Abstract

We report the domain structure of spontaneously occurring beams (subharmonics) in photorefractive bismuth silicon oxide with an applied electric field from 1 to 6 kV/cm and a running grating. The subharmonic beams are generated in a pattern of domains that evolve dynamically as they move through the crystal. We find that the domains move as a whole with a speed approximately equal to that of the primary grating, but in the opposite direction. The domains are separated by narrow boundary regions, where the phase of the subharmonic waves changes by π. The domain motion is consistent with the group velocity for running space-charge waves.

© 1996 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. D. J. Webb and L. Solymar, “Observations of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–388(1990).
    [CrossRef]
  3. J. Takacs and L. Solymar, “Subharmonics in Bi12TiO20 with an applied ac electric field,” Opt. Lett. 17, 247–248(1992).
    [CrossRef] [PubMed]
  4. D. C. Jones, S. F. Lyuksyutov, and L. Solymar, “Competition between subharmonic and signal beams for photorefractive gain in BSO with two pump beams,” Appl. Phys. B 52, 173–175(1991).
    [CrossRef]
  5. K. H. Ringhofer and L. Solymar, “New gain mechanism for wave amplification in photorefractive materials,” Appl. Phys. Lett. 53, 1039–1040(1988).
    [CrossRef]
  6. B. 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. P. Buchhave, S. F. Lyuksyutov, and M. V. Vasnetsov, “Relations between spontaneously occurring beams in bismuth silicon oxide with two frequency-detuned pump beams,” Opt. Lett. 20, 2363–2365(1995).
    [CrossRef] [PubMed]
  9. D. J. Webb, L. B. Au, D. C. Jones, and L. Solymar, “Onset of subharmonics generated by forward wave interactions in Bi12SiO20,” Appl. Phys. Lett. 57, 1602–1604(1990).
    [CrossRef]
  10. Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20/sub> crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57(1985).
    [CrossRef]
  11. A. Grunnet-Jepsen, S. J. Elston, I. Richter, J. Takacs, and L. Solymar, “Subharmonic domains in a bismuth germanate crystal,” Opt. Lett. 18, 2147–2149(1993).
    [CrossRef] [PubMed]
  12. I. Aubrecht, H. C. Ellin, A. Grunnet-Jepsen, and L. Solymar, “Space-charge fields in photorefractive materials enhanced by moving fringes: comparison of electron–hole transport models,” J. Opt. Soc. Am. B 12, 1918–1923(1995).
    [CrossRef]

1995

1993

1992

1991

D. C. Jones, S. F. Lyuksyutov, and L. Solymar, “Competition between subharmonic and signal beams for photorefractive gain in BSO with two pump beams,” Appl. Phys. B 52, 173–175(1991).
[CrossRef]

1990

D. J. Webb and L. Solymar, “Observations 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 wave interactions in Bi12SiO20,” Appl. Phys. Lett. 57, 1602–1604(1990).
[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]

1985

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20/sub> crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57(1985).
[CrossRef]

Au, L. B.

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

Aubrecht, I.

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]

Ellin, H. C.

Elston, S. J.

Grunnet-Jepsen, A.

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]

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20/sub> crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57(1985).
[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]

Jones, D. C.

D. C. Jones, S. F. Lyuksyutov, and L. Solymar, “Competition between subharmonic and signal beams for photorefractive gain in BSO with two pump beams,” Appl. Phys. B 52, 173–175(1991).
[CrossRef]

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

Lyuksyutov, S. F.

P. Buchhave, S. F. Lyuksyutov, and M. V. Vasnetsov, “Relations between spontaneously occurring beams in bismuth silicon oxide with two frequency-detuned pump beams,” Opt. Lett. 20, 2363–2365(1995).
[CrossRef] [PubMed]

D. C. Jones, S. F. Lyuksyutov, and L. Solymar, “Competition between subharmonic and signal beams for photorefractive gain in BSO with two pump beams,” Appl. Phys. B 52, 173–175(1991).
[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.

Otten, J.

Rajbenbach, H.

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20/sub> crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57(1985).
[CrossRef]

Réfrégier, Ph.

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20/sub> crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57(1985).
[CrossRef]

Richter, I.

Ringhofer, K. H.

Solymar, L.

I. Aubrecht, H. C. Ellin, A. Grunnet-Jepsen, and L. Solymar, “Space-charge fields in photorefractive materials enhanced by moving fringes: comparison of electron–hole transport models,” J. Opt. Soc. Am. B 12, 1918–1923(1995).
[CrossRef]

A. Grunnet-Jepsen, S. J. Elston, I. Richter, J. Takacs, and L. Solymar, “Subharmonic domains in a bismuth germanate crystal,” Opt. Lett. 18, 2147–2149(1993).
[CrossRef] [PubMed]

J. Takacs and L. Solymar, “Subharmonics in Bi12TiO20 with an applied ac electric field,” Opt. Lett. 17, 247–248(1992).
[CrossRef] [PubMed]

D. C. Jones, S. F. Lyuksyutov, and L. Solymar, “Competition between subharmonic and signal beams for photorefractive gain in BSO with two pump beams,” Appl. Phys. B 52, 173–175(1991).
[CrossRef]

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

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

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

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20/sub> crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57(1985).
[CrossRef]

Sturman, B.

Sturman, B. I.

Takacs, J.

Vasnetsov, M. V.

Webb, D. J.

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

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

Appl. Phys. B

D. C. Jones, S. F. Lyuksyutov, and L. Solymar, “Competition between subharmonic and signal beams for photorefractive gain in BSO with two pump beams,” Appl. Phys. B 52, 173–175(1991).
[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 wave interactions in Bi12SiO20,” Appl. Phys. Lett. 57, 1602–1604(1990).
[CrossRef]

J. Appl. Phys.

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20/sub> crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57(1985).
[CrossRef]

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, “Observations of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–388(1990).
[CrossRef]

Opt. Lett.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup: Inset: rotating radial holographic grating producing beam splitting and frequency detuning between diffracted beams.

Fig. 2
Fig. 2

Diffraction patterns from BSO crystal in the far field (a) without and (b) with frequency detuning for generation of spontaneous beams with wave vector K/2; (c) with frequency detuning for generation of wave vector K/4 with respect to the primary grating. The applied electric voltage is 6 kV.

Fig. 3
Fig. 3

Oscilloscope traces of interference light pattern existing at the rear surface of the crystal taken for different velocities of the interference fringes Vf (in mm/s): (a) 0.38, (b) 0.49, (c) 0.67.

Fig. 4
Fig. 4

Dependence of the absolute velocities of the interference fringes and the domains on applied voltage. Open circles, domain velocity; filled circles, velocity of optical interference fringes.

Fig. 5
Fig. 5

Domain structure for spontaneous K/2 beam. (a) VfVopt, Ea=4 kV/cm, large domain structure; (b) Vf<Vopt, Ea=4 kV/cm, vertical domain structure; (c) Vf>Vopt, Ea=6 kV/cm, horizontal domain structure. Vopt is the optimal velocity for maximum subharmonic power.

Fig. 6
Fig. 6

Movement of the domains from the ground electrode to the positive electrode. The applied voltage is 4 kV, and Vf>Vopt. All the pictures were taken with time intervals of 1 s from (a) to (c).

Fig. 7
Fig. 7

Domain boundaries revealed by interference. (a) Interference pattern between the spontaneous beam and a coherent plane wave. (b) Inteference between writing beams and the K/2 subharmonic beam. The near field is projected onto the screen. (c) Oscilloscope trace of interference fringes as they move past a detector with an aperture smaller than the fringe period. Two cases of a phase change of π of the subharmonic modulation are visible.

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