Abstract

A new scheme for spontaneous formation of hexagonal optical patterns in photorefractive crystals with dominant reflection gratings and a single pump wave is proposed and realized experimentally. It is shown theoretically that spontaneous hexagon formation results from random small-angle scattering of the pump wave inside the crystal. The threshold of spontaneous hexagon formation is found.

© 1999 Optical Society of America

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References

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  1. G. Grynberg, Opt. Commun. 66, 321 (1988); J. Pender and L. Hesselink, J. Opt. Soc. Am. B 7, 1361 (1990); R. Macdonald and H. J. Eichler, Opt. Commun. 89, 289 (1992); M. Tamburrini, M. Bonavita, S. Wabnitz, and E. Santamato, Opt. Lett. 18, 855 (1993).
    [CrossRef]
  2. T. Honda, Opt. Lett. 18, 598 (1993); T. Honda and P. Banerjee, Opt. Lett. 21, 779 (1996).
    [CrossRef] [PubMed]
  3. A. V. Mamaev and M. Saffman, Europhys. Lett. 34, 669 (1996).
    [CrossRef]
  4. S. N. Vlasov and E. V. Sheinina, Izv. Vyssh. Ucebn. Zaved. Radiofiz. 26, 20 (1983) [Radiophys. Quantum Electron. 27, 15 (1983)]; G. D’Alessandro and W. J. Firth, Phys. Rev. Lett. 66, 2597 (1991).
    [CrossRef] [PubMed]
  5. B. I. Sturman and A. I. Chernykh, Zh. Eksp. Teor. Fiz. 111, 1611 (1997) [JETP 84, 881 (1997)].
    [CrossRef]
  6. P. M. Lushnikov, P. Lodahl, and M. Saffman, Opt. Lett. 23, 1650 (1998).
    [CrossRef]
  7. B. Sturman and V. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials (Gordon & Breach, New York, 1992).
  8. P. M. Lushnikov, Zh. Eksp. Teor. Fiz. 113, 1122 (1998) [JETP 86, 614 (1998)].
    [CrossRef]

1998

P. M. Lushnikov, P. Lodahl, and M. Saffman, Opt. Lett. 23, 1650 (1998).
[CrossRef]

P. M. Lushnikov, Zh. Eksp. Teor. Fiz. 113, 1122 (1998) [JETP 86, 614 (1998)].
[CrossRef]

1997

B. I. Sturman and A. I. Chernykh, Zh. Eksp. Teor. Fiz. 111, 1611 (1997) [JETP 84, 881 (1997)].
[CrossRef]

1996

A. V. Mamaev and M. Saffman, Europhys. Lett. 34, 669 (1996).
[CrossRef]

1993

1988

G. Grynberg, Opt. Commun. 66, 321 (1988); J. Pender and L. Hesselink, J. Opt. Soc. Am. B 7, 1361 (1990); R. Macdonald and H. J. Eichler, Opt. Commun. 89, 289 (1992); M. Tamburrini, M. Bonavita, S. Wabnitz, and E. Santamato, Opt. Lett. 18, 855 (1993).
[CrossRef]

1983

S. N. Vlasov and E. V. Sheinina, Izv. Vyssh. Ucebn. Zaved. Radiofiz. 26, 20 (1983) [Radiophys. Quantum Electron. 27, 15 (1983)]; G. D’Alessandro and W. J. Firth, Phys. Rev. Lett. 66, 2597 (1991).
[CrossRef] [PubMed]

Chernykh, A. I.

B. I. Sturman and A. I. Chernykh, Zh. Eksp. Teor. Fiz. 111, 1611 (1997) [JETP 84, 881 (1997)].
[CrossRef]

Fridkin, V.

B. Sturman and V. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials (Gordon & Breach, New York, 1992).

Grynberg, G.

G. Grynberg, Opt. Commun. 66, 321 (1988); J. Pender and L. Hesselink, J. Opt. Soc. Am. B 7, 1361 (1990); R. Macdonald and H. J. Eichler, Opt. Commun. 89, 289 (1992); M. Tamburrini, M. Bonavita, S. Wabnitz, and E. Santamato, Opt. Lett. 18, 855 (1993).
[CrossRef]

Honda, T.

Lodahl, P.

Lushnikov, P. M.

P. M. Lushnikov, Zh. Eksp. Teor. Fiz. 113, 1122 (1998) [JETP 86, 614 (1998)].
[CrossRef]

P. M. Lushnikov, P. Lodahl, and M. Saffman, Opt. Lett. 23, 1650 (1998).
[CrossRef]

Mamaev, A. V.

A. V. Mamaev and M. Saffman, Europhys. Lett. 34, 669 (1996).
[CrossRef]

Saffman, M.

P. M. Lushnikov, P. Lodahl, and M. Saffman, Opt. Lett. 23, 1650 (1998).
[CrossRef]

A. V. Mamaev and M. Saffman, Europhys. Lett. 34, 669 (1996).
[CrossRef]

Sheinina, E. V.

S. N. Vlasov and E. V. Sheinina, Izv. Vyssh. Ucebn. Zaved. Radiofiz. 26, 20 (1983) [Radiophys. Quantum Electron. 27, 15 (1983)]; G. D’Alessandro and W. J. Firth, Phys. Rev. Lett. 66, 2597 (1991).
[CrossRef] [PubMed]

Sturman, B.

B. Sturman and V. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials (Gordon & Breach, New York, 1992).

Sturman, B. I.

B. I. Sturman and A. I. Chernykh, Zh. Eksp. Teor. Fiz. 111, 1611 (1997) [JETP 84, 881 (1997)].
[CrossRef]

Vlasov, S. N.

S. N. Vlasov and E. V. Sheinina, Izv. Vyssh. Ucebn. Zaved. Radiofiz. 26, 20 (1983) [Radiophys. Quantum Electron. 27, 15 (1983)]; G. D’Alessandro and W. J. Firth, Phys. Rev. Lett. 66, 2597 (1991).
[CrossRef] [PubMed]

Europhys. Lett.

A. V. Mamaev and M. Saffman, Europhys. Lett. 34, 669 (1996).
[CrossRef]

Izv. Vyssh. Ucebn. Zaved. Radiofiz.

S. N. Vlasov and E. V. Sheinina, Izv. Vyssh. Ucebn. Zaved. Radiofiz. 26, 20 (1983) [Radiophys. Quantum Electron. 27, 15 (1983)]; G. D’Alessandro and W. J. Firth, Phys. Rev. Lett. 66, 2597 (1991).
[CrossRef] [PubMed]

Opt. Commun.

G. Grynberg, Opt. Commun. 66, 321 (1988); J. Pender and L. Hesselink, J. Opt. Soc. Am. B 7, 1361 (1990); R. Macdonald and H. J. Eichler, Opt. Commun. 89, 289 (1992); M. Tamburrini, M. Bonavita, S. Wabnitz, and E. Santamato, Opt. Lett. 18, 855 (1993).
[CrossRef]

Opt. Lett.

Zh. Eksp. Teor. Fiz.

P. M. Lushnikov, Zh. Eksp. Teor. Fiz. 113, 1122 (1998) [JETP 86, 614 (1998)].
[CrossRef]

B. I. Sturman and A. I. Chernykh, Zh. Eksp. Teor. Fiz. 111, 1611 (1997) [JETP 84, 881 (1997)].
[CrossRef]

Other

B. Sturman and V. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials (Gordon & Breach, New York, 1992).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the setup for hexagon formation. Abbreviations are defined in text.

Fig. 2
Fig. 2

Near- and far-field images of generated light.

Fig. 3
Fig. 3

Time dynamics of the generated radiation.

Equations (9)

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

F=F0exp-αz+kexpikrFkz,t,B=F0kexpikrBkz,t,
Er,z,t=exp2in0k0z×kexpikrE2k0,kz,t+c.c.
z+ikd+αFk=iγk1+k2=kE2k0,k1Bk2,z-ikd-αBk=-iγ* exp-αzE2k0,-k*,tdE2k0,kt=-exp-2αzE2k0,k+exp-αzBk*,
Fk0=0, Bkl=Fklexpiϕr+Bkseed,
z+α+ikdFk=2iγexpαzBk2,z-α-ikdBk=-iγ*Bk.
Bkl2=1-CB*-CB±D2C2,
C=2iγr expiϕ+αl2γi-ikd-4αexp2γi-ikd-4αl-1, CB=CBkseed*, D=CB+CB*-12-4CB2.
Bkthres2=116C2 cos4ψ/2, ψ=argCB.
Bkminthresh2=116C2.

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