Abstract

We show that the nonlinearity in periodically poled photovoltaic photorefractives can be solely of the cross-phase-modulation type. The effects of self-phase modulation and asymmetric energy exchange, which exist in homogeneously poled photovoltaic photorefractives, can be considerably suppressed by the periodic poling. Finally, we demonstrate numerically that periodically poled photovoltaic photorefractives can support Thirring-type (“holographic”) solitons, which to our knowledge have never been observed.

© 2006 Optical Society of America

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995), Chap. 7.
  2. O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2033 (2002).
  3. D. R. Walker, D. D. Yavuz, M. Y. Sheverdin, G. Y. Yin, A. V. Sokolov, and S. E. Harris, Opt. Lett. 27, 2094 (2002).
    [CrossRef]
  4. D. D. Yavuz, D. R. Walker, and M. Y. Sheverdin, Phys. Rev. A 67, 041803(R) (2003).
    [CrossRef]
  5. H. Kang and Y. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
    [CrossRef] [PubMed]
  6. I. Friedler, G. Kurizki, O. Cohen, and M. Segev, Opt. Lett. 30, 3374 (2005).
    [CrossRef]
  7. J. R. Salgueiro, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 28, 1457 (2003).
    [CrossRef] [PubMed]
  8. Note the similarity between the two beam interaction in the solely XPM system and three-wave parametric interactions in quadratic media in the limit of large phase mismatch, as pointed out in Refs. .
  9. W. Thirring, Ann. Phys. (N.Y.) 3, 91 (1958).
    [CrossRef]
  10. A. V. Mikhailov, JETP Lett. 23, 320 (1976).
  11. In lithium niobate r51 is comparable to r33. However, its contribution to the nonlinearity is negligible because (a) G23=0, hence there is no photovoltaic field in the y and z directions, and (b) dI/dz, dI/dy⪡dI/dx.
  12. G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
    [CrossRef] [PubMed]
  13. M. Taya, M. C. Bashaw, and M. M. Fejer, Opt. Lett. 21, 857 (1996).
    [CrossRef] [PubMed]
  14. M. Segev, M. C. Bashaw, G. C. Valley, M. M. Fejer, and M. Taya, J. Opt. Soc. Am. A 14, 1772 (1997).
    [CrossRef]
  15. O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
    [CrossRef] [PubMed]
  16. O. Cohen, S. Lan, T. Carmon, J. A. Giordmaine, and M. Segev, Opt. Lett. 27, 2013 (2002).
    [CrossRef]
  17. B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effect in Noncentrosymmetric Materials (Gordon & Breach, 1992).
  18. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford U. Press, 1996).
  19. B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, P. G. Kazansky, and D. C. Hanna, Appl. Phys. Lett. 69, 1349 (1996).
    [CrossRef]
  20. S. Odoulov, T. Tarabrova, A. Shumelyuk, I. I. Naumova, and T. O. Chaplina, Phys. Rev. Lett. 84, 3294 (2000).
    [CrossRef] [PubMed]
  21. B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, and P. G. Kazansky, J. Opt. Soc. Am. B 14, 2641 (1997).
    [CrossRef]
  22. J. S. Liu, Opt. Lett. 28, 2237 (2003).
    [CrossRef] [PubMed]
  23. O. Cohen, B. Freedman, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 93, 103902 (2004).
    [CrossRef] [PubMed]

2005

2004

O. Cohen, B. Freedman, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 93, 103902 (2004).
[CrossRef] [PubMed]

2003

J. R. Salgueiro, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 28, 1457 (2003).
[CrossRef] [PubMed]

J. S. Liu, Opt. Lett. 28, 2237 (2003).
[CrossRef] [PubMed]

D. D. Yavuz, D. R. Walker, and M. Y. Sheverdin, Phys. Rev. A 67, 041803(R) (2003).
[CrossRef]

H. Kang and Y. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

2002

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2033 (2002).

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

O. Cohen, S. Lan, T. Carmon, J. A. Giordmaine, and M. Segev, Opt. Lett. 27, 2013 (2002).
[CrossRef]

D. R. Walker, D. D. Yavuz, M. Y. Sheverdin, G. Y. Yin, A. V. Sokolov, and S. E. Harris, Opt. Lett. 27, 2094 (2002).
[CrossRef]

2000

S. Odoulov, T. Tarabrova, A. Shumelyuk, I. I. Naumova, and T. O. Chaplina, Phys. Rev. Lett. 84, 3294 (2000).
[CrossRef] [PubMed]

1997

M. Segev, M. C. Bashaw, G. C. Valley, M. M. Fejer, and M. Taya, J. Opt. Soc. Am. A 14, 1772 (1997).
[CrossRef]

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, and P. G. Kazansky, J. Opt. Soc. Am. B 14, 2641 (1997).
[CrossRef]

1996

M. Taya, M. C. Bashaw, and M. M. Fejer, Opt. Lett. 21, 857 (1996).
[CrossRef] [PubMed]

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, P. G. Kazansky, and D. C. Hanna, Appl. Phys. Lett. 69, 1349 (1996).
[CrossRef]

1994

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

1976

A. V. Mikhailov, JETP Lett. 23, 320 (1976).

1958

W. Thirring, Ann. Phys. (N.Y.) 3, 91 (1958).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995), Chap. 7.

Aguilar, M.

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, and P. G. Kazansky, J. Opt. Soc. Am. B 14, 2641 (1997).
[CrossRef]

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, P. G. Kazansky, and D. C. Hanna, Appl. Phys. Lett. 69, 1349 (1996).
[CrossRef]

Bashaw, M.

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

Bashaw, M. C.

M. Segev, M. C. Bashaw, G. C. Valley, M. M. Fejer, and M. Taya, J. Opt. Soc. Am. A 14, 1772 (1997).
[CrossRef]

M. Taya, M. C. Bashaw, and M. M. Fejer, Opt. Lett. 21, 857 (1996).
[CrossRef] [PubMed]

Carmon, T.

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2033 (2002).

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

O. Cohen, S. Lan, T. Carmon, J. A. Giordmaine, and M. Segev, Opt. Lett. 27, 2013 (2002).
[CrossRef]

Chaplina, T. O.

S. Odoulov, T. Tarabrova, A. Shumelyuk, I. I. Naumova, and T. O. Chaplina, Phys. Rev. Lett. 84, 3294 (2000).
[CrossRef] [PubMed]

Christodoulides, D. N.

O. Cohen, B. Freedman, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 93, 103902 (2004).
[CrossRef] [PubMed]

Cohen, O.

I. Friedler, G. Kurizki, O. Cohen, and M. Segev, Opt. Lett. 30, 3374 (2005).
[CrossRef]

O. Cohen, B. Freedman, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 93, 103902 (2004).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2033 (2002).

O. Cohen, S. Lan, T. Carmon, J. A. Giordmaine, and M. Segev, Opt. Lett. 27, 2013 (2002).
[CrossRef]

Crosignani, B.

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

Fejer, M.

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

Fejer, M. M.

M. Segev, M. C. Bashaw, G. C. Valley, M. M. Fejer, and M. Taya, J. Opt. Soc. Am. A 14, 1772 (1997).
[CrossRef]

M. Taya, M. C. Bashaw, and M. M. Fejer, Opt. Lett. 21, 857 (1996).
[CrossRef] [PubMed]

Fleischer, J. W.

O. Cohen, B. Freedman, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 93, 103902 (2004).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

Freedman, B.

O. Cohen, B. Freedman, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 93, 103902 (2004).
[CrossRef] [PubMed]

Fridkin, V. M.

B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effect in Noncentrosymmetric Materials (Gordon & Breach, 1992).

Friedler, I.

Giordmaine, J. A.

Grunnet-Jepsen, A.

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

Hanna, D. C.

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, P. G. Kazansky, and D. C. Hanna, Appl. Phys. Lett. 69, 1349 (1996).
[CrossRef]

Harris, S. E.

Kang, H.

H. Kang and Y. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

Kazansky, P. G.

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, and P. G. Kazansky, J. Opt. Soc. Am. B 14, 2641 (1997).
[CrossRef]

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, P. G. Kazansky, and D. C. Hanna, Appl. Phys. Lett. 69, 1349 (1996).
[CrossRef]

Kivshar, Y. S.

Kurizki, G.

Lan, S.

Liu, J. S.

Lopez, F. A.

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, and P. G. Kazansky, J. Opt. Soc. Am. B 14, 2641 (1997).
[CrossRef]

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, P. G. Kazansky, and D. C. Hanna, Appl. Phys. Lett. 69, 1349 (1996).
[CrossRef]

Mikhailov, A. V.

A. V. Mikhailov, JETP Lett. 23, 320 (1976).

Naumova, I. I.

S. Odoulov, T. Tarabrova, A. Shumelyuk, I. I. Naumova, and T. O. Chaplina, Phys. Rev. Lett. 84, 3294 (2000).
[CrossRef] [PubMed]

Odoulov, S.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2033 (2002).

S. Odoulov, T. Tarabrova, A. Shumelyuk, I. I. Naumova, and T. O. Chaplina, Phys. Rev. Lett. 84, 3294 (2000).
[CrossRef] [PubMed]

Pruneri, V.

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, and P. G. Kazansky, J. Opt. Soc. Am. B 14, 2641 (1997).
[CrossRef]

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, P. G. Kazansky, and D. C. Hanna, Appl. Phys. Lett. 69, 1349 (1996).
[CrossRef]

Salgueiro, J. R.

Segev, M.

I. Friedler, G. Kurizki, O. Cohen, and M. Segev, Opt. Lett. 30, 3374 (2005).
[CrossRef]

O. Cohen, B. Freedman, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 93, 103902 (2004).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2033 (2002).

O. Cohen, S. Lan, T. Carmon, J. A. Giordmaine, and M. Segev, Opt. Lett. 27, 2013 (2002).
[CrossRef]

M. Segev, M. C. Bashaw, G. C. Valley, M. M. Fejer, and M. Taya, J. Opt. Soc. Am. A 14, 1772 (1997).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

Sheverdin, M. Y.

Shumelyuk, A.

S. Odoulov, T. Tarabrova, A. Shumelyuk, I. I. Naumova, and T. O. Chaplina, Phys. Rev. Lett. 84, 3294 (2000).
[CrossRef] [PubMed]

Sokolov, A. V.

Solymar, L.

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

Sturman, B.

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, and P. G. Kazansky, J. Opt. Soc. Am. B 14, 2641 (1997).
[CrossRef]

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, P. G. Kazansky, and D. C. Hanna, Appl. Phys. Lett. 69, 1349 (1996).
[CrossRef]

Sturman, B. I.

B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effect in Noncentrosymmetric Materials (Gordon & Breach, 1992).

Sukhorukov, A. A.

Tarabrova, T.

S. Odoulov, T. Tarabrova, A. Shumelyuk, I. I. Naumova, and T. O. Chaplina, Phys. Rev. Lett. 84, 3294 (2000).
[CrossRef] [PubMed]

Taya, M.

M. Segev, M. C. Bashaw, G. C. Valley, M. M. Fejer, and M. Taya, J. Opt. Soc. Am. A 14, 1772 (1997).
[CrossRef]

M. Taya, M. C. Bashaw, and M. M. Fejer, Opt. Lett. 21, 857 (1996).
[CrossRef] [PubMed]

Thirring, W.

W. Thirring, Ann. Phys. (N.Y.) 3, 91 (1958).
[CrossRef]

Uzdin, R.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

Valley, G. C.

M. Segev, M. C. Bashaw, G. C. Valley, M. M. Fejer, and M. Taya, J. Opt. Soc. Am. A 14, 1772 (1997).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

Walker, D. R.

Webb, D. J.

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

Yariv, A.

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

Yavuz, D. D.

Yin, G. Y.

Zhu, Y.

H. Kang and Y. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

Ann. Phys. (N.Y.)

W. Thirring, Ann. Phys. (N.Y.) 3, 91 (1958).
[CrossRef]

Appl. Phys. Lett.

B. Sturman, M. Aguilar, F. A. Lopez, V. Pruneri, P. G. Kazansky, and D. C. Hanna, Appl. Phys. Lett. 69, 1349 (1996).
[CrossRef]

J. Opt. Soc. Am. A

M. Segev, M. C. Bashaw, G. C. Valley, M. M. Fejer, and M. Taya, J. Opt. Soc. Am. A 14, 1772 (1997).
[CrossRef]

J. Opt. Soc. Am. B

JETP Lett.

A. V. Mikhailov, JETP Lett. 23, 320 (1976).

Opt. Lett.

Phys. Rev. A

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

D. D. Yavuz, D. R. Walker, and M. Y. Sheverdin, Phys. Rev. A 67, 041803(R) (2003).
[CrossRef]

Phys. Rev. Lett.

H. Kang and Y. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

S. Odoulov, T. Tarabrova, A. Shumelyuk, I. I. Naumova, and T. O. Chaplina, Phys. Rev. Lett. 84, 3294 (2000).
[CrossRef] [PubMed]

O. Cohen, B. Freedman, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 93, 103902 (2004).
[CrossRef] [PubMed]

Other

B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effect in Noncentrosymmetric Materials (Gordon & Breach, 1992).

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

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995), Chap. 7.

Note the similarity between the two beam interaction in the solely XPM system and three-wave parametric interactions in quadratic media in the limit of large phase mismatch, as pointed out in Refs. .

In lithium niobate r51 is comparable to r33. However, its contribution to the nonlinearity is negligible because (a) G23=0, hence there is no photovoltaic field in the y and z directions, and (b) dI/dz, dI/dy⪡dI/dx.

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Figures (2)

Fig. 1
Fig. 1

Top, scheme for mutually coherent beams propagating in (a) a homogeneously poled crystal and (b) a periodically poled crystal. Bottom, scheme for photovoltaic charge separation due to (c) a uniform beam and (d) an interference pattern.

Fig. 2
Fig. 2

(Color online) Holographic soliton in a periodically poled phovoltaic photorefractive crystal. (a) Intensity of the beam launched into the medium in the presence of 10% noise. (b), (c) Output intensity after z = 2 cm : (b) nonlinear and (c) linear propagation. (d) Index structure induced by the holographic soliton beam.

Equations (5)

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

Δ n = 1 2 n 0 3 r 33 E PV I + E D d I d x A 2 + B 2 + I dark ,
Δ n = 1 2 n 0 3 δ 1 + δ 2 + δ 3 A 2 + B 2 + I dark .
i Ψ z + 1 2 k 2 Ψ + k Δ n n 0 Ψ = 0 ,
i A z + 1 2 k 2 A y 2 + Δ n 0 B 2 A 2 + B 2 + I Dark A = 0 ,
i B z + 1 2 k 2 B y 2 + Δ n 0 A 2 A 2 + B 2 + I Dark B = 0 ,

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