Abstract

We develop a theory of the photorefractive nonlinear response for Sn2P2S6 crystals. The theory incorporates two types of charge carrier (optically active and passive), provides explicit expressions for the characteristic buildup–relaxation rates and gain factors, explains naturally a big variety of accumulated experimental data, and facilitates characterization–optimization of this important nonlinear material.

© 2007 Optical Society of America

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  1. A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, "Photorefractive effects in Sn2P2S6," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2006), Vol. 2.
  2. S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, and A. A. Grabar, "Photorefractive beam coupling in tin hypothiodiphosphate in the near infrared," Opt. Lett. 21, 752-754 (1996).
    [CrossRef] [PubMed]
  3. S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, A. A. Grabar, and I. M. Stoika, "Photorefraction in tin hypothiodiphosphate in the near infrared," J. Opt. Soc. Am. B 13, 2352-2360 (1996).
    [CrossRef]
  4. S. G. Odoulov, A. N. Shumelyuk, G. A. Brost, and K. M. Magde, "Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate," Appl. Phys. Lett. 69, 3665-3667 (1996).
    [CrossRef]
  5. A. Shumelyuk, S. Odoulov, and G. Brost, "Nearly degenerate two-beam coupling in photorefractive crystals with two species of movable carriers," J. Opt. Soc. Am. B 15, 2125-2131 (1998).
    [CrossRef]
  6. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).
  7. A. Shumelyuk, S. Odoulov, and G. Brost, "Multiline coherent oscillation in photorefractive crystals with two species of movable carriers," Appl. Phys. B 68, 959-966 (1999).
    [CrossRef]
  8. K. Seeger, Semiconductor Physics (Springer, 1973).
  9. M. Carrascosa, L. Arizmendi, and J. M. Cabrera, "Thermal fixing of photoinduced grating," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2005), Vol. 1, Chap. 12.
  10. B. Sturman, M. Carrascosa, F. Agullo-Lopez, and J. Limeres, "Theory of high-temperature photorefractive phenomena in LiNbO3 crystals and applications to experiment," Phys. Rev. B 57, 12792-12805 (1998).
    [CrossRef]
  11. I. Seres, S. Stepanov, S. Mansurova, and A. Grabar, "Non-steady-state photoelectromotive force effect in photorefractive Sn2P2S6 crystals," J. Opt. Soc. Am. B 17, 1986-1991 (2000).
    [CrossRef]
  12. A. Shumelyuk, S. Odoulov, D. Kip, and E. Krätzig, "Electric-field enhancement of beam coupling in Sn2P2S6," Appl. Phys. B 72, 707-710 (2001).
    [CrossRef]
  13. Note that the values of the Debye screening length from Ref. (it is denoted there by ls) have to be divided by a factor of 2π owing to a technical error in the estimates.
  14. A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, "Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques," Appl. Phys. B 76, 417-421 (2003).
    [CrossRef]
  15. D. Z. Anderson and J. Feinberg, "Optical novelty filters," IEEE J. Quantum Electron. 24, 635-647 (1989).
    [CrossRef]
  16. 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, 243604 (2004).
    [CrossRef]
  17. M. Weber, G. von Bally, A. Shumelyuk, and S. Odoulov, "Reflection-type photorefractive gratings in tin hypothiodiphosphate," Appl. Phys. B 74, 29-33 (2002).
    [CrossRef]
  18. A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, "Coherent optical oscillator with periodic zero-π phase modulation," Phys. Rev. A 72, 023819 (2005).
    [CrossRef]
  19. A. Donnermeyer, H. Vogt, and E. Krätzig, "Complementary gratings due to electron and hole conductivity in aluminium-doped bismuth titanium oxide crystals," Phys. Status Solidi A 200, 451-456 (2003).
    [CrossRef]
  20. X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, "Photorefractive properties of Bi4Ti3O12," Phys. Rev. B 55, 9495-9502 (1997).
    [CrossRef]

2005 (1)

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, "Coherent optical oscillator with periodic zero-π phase modulation," Phys. Rev. A 72, 023819 (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, 243604 (2004).
[CrossRef]

2003 (2)

A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, "Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques," Appl. Phys. B 76, 417-421 (2003).
[CrossRef]

A. Donnermeyer, H. Vogt, and E. Krätzig, "Complementary gratings due to electron and hole conductivity in aluminium-doped bismuth titanium oxide crystals," Phys. Status Solidi A 200, 451-456 (2003).
[CrossRef]

2002 (1)

M. Weber, G. von Bally, A. Shumelyuk, and S. Odoulov, "Reflection-type photorefractive gratings in tin hypothiodiphosphate," Appl. Phys. B 74, 29-33 (2002).
[CrossRef]

2001 (1)

A. Shumelyuk, S. Odoulov, D. Kip, and E. Krätzig, "Electric-field enhancement of beam coupling in Sn2P2S6," Appl. Phys. B 72, 707-710 (2001).
[CrossRef]

2000 (1)

1999 (1)

A. Shumelyuk, S. Odoulov, and G. Brost, "Multiline coherent oscillation in photorefractive crystals with two species of movable carriers," Appl. Phys. B 68, 959-966 (1999).
[CrossRef]

1998 (2)

B. Sturman, M. Carrascosa, F. Agullo-Lopez, and J. Limeres, "Theory of high-temperature photorefractive phenomena in LiNbO3 crystals and applications to experiment," Phys. Rev. B 57, 12792-12805 (1998).
[CrossRef]

A. Shumelyuk, S. Odoulov, and G. Brost, "Nearly degenerate two-beam coupling in photorefractive crystals with two species of movable carriers," J. Opt. Soc. Am. B 15, 2125-2131 (1998).
[CrossRef]

1997 (1)

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, "Photorefractive properties of Bi4Ti3O12," Phys. Rev. B 55, 9495-9502 (1997).
[CrossRef]

1996 (3)

1989 (1)

D. Z. Anderson and J. Feinberg, "Optical novelty filters," IEEE J. Quantum Electron. 24, 635-647 (1989).
[CrossRef]

Agullo-Lopez, F.

B. Sturman, M. Carrascosa, F. Agullo-Lopez, and J. Limeres, "Theory of high-temperature photorefractive phenomena in LiNbO3 crystals and applications to experiment," Phys. Rev. B 57, 12792-12805 (1998).
[CrossRef]

Anderson, D. Z.

D. Z. Anderson and J. Feinberg, "Optical novelty filters," IEEE J. Quantum Electron. 24, 635-647 (1989).
[CrossRef]

Arizmendi, L.

M. Carrascosa, L. Arizmendi, and J. M. Cabrera, "Thermal fixing of photoinduced grating," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2005), Vol. 1, Chap. 12.

Barilov, D.

A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, "Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques," Appl. Phys. B 76, 417-421 (2003).
[CrossRef]

Brost, G.

A. Shumelyuk, S. Odoulov, and G. Brost, "Multiline coherent oscillation in photorefractive crystals with two species of movable carriers," Appl. Phys. B 68, 959-966 (1999).
[CrossRef]

A. Shumelyuk, S. Odoulov, and G. Brost, "Nearly degenerate two-beam coupling in photorefractive crystals with two species of movable carriers," J. Opt. Soc. Am. B 15, 2125-2131 (1998).
[CrossRef]

Brost, G. A.

S. G. Odoulov, A. N. Shumelyuk, G. A. Brost, and K. M. 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, 243604 (2004).
[CrossRef]

Cabrera, J. M.

M. Carrascosa, L. Arizmendi, and J. M. Cabrera, "Thermal fixing of photoinduced grating," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2005), Vol. 1, Chap. 12.

Carrascosa, M.

B. Sturman, M. Carrascosa, F. Agullo-Lopez, and J. Limeres, "Theory of high-temperature photorefractive phenomena in LiNbO3 crystals and applications to experiment," Phys. Rev. B 57, 12792-12805 (1998).
[CrossRef]

M. Carrascosa, L. Arizmendi, and J. M. Cabrera, "Thermal fixing of photoinduced grating," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2005), Vol. 1, Chap. 12.

Donnermeyer, A.

A. Donnermeyer, H. Vogt, and E. Krätzig, "Complementary gratings due to electron and hole conductivity in aluminium-doped bismuth titanium oxide crystals," Phys. Status Solidi A 200, 451-456 (2003).
[CrossRef]

Feinberg, J.

D. Z. Anderson and J. Feinberg, "Optical novelty filters," IEEE J. Quantum Electron. 24, 635-647 (1989).
[CrossRef]

Grabar, A.

Grabar, A. A.

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, "Photorefractive effects in Sn2P2S6," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2006), Vol. 2.

Hellwig, U.

Hryhorashchuk, A.

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, "Coherent optical oscillator with periodic zero-π phase modulation," Phys. Rev. A 72, 023819 (2005).
[CrossRef]

Jazbinsek, M.

A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, "Photorefractive effects in Sn2P2S6," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2006), Vol. 2.

Kip, D.

A. Shumelyuk, S. Odoulov, D. Kip, and E. Krätzig, "Electric-field enhancement of beam coupling in Sn2P2S6," Appl. Phys. B 72, 707-710 (2001).
[CrossRef]

Krätzig, E.

A. Donnermeyer, H. Vogt, and E. Krätzig, "Complementary gratings due to electron and hole conductivity in aluminium-doped bismuth titanium oxide crystals," Phys. Status Solidi A 200, 451-456 (2003).
[CrossRef]

A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, "Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques," Appl. Phys. B 76, 417-421 (2003).
[CrossRef]

A. Shumelyuk, S. Odoulov, D. Kip, and E. Krätzig, "Electric-field enhancement of beam coupling in Sn2P2S6," Appl. Phys. B 72, 707-710 (2001).
[CrossRef]

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, "Photorefractive properties of Bi4Ti3O12," Phys. Rev. B 55, 9495-9502 (1997).
[CrossRef]

Limeres, J.

B. Sturman, M. Carrascosa, F. Agullo-Lopez, and J. Limeres, "Theory of high-temperature photorefractive phenomena in LiNbO3 crystals and applications to experiment," Phys. Rev. B 57, 12792-12805 (1998).
[CrossRef]

Magde, K. M.

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

Mansurova, S.

Mersch, F.

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, "Photorefractive properties of Bi4Ti3O12," Phys. Rev. B 55, 9495-9502 (1997).
[CrossRef]

Montemezzani, G.

A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, "Photorefractive effects in Sn2P2S6," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2006), Vol. 2.

Odoulov, S.

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, "Coherent optical oscillator with periodic zero-π phase modulation," Phys. Rev. A 72, 023819 (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, 243604 (2004).
[CrossRef]

A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, "Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques," Appl. Phys. B 76, 417-421 (2003).
[CrossRef]

M. Weber, G. von Bally, A. Shumelyuk, and S. Odoulov, "Reflection-type photorefractive gratings in tin hypothiodiphosphate," Appl. Phys. B 74, 29-33 (2002).
[CrossRef]

A. Shumelyuk, S. Odoulov, D. Kip, and E. Krätzig, "Electric-field enhancement of beam coupling in Sn2P2S6," Appl. Phys. B 72, 707-710 (2001).
[CrossRef]

A. Shumelyuk, S. Odoulov, and G. Brost, "Multiline coherent oscillation in photorefractive crystals with two species of movable carriers," Appl. Phys. B 68, 959-966 (1999).
[CrossRef]

A. Shumelyuk, S. Odoulov, and G. Brost, "Nearly degenerate two-beam coupling in photorefractive crystals with two species of movable carriers," J. Opt. Soc. Am. B 15, 2125-2131 (1998).
[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, 243604 (2004).
[CrossRef]

Rupp, R. A.

Seeger, K.

K. Seeger, Semiconductor Physics (Springer, 1973).

Seres, I.

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, 243604 (2004).
[CrossRef]

Shumelyuk, A.

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, "Coherent optical oscillator with periodic zero-π phase modulation," Phys. Rev. A 72, 023819 (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, 243604 (2004).
[CrossRef]

A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, "Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques," Appl. Phys. B 76, 417-421 (2003).
[CrossRef]

M. Weber, G. von Bally, A. Shumelyuk, and S. Odoulov, "Reflection-type photorefractive gratings in tin hypothiodiphosphate," Appl. Phys. B 74, 29-33 (2002).
[CrossRef]

A. Shumelyuk, S. Odoulov, D. Kip, and E. Krätzig, "Electric-field enhancement of beam coupling in Sn2P2S6," Appl. Phys. B 72, 707-710 (2001).
[CrossRef]

A. Shumelyuk, S. Odoulov, and G. Brost, "Multiline coherent oscillation in photorefractive crystals with two species of movable carriers," Appl. Phys. B 68, 959-966 (1999).
[CrossRef]

A. Shumelyuk, S. Odoulov, and G. Brost, "Nearly degenerate two-beam coupling in photorefractive crystals with two species of movable carriers," J. Opt. Soc. Am. B 15, 2125-2131 (1998).
[CrossRef]

Shumelyuk, A. N.

S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, A. A. Grabar, and I. M. Stoika, "Photorefraction in tin hypothiodiphosphate in the near infrared," J. Opt. Soc. Am. B 13, 2352-2360 (1996).
[CrossRef]

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

S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, and A. A. Grabar, "Photorefractive beam coupling in tin hypothiodiphosphate in the near infrared," Opt. Lett. 21, 752-754 (1996).
[CrossRef] [PubMed]

A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, "Photorefractive effects in Sn2P2S6," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2006), Vol. 2.

Solymar, L.

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

Stepanov, S.

Stoika, I. M.

Sturman, B.

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, 243604 (2004).
[CrossRef]

B. Sturman, M. Carrascosa, F. Agullo-Lopez, and J. Limeres, "Theory of high-temperature photorefractive phenomena in LiNbO3 crystals and applications to experiment," Phys. Rev. B 57, 12792-12805 (1998).
[CrossRef]

Vogt, H.

A. Donnermeyer, H. Vogt, and E. Krätzig, "Complementary gratings due to electron and hole conductivity in aluminium-doped bismuth titanium oxide crystals," Phys. Status Solidi A 200, 451-456 (2003).
[CrossRef]

von Bally, G.

M. Weber, G. von Bally, A. Shumelyuk, and S. Odoulov, "Reflection-type photorefractive gratings in tin hypothiodiphosphate," Appl. Phys. B 74, 29-33 (2002).
[CrossRef]

Vysochanskii, Yu. M.

A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, "Photorefractive effects in Sn2P2S6," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2006), Vol. 2.

Webb, D. J.

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

Weber, M.

M. Weber, G. von Bally, A. Shumelyuk, and S. Odoulov, "Reflection-type photorefractive gratings in tin hypothiodiphosphate," Appl. Phys. B 74, 29-33 (2002).
[CrossRef]

Xu, J.

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, "Photorefractive properties of Bi4Ti3O12," Phys. Rev. B 55, 9495-9502 (1997).
[CrossRef]

Yue, X.

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, "Photorefractive properties of Bi4Ti3O12," Phys. Rev. B 55, 9495-9502 (1997).
[CrossRef]

Appl. Phys. B (4)

A. Shumelyuk, S. Odoulov, and G. Brost, "Multiline coherent oscillation in photorefractive crystals with two species of movable carriers," Appl. Phys. B 68, 959-966 (1999).
[CrossRef]

A. Shumelyuk, S. Odoulov, D. Kip, and E. Krätzig, "Electric-field enhancement of beam coupling in Sn2P2S6," Appl. Phys. B 72, 707-710 (2001).
[CrossRef]

A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, "Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques," Appl. Phys. B 76, 417-421 (2003).
[CrossRef]

M. Weber, G. von Bally, A. Shumelyuk, and S. Odoulov, "Reflection-type photorefractive gratings in tin hypothiodiphosphate," Appl. Phys. B 74, 29-33 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

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

IEEE J. Quantum Electron. (1)

D. Z. Anderson and J. Feinberg, "Optical novelty filters," IEEE J. Quantum Electron. 24, 635-647 (1989).
[CrossRef]

J. Opt. Soc. Am. B (3)

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, 023819 (2005).
[CrossRef]

Phys. Rev. B (2)

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, "Photorefractive properties of Bi4Ti3O12," Phys. Rev. B 55, 9495-9502 (1997).
[CrossRef]

B. Sturman, M. Carrascosa, F. Agullo-Lopez, and J. Limeres, "Theory of high-temperature photorefractive phenomena in LiNbO3 crystals and applications to experiment," Phys. Rev. B 57, 12792-12805 (1998).
[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, 243604 (2004).
[CrossRef]

Phys. Status Solidi A (1)

A. Donnermeyer, H. Vogt, and E. Krätzig, "Complementary gratings due to electron and hole conductivity in aluminium-doped bismuth titanium oxide crystals," Phys. Status Solidi A 200, 451-456 (2003).
[CrossRef]

Other (5)

A. A. Grabar, Yu. M. Vysochanskii, A. N. Shumelyuk, M. Jazbinsek, G. Montemezzani, and P. Günter, "Photorefractive effects in Sn2P2S6," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2006), Vol. 2.

Note that the values of the Debye screening length from Ref. (it is denoted there by ls) have to be divided by a factor of 2π owing to a technical error in the estimates.

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

K. Seeger, Semiconductor Physics (Springer, 1973).

M. Carrascosa, L. Arizmendi, and J. M. Cabrera, "Thermal fixing of photoinduced grating," in Photorefractive Materials and Their Applications, P.Günter and J.-P.Huignard, eds. (Springer-Verlag, 2005), Vol. 1, Chap. 12.

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Figures (5)

Fig. 1
Fig. 1

Dependence of the maximum gain factor Γ f 0 on the grating spacing Λ.

Fig. 2
Fig. 2

Dependence of τ f 1 on K R p for L D R p = 2 .

Fig. 3
Fig. 3

Dependence of 1 γ H τ s on K R p for three representative values of N t H 0 .

Fig. 4
Fig. 4

Recording kinetics of Δ n K for K R p = 1 , L D R p = 2 , γ p γ H = 250 , and N t H 0 = 0.1 .

Fig. 5
Fig. 5

Dependence of the gain factor Γ on the frequency detuning for the parameters of Fig. 4.

Equations (28)

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

E s c z = e ϵ ϵ 0 ( N N C + H H 0 p ) ,
N t = s i I ( N Σ N ) s r N p ,
p t = N t 1 e j p z ,
H t = 1 e j H z .
j p = e μ p p E s c e D p p z ,
j H = e μ H H E s c + e D H H z ,
I = I 0 ( 1 + m 2 e i K z + m * 2 e i K z ) ,
E s c = E K e i K z + c.c. ,
N N 0 = N K e i K z + c.c. ,
H H 0 = H K e i K z + c.c. ,
d N K d t + γ 11 N K + γ 12 H K = F K ,
d H K d t + γ 21 N K + γ 22 H K = 0 .
F K = m γ p ̃ N t ξ e 2 ,
γ 11 = γ p ̃ ( 1 + ξ e ) , γ 12 = γ e ̃ ,
γ 21 = γ H , γ 22 = γ H ( 1 + ξ h ) .
E K = i e ( N K + H K ) ϵ ϵ 0 K .
τ f , s 1 = 1 2 [ γ 11 + γ 22 ± ( γ 11 γ 22 ) 2 + 4 γ 12 γ 21 ] .
τ f 1 γ p ̃ ( 1 + ξ p ) , τ s 1 γ H ξ p ξ H + ξ p + ξ H 1 + ξ p .
τ f 1 γ p ̃ + γ H , τ s 1 γ p ̃ γ H γ p ̃ + γ H ( ξ p + ξ H ) ,
E f , s = E f , s 0 ( 1 e t τ f , s ) ,
E f 0 i m E D 2 1 1 + ξ p ,
E s 0 i m E D 2 ξ p ( 1 + ξ p ) ( ξ p ξ H + ξ p ξ H ) ,
E K 0 = i m E D 2 γ p ̃ ( γ H ξ H i Ω ) ( τ f 1 i Ω ) ( τ s 1 i Ω ) .
E K 0 = i m E D 2 1 1 + ξ p + H 0 N t .
E K 0 = i m E D 2 1 1 + ξ p .
τ s 1 = γ H ( N t H 0 + 1 1 + K 2 R p 2 ) K 2 R p 2 .
E f 0 + E s 0 E f 0 = 1 + K 2 R p 2 1 + K 2 R p 2 + H 0 N t 1 ,
τ f τ s = K 2 R p 2 ( 1 + K 2 L D 2 ) [ 1 + N t H 0 1 ( 1 + K 2 R p 2 ) ] γ p γ H 1 ( 1 + K 2 R p 2 ) 2 .

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