Abstract

Using the so-called ac field technique, we investigate experimentally the influence of optical beam coupling on the generation of subharmonic gratings in a photorefractive sillenite crystal. By the use of two different recording configurations, we are able to distinguish between effects caused by material nonlinearities and effects caused by optical beam coupling.

© 1998 Optical Society of America

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References

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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. K. H. Ringhofer and L. Solymar, “New gain mechanism for wave amplification in photorefractive materials,” Appl. Phys. Lett. 53, 1039–1040 (1988).
    [CrossRef]
  3. K. H. Ringhofer and L. Solymar, “Three-wave and four-wave forward mixing in photorefractive materials,” Appl. Phys. B 48, 395–400 (1989).
    [CrossRef]
  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.
  5. B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A 55, 55–60 (1992).
    [CrossRef]
  6. 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]
  7. 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]
  8. 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]
  9. B. I. Sturman, T. E. McClelland, D. J. Webb, E. Shamonina, and K. H. Ringhofer, “Investigation of photorefractive sub-harmonics in the absence of wave mixing,” J. Opt. Soc. Am. B 12, 1621–1627 (1995).
    [CrossRef]
  10. D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–388 (1990).
    [CrossRef]
  11. P. Buchhave, S. Lyuksyutov, and M. Vasnetsov, “Relations between spontaneously occurring beams in bismuth silicon oxide with two frequency-detuned pump beams,” Opt. Lett. 20, 2363–2365 (1995).
    [CrossRef] [PubMed]
  12. P. Buchhave, S. Lyuksyutov, M. Vasnetsov, and C. Heyde, “Dynamical spatial structure of spontaneous beams in photorefractive bismuth silicon oxide,” J. Opt. Soc. Am. B 13, 2595–2601 (1996).
    [CrossRef]
  13. J. Takacs and L. Solymar, “Subharmonics in Bi12SiO20 with an applied ac electric field,” Opt. Lett. 17, 247–248 (1992).
    [CrossRef] [PubMed]
  14. C. H. Kwak, S. Shim, and E. H. Lee, “Coupled wave analy-sis of spatial subharmonics in photorefractive Bi12SiO20 crystal,” Electron. Lett. 30, 2063–2064 (1994).
    [CrossRef]
  15. P. M. Johansen, R. S. Hansen, and T. Olsen, “Experimental characteristics of spatial subharmonics in BSO,” Opt. Commun. 115, 308–314 (1995).
    [CrossRef]
  16. 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]
  17. C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instability in photorefractive Bi12SiO20 crystal,” Elec. Lett. 28, 530–531 (1992).
    [CrossRef]
  18. J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
    [CrossRef]
  19. C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instabilities,” Opt. Commun. 96, 278–282 (1993).
    [CrossRef]

1996

1995

1994

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]

C. H. Kwak, S. Shim, and E. H. Lee, “Coupled wave analy-sis of spatial subharmonics in photorefractive Bi12SiO20 crystal,” Electron. Lett. 30, 2063–2064 (1994).
[CrossRef]

1993

1992

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A 55, 55–60 (1992).
[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]

J. Takacs and L. Solymar, “Subharmonics in Bi12SiO20 with an applied ac electric field,” Opt. Lett. 17, 247–248 (1992).
[CrossRef] [PubMed]

C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instability in photorefractive Bi12SiO20 crystal,” Elec. Lett. 28, 530–531 (1992).
[CrossRef]

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

1990

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]

1989

K. H. Ringhofer and L. Solymar, “Three-wave and four-wave forward mixing in photorefractive materials,” Appl. Phys. B 48, 395–400 (1989).
[CrossRef]

1988

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]

K. H. Ringhofer and L. Solymar, “New gain mechanism for wave amplification in photorefractive materials,” Appl. Phys. Lett. 53, 1039–1040 (1988).
[CrossRef]

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.

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A 55, 55–60 (1992).
[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]

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]

Hansen, R. S.

P. M. Johansen, R. S. Hansen, and T. Olsen, “Experimental characteristics of spatial subharmonics in BSO,” Opt. Commun. 115, 308–314 (1995).
[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]

Heyde, C.

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.

P. M. Johansen, R. S. Hansen, and T. Olsen, “Experimental characteristics of spatial subharmonics in BSO,” Opt. Commun. 115, 308–314 (1995).
[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, S. Shim, and E. H. Lee, “Coupled wave analy-sis of spatial subharmonics in photorefractive Bi12SiO20 crystal,” Electron. Lett. 30, 2063–2064 (1994).
[CrossRef]

C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instabilities,” Opt. Commun. 96, 278–282 (1993).
[CrossRef]

C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instability in photorefractive Bi12SiO20 crystal,” Elec. Lett. 28, 530–531 (1992).
[CrossRef]

Lee, E. H.

C. H. Kwak, S. Shim, and E. H. Lee, “Coupled wave analy-sis of spatial subharmonics in photorefractive Bi12SiO20 crystal,” Electron. Lett. 30, 2063–2064 (1994).
[CrossRef]

Lyuksyutov, S.

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.

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, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A 55, 55–60 (1992).
[CrossRef]

McClelland, T. E.

B. I. Sturman, T. E. McClelland, D. J. Webb, E. Shamonina, and K. H. Ringhofer, “Investigation of photorefractive sub-harmonics in the absence of wave mixing,” J. Opt. Soc. Am. B 12, 1621–1627 (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]

Olsen, T.

P. M. Johansen, R. S. Hansen, and T. Olsen, “Experimental characteristics of spatial subharmonics in BSO,” Opt. Commun. 115, 308–314 (1995).
[CrossRef]

Otten, J.

Ringhofer, K. H.

B. I. Sturman, T. E. McClelland, D. J. Webb, E. Shamonina, and K. H. Ringhofer, “Investigation of photorefractive sub-harmonics in the absence of wave mixing,” J. Opt. Soc. Am. B 12, 1621–1627 (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]

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A 55, 55–60 (1992).
[CrossRef]

K. H. Ringhofer and L. Solymar, “Three-wave and four-wave forward mixing in photorefractive materials,” Appl. Phys. B 48, 395–400 (1989).
[CrossRef]

K. H. Ringhofer and L. Solymar, “New gain mechanism for wave amplification in photorefractive materials,” Appl. Phys. Lett. 53, 1039–1040 (1988).
[CrossRef]

Schaub, M.

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

Shamonina, E.

Shim, S.

C. H. Kwak, S. Shim, and E. H. Lee, “Coupled wave analy-sis of spatial subharmonics in photorefractive Bi12SiO20 crystal,” Electron. Lett. 30, 2063–2064 (1994).
[CrossRef]

Solymar, L.

C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instabilities,” Opt. Commun. 96, 278–282 (1993).
[CrossRef]

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

J. Takacs and L. Solymar, “Subharmonics in Bi12SiO20 with an applied ac electric field,” Opt. Lett. 17, 247–248 (1992).
[CrossRef] [PubMed]

C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instability in photorefractive Bi12SiO20 crystal,” Elec. Lett. 28, 530–531 (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]

K. H. Ringhofer and L. Solymar, “Three-wave and four-wave forward mixing in photorefractive materials,” Appl. Phys. B 48, 395–400 (1989).
[CrossRef]

K. H. Ringhofer and L. Solymar, “New gain mechanism for wave amplification in photorefractive materials,” Appl. Phys. Lett. 53, 1039–1040 (1988).
[CrossRef]

Sturman, B. I.

Takacs, J.

C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instabilities,” Opt. Commun. 96, 278–282 (1993).
[CrossRef]

J. Takacs and L. Solymar, “Subharmonics in Bi12SiO20 with an applied ac electric field,” Opt. Lett. 17, 247–248 (1992).
[CrossRef] [PubMed]

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

C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instability in photorefractive Bi12SiO20 crystal,” Elec. Lett. 28, 530–531 (1992).
[CrossRef]

Vasnetsov, M.

Webb, D. J.

B. I. Sturman, T. E. McClelland, D. J. Webb, E. Shamonina, and K. H. Ringhofer, “Investigation of photorefractive sub-harmonics in the absence of wave mixing,” J. Opt. Soc. Am. B 12, 1621–1627 (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. A

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A 55, 55–60 (1992).
[CrossRef]

Appl. Phys. B

K. H. Ringhofer and L. Solymar, “Three-wave and four-wave forward mixing in photorefractive materials,” Appl. Phys. B 48, 395–400 (1989).
[CrossRef]

Appl. Phys. Lett.

K. H. Ringhofer and L. Solymar, “New gain mechanism for wave amplification in photorefractive materials,” Appl. Phys. Lett. 53, 1039–1040 (1988).
[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]

Elec. Lett.

C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instability in photorefractive Bi12SiO20 crystal,” Elec. Lett. 28, 530–531 (1992).
[CrossRef]

Electron. Lett.

C. H. Kwak, S. Shim, and E. H. Lee, “Coupled wave analy-sis of spatial subharmonics in photorefractive Bi12SiO20 crystal,” Electron. Lett. 30, 2063–2064 (1994).
[CrossRef]

J. Appl. Phys.

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

Opt. Commun.

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

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

C. H. Kwak, J. Takacs, and L. Solymar, “Spatial subharmonic instabilities,” Opt. Commun. 96, 278–282 (1993).
[CrossRef]

P. M. Johansen, R. S. Hansen, and T. Olsen, “Experimental characteristics of spatial subharmonics in BSO,” Opt. Commun. 115, 308–314 (1995).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

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]

Other

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.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of subharmonic generation in a photorefractive crystal. V is the voltage applied to the crystal.

Fig. 2
Fig. 2

Experimental setup for the traditional configuration. L1, frequency doubled, diode pumped ND:YAG laser emitting light at 532 nm; L2, He–Ne laser emitting light at 633 nm; BE’s, are beam expanders; BS, beam splitter; λ/2, half-wave plate; M’s mirrors; S, screen.

Fig. 3
Fig. 3

Diffraction patterns obtained at the screen in the traditional configuration. The large spot on the left is due to the directly transmitted read-out beam (zeroth order), the spot on the right is due to diffraction in the fundamental grating with grating vector K (first order), and the light patterns between are due to diffraction in secondary gratings with grating vectors between 0 and K. Note that the contrast has been increased in the upper picture to be able to visualize the weak subharmonic pattern.

Fig. 4
Fig. 4

Threshold values of f and Eac for the different subharmonic gratings. The K/2 and K/4 curves are obtained at m=0.78, whereas the K/3 curve is obtained for m=0.88.

Fig. 5
Fig. 5

Central part of the setup for the new configuration.

Fig. 6
Fig. 6

Diffraction patterns obtained at the screen in the new configuration.

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