Abstract

We show analytically and numerically that the unusual photorefractive nonlinear response of Sn2P2S6 crystals leads to a variety of new features of coherent optical oscillation. In addition to the explanation of the known peculiarities, new features are predicted.

© 2010 Optical Society of America

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References

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  1. S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, and A. A. Grabar, “Photorefractive beam coupling in tin hypothiodiphosphate in near infrared,” Opt. Lett. 21, 752-754 (1996).
    [CrossRef] [PubMed]
  2. S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, A. A. Grabar, and I. M. Stoika, “Photorefraction in tin hypothiodiphosphate in near infrared,” J. Opt. Soc. Am. B 13, 2352-2360 (1996).
    [CrossRef]
  3. A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, “Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero,” Phys. Rev. Lett. 93, 2436041-2436044 (2004).
    [CrossRef]
  4. A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, in Photorefractive Materials and Their Applications, Vol. 2, P.Günter and J.-P.Huignard, eds. (Springer, 2006).
  5. B. Sturman, P. Mathey, H. R. Jauslin, S. Odoulov, and A. Shumelyuk, “Modeling of the photorefractive nonlinear response in Sn2P2S6 crystals,” J. Opt. Soc. Am. B 24, 1303-1309 (2007).
    [CrossRef]
  6. A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 0238191-0238196 (2005).
    [CrossRef]
  7. M. Cronin-Golomb, B. Fischer, 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]
  8. P.Günter and J.-P.Huignard, eds., Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Appl. Phys. (Springer-Verlag, 1989).
  9. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).
  10. P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” Eur. Phys. J. D 39, 445-451 (2006).
    [CrossRef]
  11. S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665-3667 (1996).
    [CrossRef]
  12. M. Grapinet, P. Mathey, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Frequency degenerate and non-degenerate nonlinear regimes for semi-linear photorefractive oscillator,” Eur. Phys. J. D 41, 363-369 (2007).
    [CrossRef]

2007 (2)

B. Sturman, P. Mathey, H. R. Jauslin, S. Odoulov, and A. Shumelyuk, “Modeling of the photorefractive nonlinear response in Sn2P2S6 crystals,” J. Opt. Soc. Am. B 24, 1303-1309 (2007).
[CrossRef]

M. Grapinet, P. Mathey, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Frequency degenerate and non-degenerate nonlinear regimes for semi-linear photorefractive oscillator,” Eur. Phys. J. D 41, 363-369 (2007).
[CrossRef]

2006 (1)

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” Eur. Phys. J. D 39, 445-451 (2006).
[CrossRef]

2005 (1)

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 0238191-0238196 (2005).
[CrossRef]

2004 (1)

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, “Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero,” Phys. Rev. Lett. 93, 2436041-2436044 (2004).
[CrossRef]

1996 (3)

1984 (1)

M. Cronin-Golomb, B. Fischer, 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]

Brost, G.

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665-3667 (1996).
[CrossRef]

Buse, K.

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, “Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero,” Phys. Rev. Lett. 93, 2436041-2436044 (2004).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, 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]

Fischer, B.

M. Cronin-Golomb, B. Fischer, 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]

Grabar, A. A.

Grapinet, M.

M. Grapinet, P. Mathey, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Frequency degenerate and non-degenerate nonlinear regimes for semi-linear photorefractive oscillator,” Eur. Phys. J. D 41, 363-369 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” Eur. Phys. J. D 39, 445-451 (2006).
[CrossRef]

Grunnet-Jepsen, A.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

Günter, P.

A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, in Photorefractive Materials and Their Applications, Vol. 2, P.Günter and J.-P.Huignard, eds. (Springer, 2006).

Hellwig, U.

Hryhorashchuk, A.

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 0238191-0238196 (2005).
[CrossRef]

Jauslin, H. R.

B. Sturman, P. Mathey, H. R. Jauslin, S. Odoulov, and A. Shumelyuk, “Modeling of the photorefractive nonlinear response in Sn2P2S6 crystals,” J. Opt. Soc. Am. B 24, 1303-1309 (2007).
[CrossRef]

M. Grapinet, P. Mathey, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Frequency degenerate and non-degenerate nonlinear regimes for semi-linear photorefractive oscillator,” Eur. Phys. J. D 41, 363-369 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” Eur. Phys. J. D 39, 445-451 (2006).
[CrossRef]

Jazbinsek, M.

A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, in Photorefractive Materials and Their Applications, Vol. 2, P.Günter and J.-P.Huignard, eds. (Springer, 2006).

Magde, K.

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665-3667 (1996).
[CrossRef]

Mathey, P.

M. Grapinet, P. Mathey, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Frequency degenerate and non-degenerate nonlinear regimes for semi-linear photorefractive oscillator,” Eur. Phys. J. D 41, 363-369 (2007).
[CrossRef]

B. Sturman, P. Mathey, H. R. Jauslin, S. Odoulov, and A. Shumelyuk, “Modeling of the photorefractive nonlinear response in Sn2P2S6 crystals,” J. Opt. Soc. Am. B 24, 1303-1309 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” Eur. Phys. J. D 39, 445-451 (2006).
[CrossRef]

Montemezzani, G.

A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, in Photorefractive Materials and Their Applications, Vol. 2, P.Günter and J.-P.Huignard, eds. (Springer, 2006).

Odoulov, S.

B. Sturman, P. Mathey, H. R. Jauslin, S. Odoulov, and A. Shumelyuk, “Modeling of the photorefractive nonlinear response in Sn2P2S6 crystals,” J. Opt. Soc. Am. B 24, 1303-1309 (2007).
[CrossRef]

M. Grapinet, P. Mathey, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Frequency degenerate and non-degenerate nonlinear regimes for semi-linear photorefractive oscillator,” Eur. Phys. J. D 41, 363-369 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” Eur. Phys. J. D 39, 445-451 (2006).
[CrossRef]

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 0238191-0238196 (2005).
[CrossRef]

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, “Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero,” Phys. Rev. Lett. 93, 2436041-2436044 (2004).
[CrossRef]

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665-3667 (1996).
[CrossRef]

Odoulov, S. G.

Podivilov, E.

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, “Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero,” Phys. Rev. Lett. 93, 2436041-2436044 (2004).
[CrossRef]

Rupp, R. A.

Rytz, D.

M. Grapinet, P. Mathey, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Frequency degenerate and non-degenerate nonlinear regimes for semi-linear photorefractive oscillator,” Eur. Phys. J. D 41, 363-369 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” Eur. Phys. J. D 39, 445-451 (2006).
[CrossRef]

Shcherbin, K.

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, “Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero,” Phys. Rev. Lett. 93, 2436041-2436044 (2004).
[CrossRef]

Shumelyuk, A.

B. Sturman, P. Mathey, H. R. Jauslin, S. Odoulov, and A. Shumelyuk, “Modeling of the photorefractive nonlinear response in Sn2P2S6 crystals,” J. Opt. Soc. Am. B 24, 1303-1309 (2007).
[CrossRef]

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 0238191-0238196 (2005).
[CrossRef]

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, “Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero,” Phys. Rev. Lett. 93, 2436041-2436044 (2004).
[CrossRef]

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665-3667 (1996).
[CrossRef]

Shumelyuk, A. N.

Solymar, L.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

Stoika, I. M.

Sturman, B.

B. Sturman, P. Mathey, H. R. Jauslin, S. Odoulov, and A. Shumelyuk, “Modeling of the photorefractive nonlinear response in Sn2P2S6 crystals,” J. Opt. Soc. Am. B 24, 1303-1309 (2007).
[CrossRef]

M. Grapinet, P. Mathey, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Frequency degenerate and non-degenerate nonlinear regimes for semi-linear photorefractive oscillator,” Eur. Phys. J. D 41, 363-369 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” Eur. Phys. J. D 39, 445-451 (2006).
[CrossRef]

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, “Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero,” Phys. Rev. Lett. 93, 2436041-2436044 (2004).
[CrossRef]

Vysochanskii, Yu. M.

A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, in Photorefractive Materials and Their Applications, Vol. 2, P.Günter and J.-P.Huignard, eds. (Springer, 2006).

Webb, D. J.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

White, J. O.

M. Cronin-Golomb, B. Fischer, 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. Fischer, 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]

Appl. Phys. Lett. (1)

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665-3667 (1996).
[CrossRef]

Eur. Phys. J. D (2)

M. Grapinet, P. Mathey, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Frequency degenerate and non-degenerate nonlinear regimes for semi-linear photorefractive oscillator,” Eur. Phys. J. D 41, 363-369 (2007).
[CrossRef]

P. Mathey, M. Grapinet, H. R. Jauslin, B. Sturman, D. Rytz, and S. Odoulov, “Threshold behavior of semi-linear photorefractive oscillator,” Eur. Phys. J. D 39, 445-451 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fischer, 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 (2)

Opt. Lett. (1)

Phys. Rev. A (1)

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 0238191-0238196 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, “Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero,” Phys. Rev. Lett. 93, 2436041-2436044 (2004).
[CrossRef]

Other (3)

A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, in Photorefractive Materials and Their Applications, Vol. 2, P.Günter and J.-P.Huignard, eds. (Springer, 2006).

P.Günter and J.-P.Huignard, eds., Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Appl. Phys. (Springer-Verlag, 1989).

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

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Figures (6)

Fig. 1
Fig. 1

(a) Geometric scheme of the semilinear oscillator. (b) The corresponding wavevector diagram.

Fig. 2
Fig. 2

Dependence of Re F and Im F on the frequency detuning Ω in the low-frequency range Ω τ f 1 for τ f τ s = 0.03 and a = 0.1 .

Fig. 3
Fig. 3

Dependences p ( g ) (a) and p ( g ) (b) for τ f τ s = 0.01 , a = 0.3 , and r = 5.76 . The solid and dotted lines refer to the degenerate and nondegenerate branches. The inset shows changing sign of p at g 5.87 for the lowest branch. The dots mark the special points mentioned in the text.

Fig. 4
Fig. 4

Degenerate oscillation with strong periodic pulsations, for g = 3.5 , τ f τ s = 0.01 , r = 5.76 , and a = 0.3 . (a) Normalized light and field amplitudes. (b) Compensating contributions to the field amplitude.

Fig. 5
Fig. 5

Nondegenerate oscillation regime for g = 1.85 and the same for other parameters, see Fig. 4. The solid and dotted lines correspond to A ̂ 3 and N ̂ K + H ̂ K , respectively.

Fig. 6
Fig. 6

Degenerate oscillation regime for g = 4.8 and the same for other parameters, see Fig. 4. The inset shows the fine structure of the jerk of N ̂ K + H ̂ K in the range 0 < t τ f < 10 .

Equations (9)

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A 1 z = u * A 4 , A 2 z = u A 3 ,
A 3 z = u * A 2 , A 4 z = u A 1 .
N K t + γ 11 N K + γ 12 H K = F K ,
H K t + γ 21 N K + γ 22 H K = 0 .
F K = 2 γ p N t ξ p ( A 1 * A 4 + A 2 A 3 * ) I 0 ,
γ 11 = γ p ( 1 + ξ p ) , γ 12 = γ p ,
γ 21 = γ h , γ 22 = γ h ( 1 + ξ h ) ,
τ f 1 γ p ( 1 + ξ p ) , τ s 1 γ h ξ p ( 1 + ξ p ) ,
F ( p ) p τ s + a ( p τ s + 1 ) ( p τ f + 1 ) = 1 g ln ( r R ± r r R 1 ) .

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