “Subharmonics in BSO,” in Technical Digest on Photorefractive Materials, Effects and Devices II (Société Francais d’Optique, Aussois, France, 1990), pp. 87–91.

See, for example, 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); Ph. Réfrégier, 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. Takacs and L. Solymar, “Observation of split subharmonics in a Bi12SiO20 crystal” (personal communication, 1991).

See, for example, A. Marrakchi, R. V. Johnson, and A. R. Tanguay, Jr., “Polarization properties of photorefractive diffraction in electrooptic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321–336 (1986); or P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup used for beam-coupling experiments. L1, diode pumped, frequency doubled ND:YAG laser emitting light at λ=532 nm; L2, He–Ne laser emitting light at λ=633 nm; BE, beam expander; BS, beam splitter; ND, neutral-density filter; Σ, electrical switch; PZT, piezo stack; S, screen; and M’s, mirrors. ω is the ND:YAG laser frequency and Ω is a frequency detuning induced by the moving piezo mirror.

Fig. 2
Fig. 2

Diffraction patterns observed at the screen in the beam-coupling geometry. The spot on the left is due to diffraction in the fundamental grating; the one on the right is due to the directly transmitted readout beam. The central part of the latter spot has been damped to avoid overflow of the CCD camera; the broadened pattern around this spot is due to simple scattering in the crystal. The patterns in between are due to PPO. The horizontal and vertical directions follow the x and y axes, respectively, shown in Fig. 1.  

Fig. 3
Fig. 3

Central part of the configuration without beam coupling in which the recording beams have been redirected to impinge the crystal’s upper (001) face.

Fig. 4
Fig. 4

Diffraction patterns in steady state obtained in the geometry in which beam coupling is absent. Here is a normalized detuning parameter given by Ωmax/Ω. The left spot is due to diffraction in the fundamental grating; the right is due to the directly transmitted readout beam.

Fig. 5
Fig. 5

Transient evolution of the diffraction pattern at =0.20.

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