Abstract

It is shown that counterpropagation of two light beams in a photorefractive medium can be unstable against spontaneous emission of light waves of the same frequency and polarization traveling at small angles. The mechanism of the instability is based on the buildup of a set of spatial reflection gratings. The threshold thickness and the corresponding emission angle are found. Results of the theory are applied to interpretation of existing experimental data.

© 1995 Optical Society of America

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References

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  1. P. Güunter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1988,1989), Vols. I and II.
    [CrossRef]
  2. V. V. Lemeshko and V. V. Obukhovsky, "Autowaves of photoinduced light scattering," Sov. Tech. Phys. Lett. 11, 573–574 (1985).
  3. T. Honda, "Hexagonal pattern formation due to counterpropagation in KNbO3," Opt. Lett. 18, 598–600 (1993).
    [CrossRef] [PubMed]
  4. G. Grynberg, "Mirrorless four-wave mixing oscillation in atomic vapours," Opt. Commun. 66, 321–324 (1988).
    [CrossRef]
  5. J. Pender and L. Hesselink, "Degenerate conical emission in atomic-sodium vapour," J. Opt. Soc. Am. B 7, 1361–1373 (1990).
    [CrossRef]
  6. W. J. Firth, A. Fitzgerald, and C. Pare, "Transverse instabilities due to counterpropagation in Kerr media," J. Opt. Soc. Am. B 7, 1087–1097 (1990).
    [CrossRef]
  7. G. G. Luther and C. J. McKinstrie, "Transverse modulation instability of collinear waves," J. Opt. Soc. Am. B 7, 1125–1141 (1990).
    [CrossRef]
  8. M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12–30 (1984).
    [CrossRef]
  9. B. Sturman, M. Goulkov, and S. Odoulov, "Polarizationdegenerate parametric light scattering in photorefractive crystals," Appl. Phys. B 56, 193–199 (1993).
    [CrossRef]
  10. B. Sturman and V. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials (Gordon & Breach, New York, 1992).
  11. A. Novikov, V. Obukhovskii, S. Odoulov, and B. Sturman, "Mirrorless coherent oscillation due to six-beam vectorial mixing in photorefractive crystals," Opt. Lett. 13, 1017–1019 (1988).
    [CrossRef] [PubMed]
  12. B. Sturman, S. Odoulov, U. van Olfen, G. Jäkel, R. Schulz, and E. Krätzig, "Physical origin of mirrorloss parametric oscillation in BaTiO3," J. Opt. Soc. Am. B 11, 1700–1707 (1994).
    [CrossRef]
  13. M. Saffman, A. A. Zozulya, and D. Z. Anderson, "Transverse instability of energy-exchanging counterpropagating waves in photorefractive media," J. Opt. Soc. Am. B 11, 1409–1417 (1994).
    [CrossRef]

1994 (2)

1993 (2)

T. Honda, "Hexagonal pattern formation due to counterpropagation in KNbO3," Opt. Lett. 18, 598–600 (1993).
[CrossRef] [PubMed]

B. Sturman, M. Goulkov, and S. Odoulov, "Polarizationdegenerate parametric light scattering in photorefractive crystals," Appl. Phys. B 56, 193–199 (1993).
[CrossRef]

1990 (3)

1988 (2)

1985 (1)

V. V. Lemeshko and V. V. Obukhovsky, "Autowaves of photoinduced light scattering," Sov. Tech. Phys. Lett. 11, 573–574 (1985).

1984 (1)

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Anderson, D. Z.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Firth, W. J.

Fisher, B.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Fitzgerald, A.

Fridkin, V.

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

Goulkov, M.

B. Sturman, M. Goulkov, and S. Odoulov, "Polarizationdegenerate parametric light scattering in photorefractive crystals," Appl. Phys. B 56, 193–199 (1993).
[CrossRef]

Grynberg, G.

G. Grynberg, "Mirrorless four-wave mixing oscillation in atomic vapours," Opt. Commun. 66, 321–324 (1988).
[CrossRef]

Hesselink, L.

Honda, T.

Jäkel, G.

Krätzig, E.

Lemeshko, V. V.

V. V. Lemeshko and V. V. Obukhovsky, "Autowaves of photoinduced light scattering," Sov. Tech. Phys. Lett. 11, 573–574 (1985).

Luther, G. G.

McKinstrie, C. J.

Novikov, A.

Obukhovskii, V.

Obukhovsky, V. V.

V. V. Lemeshko and V. V. Obukhovsky, "Autowaves of photoinduced light scattering," Sov. Tech. Phys. Lett. 11, 573–574 (1985).

Odoulov, S.

Olfen, U. van

Pare, C.

Pender, J.

Saffman, M.

Schulz, R.

Sturman, B.

B. Sturman, S. Odoulov, U. van Olfen, G. Jäkel, R. Schulz, and E. Krätzig, "Physical origin of mirrorloss parametric oscillation in BaTiO3," J. Opt. Soc. Am. B 11, 1700–1707 (1994).
[CrossRef]

B. Sturman, M. Goulkov, and S. Odoulov, "Polarizationdegenerate parametric light scattering in photorefractive crystals," Appl. Phys. B 56, 193–199 (1993).
[CrossRef]

A. Novikov, V. Obukhovskii, S. Odoulov, and B. Sturman, "Mirrorless coherent oscillation due to six-beam vectorial mixing in photorefractive crystals," Opt. Lett. 13, 1017–1019 (1988).
[CrossRef] [PubMed]

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

White, J. O.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Zozulya, A. A.

Appl. Phys. B (1)

B. Sturman, M. Goulkov, and S. Odoulov, "Polarizationdegenerate parametric light scattering in photorefractive crystals," Appl. Phys. B 56, 193–199 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

J. Opt. Soc. Am. B (5)

Opt. Commun. (1)

G. Grynberg, "Mirrorless four-wave mixing oscillation in atomic vapours," Opt. Commun. 66, 321–324 (1988).
[CrossRef]

Opt. Lett. (2)

Sov. Tech. Phys. Lett. (1)

V. V. Lemeshko and V. V. Obukhovsky, "Autowaves of photoinduced light scattering," Sov. Tech. Phys. Lett. 11, 573–574 (1985).

Other (2)

P. Güunter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1988,1989), Vols. I and II.
[CrossRef]

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

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Figures (2)

Fig. 1
Fig. 1

Geometrical schemes for (a) the wave vectors and (b) the grating vectors.

Fig. 2
Fig. 2

Dependence of the threshold thickness on the angular parameter Δ.

Equations (7)

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k γ - k δ = k γ - k δ = k α - k β K f , k δ - k α = k β - k γ K p , k γ - k β = k α - k δ K d .
( d d z + i Δ ) A γ = - i s ( E d A β + E f A δ ) , ( d d z + i Δ ) A γ = - i s ( E p * A β + E f A δ ) , ( d d z - i Δ ) A δ = i s ( E p A α + E f * A γ ) , ( d d z - i Δ ) A δ = i s ( E d * A α + E f * A γ ) .
E f = E p h I 0 - 1 A α A β * , E p = E p h I 0 - 1 ( A δ A α * + A β A γ * ) , E d = E p h I 0 - 1 ( A γ A β * + A α A δ * ) ,
A α , β = I α , β 1 / 2 exp ( i z δ k α , β + i φ α , β ) , A γ , γ = a γ , γ exp ( i z δ k α + i φ α ) , A δ , δ = a δ , δ exp ( i z δ k β + i φ β ) .
( d d z + i Δ ) a γ = - i g m ( a δ + a δ * ) / 2 , ( d d z - i Δ ) a γ * = i g m ( a δ + a δ * ) / 2 , ( d d z + i Δ ) a δ = i g m ( a γ + a γ * ) / 2 , ( d d z + i Δ ) a δ * = - i g m ( a γ + a γ * ) / 2 ,
1 + cos ( Γ + l th ) cosh ( Γ - - l th ) + Δ 2 Γ + Γ - sin ( Γ + l th ) sinh ( Γ - l th ) = 0 ,
l th min π / ( 2 1 / 2 g m ) ,             ϑ th a n 2 ( m r E p h ) 1 / 2 .

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