Abstract

The conditions for the existence and the main characteristics of weakly damped space-charge waves are investigated for photorefractive ferroelectrics. These conditions are opposite those derived previously for sillenites and may be fulfilled in such crystals as LiNbO3, BaTiO3, and SrBaNb2O6. The waves exist for sufficiently large values of the applied or photovoltaic field and have a linear dispersion law. The resonance excitation of space-charge waves by a moving light pattern is investigated. Possible manifestations of the instability of the photorefractive grating against parametric excitation of eigenmodes are considered.

© 1995 Optical Society of America

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  1. S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660–5663 (1988).
    [CrossRef]
  2. D. J. Webb and L. Solymar, "Observation of spatial subharmonics arising during two-wave mixing in BSO," Opt. Commun. 74, 386–389 (1990).
    [CrossRef]
  3. J. Takacs and L. Solymar, "Subharmonic in Bi12SiO20 with an applied ac electric field," Opt. Lett. 17, 247–248 (1992).
    [CrossRef] [PubMed]
  4. A. Grunnet-Jepsen and L. Solymar, "Effect of subharmonics on two-wave gain in Bi12SiO20 under alternating electric fields," Opt. Lett. 19, 1299–1301 (1994).
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  5. B. Sturman, A. Bledowski, J. Otten, and K. H. Ringhofer, "Spatial subharmonics in photorefractive crystals," J. Opt. Soc. Am. B 9, 672–681 (1992).
    [CrossRef]
  6. B. I. Sturman, M. Mann, and K. H. Ringhofer, "Instability of moving gratings in photorefractive crystals," Appl. Phys. A 55, 235–241 (1992).
    [CrossRef]
  7. B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, "Space-charge waves and their parametric excitation," J. Opt. Soc. Am. B 10, 1919–1932 (1993).
    [CrossRef]
  8. A. Grunnet-Jepsen, I. Richter, M. Shamonin, and L. Solymar, "Subharmonic instabilities in photorefractive crystals for an applied alternating electric field: theoretical analysis," J. Opt. Soc. Am. B 11, 132–135 (1994).
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  10. T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, "Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling," Phys. Rev. Lett. 73, 3082–3084 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45–57 (1985).
    [CrossRef]
  14. A. Furman, "Photovoltaic instabilities," Ferroelectrics 83, 41–52 (1988).
    [CrossRef]
  15. O. P. Nestiorkin and Y. P. Shershakov, "Parametric generation of a spatial subharmonic photorefractive grating in an external dc field with a small electron drift length," presented at the meeting on Photorefractive Materials, Effects, and Devices, PRM'93, August 11–14, 1993. Theophania, Kiev, Ukraine.
  16. G. C. Valley and J. F. Lam, "Theory of photorefractive effects in electro-optic crystals," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., volume 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 75–98.
    [CrossRef]
  17. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–960, 961–964 (1979).
    [CrossRef]
  18. B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effect in Noncentrosymmetric Materials (Gordon & Breach, Philadelphia, Pa., 1992).
  19. M. Klein, "Photorefractive properties of BaTiO3," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 195–236.
    [CrossRef]
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  21. G. A. Brost and R. A. Motes, "Origin of sublinear photorefractive response time in BaTiO3," Opt. Lett. 15, 1194–1196 (1990).
    [CrossRef] [PubMed]
  22. N. Bary, L. Duffault, R. Troth, R. Ramos-Garsia, and M. J. Damzen, "Comparison between continuous-wave and pulsed photorefraction in barium titanate," J. Opt. Soc. Am. B 11, 1758–1763 (1994).
    [CrossRef]
  23. R. A. Vasquez, M. D. Ewbank, and R. R. Neurgaonkar, "Photorefractive properties of doped strontium-barium niobate," Opt. Commun. 80, 253–258 (1991).
    [CrossRef]
  24. M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium-barium niobate," J. Appl. Phys. 62, 374–380 (1987).
    [CrossRef]
  25. R. A. Vasquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416–1427 (1992).
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  26. H.-J. Eichler, P. Günter, and D. W. Pohl, eds., Laser-Induced Dynamic Gratings, Vol. 50 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986).
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  27. C. Medrano, E. Voit, P. Amrhein, and P. Günter, "Optimization of the photorefractive properties of KNbO3 crystals," J. Appl. Phys. 64, 4668–4673 (1988).
    [CrossRef]
  28. M. C. Bashaw, M. Jeganathan, and L. Hesselink, "Theory of two-center transport in photorefractive media for low-intensity, continuous-wave illumination in the quasi-steady-state limit," J. Opt. Soc. Am. B 11, 1743–1757 (1994).
    [CrossRef]
  29. D. Mahgereften and J. Feinberg, "Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate," Phys. Rev. Lett. 64, 2195–2198 (1990).
    [CrossRef]
  30. S. Sochava, K. Buse, and E. Krätzig, "Non-steady state photocurrent technique for the characterization of photorefractive BaTiO3," Opt. Commun. 98, 265–268 (1993).
    [CrossRef]
  31. D. A. Temple, R. S. Hathcock, and C. Warde, "Holographic light scattering in photorefractive materials," in Digest of Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), paper ThB1, p. 122.
  32. We have no information on the anisotropy of the electron mobility.
  33. E. Krätzig and O. F. Schirmer, "Photorefractive centers in electro-optic crystals," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 131–163.
    [CrossRef]
  34. E. Krätzig and R. Orlowski, "Light induced charge transport in doped LiNbO3 and LiTaO3," Ferroelectrics 27, 241–244 (1980).
    [CrossRef]
  35. R. Sommerfeldt, "The influence of further impurities on the photorefractive properties of Fe-doped LiNbO3 crystals," Ph.D. dissertation (University of Osnabrück, Osnabrück, Germany, 1989).
  36. G. A. Brost, K. M. Madge, J. J. Larkin, and T. Harris, "Modulation dependence of the photorefractive response with moving gratings: numerical analysis and experiment," J. Opt. Soc. Am. B 11, 1764–1772 (1994).
    [CrossRef]
  37. T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, "Low frequency peculiarities of the photorefractive response in sillenites," Opt. Commun. 113, 371–377 (1995).
    [CrossRef]
  38. E. Serrano, M. Carrascosa, F. A. López, and L. Solymar, "Subharmonic instability taking into account higher harmonics," Appl. Phys. Lett. 64, 658–660 (1994).
    [CrossRef]
  39. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
  40. In crystals with small μτ the frequency shift between the pump beams probably can be replaced by the application of an alternating external field.
  41. V. V. Lemeshko and V. V. Obukhovskii, "Autowaves of photoinduced light scattering," Sov. Tech. Phys. Lett. 11, 573–574 (1985).
  42. I. F. Kanaev, V. K. Malinovski, and B. I. Sturman, "Induced reflection and bleaching effects in electro-optic crystals," Sov. Phys.-JETP 47, 834–837 (1978).
  43. K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146–149 (1984).
    [CrossRef]

1995

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, "Low frequency peculiarities of the photorefractive response in sillenites," Opt. Commun. 113, 371–377 (1995).
[CrossRef]

1994

1993

O. P. Nestiorkin and Y. P. Shershakov, "Parametric generation of a spatial subharmonic grating in photorefractive crystals: theory," J. Opt. Soc. Am. B 10, 1909–1918 (1993).
[CrossRef]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, "Space-charge waves and their parametric excitation," J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

S. Sochava, K. Buse, and E. Krätzig, "Non-steady state photocurrent technique for the characterization of photorefractive BaTiO3," Opt. Commun. 98, 265–268 (1993).
[CrossRef]

1992

1991

R. A. Vasquez, M. D. Ewbank, and R. R. Neurgaonkar, "Photorefractive properties of doped strontium-barium niobate," Opt. Commun. 80, 253–258 (1991).
[CrossRef]

1990

D. Mahgereften and J. Feinberg, "Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate," Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef]

D. J. Webb and L. Solymar, "Observation of spatial subharmonics arising during two-wave mixing in BSO," Opt. Commun. 74, 386–389 (1990).
[CrossRef]

G. A. Brost and R. A. Motes, "Origin of sublinear photorefractive response time in BaTiO3," Opt. Lett. 15, 1194–1196 (1990).
[CrossRef] [PubMed]

1988

G. A. Brost, R. A. Motes, and J. R. Rotge, "Intensity-dependent absorption and photorefractive effects in barium titanate," J. Opt. Soc. Am. B 5, 1879–1885 (1988).
[CrossRef]

A. Furman, "Photovoltaic instabilities," Ferroelectrics 83, 41–52 (1988).
[CrossRef]

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

C. Medrano, E. Voit, P. Amrhein, and P. Günter, "Optimization of the photorefractive properties of KNbO3 crystals," J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

1987

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium-barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

1985

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

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

1984

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146–149 (1984).
[CrossRef]

1982

S. Stepanov, V. V. Kulikov, and M. P. Petrov, "'Running' holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19–23 (1982).
[CrossRef]

1980

E. Krätzig and R. Orlowski, "Light induced charge transport in doped LiNbO3 and LiTaO3," Ferroelectrics 27, 241–244 (1980).
[CrossRef]

1979

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–960, 961–964 (1979).
[CrossRef]

1978

I. F. Kanaev, V. K. Malinovski, and B. I. Sturman, "Induced reflection and bleaching effects in electro-optic crystals," Sov. Phys.-JETP 47, 834–837 (1978).

1973

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480–485 (1973).

Amrhein, P.

C. Medrano, E. Voit, P. Amrhein, and P. Günter, "Optimization of the photorefractive properties of KNbO3 crystals," J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

Bary, N.

Bashaw, M. C.

Bledowski, A.

Brost, G. A.

Buse, K.

S. Sochava, K. Buse, and E. Krätzig, "Non-steady state photocurrent technique for the characterization of photorefractive BaTiO3," Opt. Commun. 98, 265–268 (1993).
[CrossRef]

Carrascosa, M.

E. Serrano, M. Carrascosa, F. A. López, and L. Solymar, "Subharmonic instability taking into account higher harmonics," Appl. Phys. Lett. 64, 658–660 (1994).
[CrossRef]

Cory, W. K.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium-barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

Damzen, M. J.

Ducollet, H.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

Duffault, L.

Ewbank, M. D.

R. A. Vasquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416–1427 (1992).
[CrossRef]

R. A. Vasquez, M. D. Ewbank, and R. R. Neurgaonkar, "Photorefractive properties of doped strontium-barium niobate," Opt. Commun. 80, 253–258 (1991).
[CrossRef]

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium-barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

Feinberg, J.

D. Mahgereften and J. Feinberg, "Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate," Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef]

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium-barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146–149 (1984).
[CrossRef]

Fridkin, V. M.

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

Fuks, B. I.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480–485 (1973).

Furman, A.

A. Furman, "Photovoltaic instabilities," Ferroelectrics 83, 41–52 (1988).
[CrossRef]

Grunnet-Jepsen, A.

Günter, P.

C. Medrano, E. Voit, P. Amrhein, and P. Günter, "Optimization of the photorefractive properties of KNbO3 crystals," J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146–149 (1984).
[CrossRef]

Harris, T.

Hathcock, R. S.

D. A. Temple, R. S. Hathcock, and C. Warde, "Holographic light scattering in photorefractive materials," in Digest of Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), paper ThB1, p. 122.

Herriau, J. P.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

Hesselink, L.

Huignard, J.-P.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Imbert, B.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

Jeganathan, M.

Kanaev, I. F.

I. F. Kanaev, V. K. Malinovski, and B. I. Sturman, "Induced reflection and bleaching effects in electro-optic crystals," Sov. Phys.-JETP 47, 834–837 (1978).

Kazarinov, R. F.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480–485 (1973).

Klein, M.

M. Klein, "Photorefractive properties of BaTiO3," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 195–236.
[CrossRef]

Krätzig, E.

S. Sochava, K. Buse, and E. Krätzig, "Non-steady state photocurrent technique for the characterization of photorefractive BaTiO3," Opt. Commun. 98, 265–268 (1993).
[CrossRef]

E. Krätzig and R. Orlowski, "Light induced charge transport in doped LiNbO3 and LiTaO3," Ferroelectrics 27, 241–244 (1980).
[CrossRef]

E. Krätzig and O. F. Schirmer, "Photorefractive centers in electro-optic crystals," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 131–163.
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–960, 961–964 (1979).
[CrossRef]

Kulikov, V. V.

S. Stepanov, V. V. Kulikov, and M. P. Petrov, "'Running' holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19–23 (1982).
[CrossRef]

Lam, J. F.

G. C. Valley and J. F. Lam, "Theory of photorefractive effects in electro-optic crystals," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., volume 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 75–98.
[CrossRef]

Larkin, J. J.

Lemeshko, V. V.

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

López, F. A.

E. Serrano, M. Carrascosa, F. A. López, and L. Solymar, "Subharmonic instability taking into account higher harmonics," Appl. Phys. Lett. 64, 658–660 (1994).
[CrossRef]

MacDonald, K. R.

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146–149 (1984).
[CrossRef]

Madge, K. M.

Mahgereften, D.

D. Mahgereften and J. Feinberg, "Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate," Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef]

Malinovski, V. K.

I. F. Kanaev, V. K. Malinovski, and B. I. Sturman, "Induced reflection and bleaching effects in electro-optic crystals," Sov. Phys.-JETP 47, 834–837 (1978).

Mallick, S.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

Mann, M.

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, "Low frequency peculiarities of the photorefractive response in sillenites," Opt. Commun. 113, 371–377 (1995).
[CrossRef]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, "Space-charge waves and their parametric excitation," J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

B. I. Sturman, M. Mann, and K. H. Ringhofer, "Instability of moving gratings in photorefractive crystals," Appl. Phys. A 55, 235–241 (1992).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–960, 961–964 (1979).
[CrossRef]

McClelland, T. E.

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, "Low frequency peculiarities of the photorefractive response in sillenites," Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, "Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling," Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

Medrano, C.

C. Medrano, E. Voit, P. Amrhein, and P. Günter, "Optimization of the photorefractive properties of KNbO3 crystals," J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

Motes, R. A.

Nestiorkin, O. P.

O. P. Nestiorkin and Y. P. Shershakov, "Parametric generation of a spatial subharmonic grating in photorefractive crystals: theory," J. Opt. Soc. Am. B 10, 1909–1918 (1993).
[CrossRef]

O. P. Nestiorkin and Y. P. Shershakov, "Parametric generation of a spatial subharmonic photorefractive grating in an external dc field with a small electron drift length," presented at the meeting on Photorefractive Materials, Effects, and Devices, PRM'93, August 11–14, 1993. Theophania, Kiev, Ukraine.

Neurgaonkar, R. R.

R. A. Vasquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416–1427 (1992).
[CrossRef]

R. A. Vasquez, M. D. Ewbank, and R. R. Neurgaonkar, "Photorefractive properties of doped strontium-barium niobate," Opt. Commun. 80, 253–258 (1991).
[CrossRef]

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium-barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

Obukhovskii, V. V.

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

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–960, 961–964 (1979).
[CrossRef]

Orlowski, R.

E. Krätzig and R. Orlowski, "Light induced charge transport in doped LiNbO3 and LiTaO3," Ferroelectrics 27, 241–244 (1980).
[CrossRef]

Otten, J.

Petrov, M. P.

S. Stepanov, V. V. Kulikov, and M. P. Petrov, "'Running' holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19–23 (1982).
[CrossRef]

Rajbenbach, H.

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Ramos-Garsia, R.

Réfrégier, P.

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Richter, I.

Ringhofer, K. H.

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, "Low frequency peculiarities of the photorefractive response in sillenites," Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, "Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling," Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, "Space-charge waves and their parametric excitation," J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

B. Sturman, A. Bledowski, J. Otten, and K. H. Ringhofer, "Spatial subharmonics in photorefractive crystals," J. Opt. Soc. Am. B 9, 672–681 (1992).
[CrossRef]

B. I. Sturman, M. Mann, and K. H. Ringhofer, "Instability of moving gratings in photorefractive crystals," Appl. Phys. A 55, 235–241 (1992).
[CrossRef]

Rotge, J. R.

Schirmer, O. F.

E. Krätzig and O. F. Schirmer, "Photorefractive centers in electro-optic crystals," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 131–163.
[CrossRef]

Serrano, E.

E. Serrano, M. Carrascosa, F. A. López, and L. Solymar, "Subharmonic instability taking into account higher harmonics," Appl. Phys. Lett. 64, 658–660 (1994).
[CrossRef]

Shamonin, M.

Shershakov, Y. P.

O. P. Nestiorkin and Y. P. Shershakov, "Parametric generation of a spatial subharmonic grating in photorefractive crystals: theory," J. Opt. Soc. Am. B 10, 1909–1918 (1993).
[CrossRef]

O. P. Nestiorkin and Y. P. Shershakov, "Parametric generation of a spatial subharmonic photorefractive grating in an external dc field with a small electron drift length," presented at the meeting on Photorefractive Materials, Effects, and Devices, PRM'93, August 11–14, 1993. Theophania, Kiev, Ukraine.

Sochava, S.

S. Sochava, K. Buse, and E. Krätzig, "Non-steady state photocurrent technique for the characterization of photorefractive BaTiO3," Opt. Commun. 98, 265–268 (1993).
[CrossRef]

Solymar, L.

E. Serrano, M. Carrascosa, F. A. López, and L. Solymar, "Subharmonic instability taking into account higher harmonics," Appl. Phys. Lett. 64, 658–660 (1994).
[CrossRef]

A. Grunnet-Jepsen, I. Richter, M. Shamonin, and L. Solymar, "Subharmonic instabilities in photorefractive crystals for an applied alternating electric field: theoretical analysis," J. Opt. Soc. Am. B 11, 132–135 (1994).
[CrossRef]

A. Grunnet-Jepsen and L. Solymar, "Effect of subharmonics on two-wave gain in Bi12SiO20 under alternating electric fields," Opt. Lett. 19, 1299–1301 (1994).
[CrossRef] [PubMed]

J. Takacs and L. Solymar, "Subharmonic in Bi12SiO20 with an applied ac electric field," Opt. Lett. 17, 247–248 (1992).
[CrossRef] [PubMed]

D. J. Webb and L. Solymar, "Observation of spatial subharmonics arising during two-wave mixing in BSO," Opt. Commun. 74, 386–389 (1990).
[CrossRef]

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Sommerfeldt, R.

R. Sommerfeldt, "The influence of further impurities on the photorefractive properties of Fe-doped LiNbO3 crystals," Ph.D. dissertation (University of Osnabrück, Osnabrück, Germany, 1989).

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–960, 961–964 (1979).
[CrossRef]

Stepanov, S.

S. Stepanov, V. V. Kulikov, and M. P. Petrov, "'Running' holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19–23 (1982).
[CrossRef]

Sturman, B.

Sturman, B. I.

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, "Low frequency peculiarities of the photorefractive response in sillenites," Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, "Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling," Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, "Space-charge waves and their parametric excitation," J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

B. I. Sturman, M. Mann, and K. H. Ringhofer, "Instability of moving gratings in photorefractive crystals," Appl. Phys. A 55, 235–241 (1992).
[CrossRef]

I. F. Kanaev, V. K. Malinovski, and B. I. Sturman, "Induced reflection and bleaching effects in electro-optic crystals," Sov. Phys.-JETP 47, 834–837 (1978).

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

Suris, R. A.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480–485 (1973).

Takacs, J.

Temple, D. A.

D. A. Temple, R. S. Hathcock, and C. Warde, "Holographic light scattering in photorefractive materials," in Digest of Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), paper ThB1, p. 122.

Troth, R.

Valley, G. C.

G. C. Valley and J. F. Lam, "Theory of photorefractive effects in electro-optic crystals," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., volume 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 75–98.
[CrossRef]

Vasquez, R. A.

R. A. Vasquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416–1427 (1992).
[CrossRef]

R. A. Vasquez, M. D. Ewbank, and R. R. Neurgaonkar, "Photorefractive properties of doped strontium-barium niobate," Opt. Commun. 80, 253–258 (1991).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–960, 961–964 (1979).
[CrossRef]

Voit, E.

C. Medrano, E. Voit, P. Amrhein, and P. Günter, "Optimization of the photorefractive properties of KNbO3 crystals," J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

Warde, C.

D. A. Temple, R. S. Hathcock, and C. Warde, "Holographic light scattering in photorefractive materials," in Digest of Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), paper ThB1, p. 122.

Webb, D. J.

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, "Low frequency peculiarities of the photorefractive response in sillenites," Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, "Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling," Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

D. J. Webb and L. Solymar, "Observation of spatial subharmonics arising during two-wave mixing in BSO," Opt. Commun. 74, 386–389 (1990).
[CrossRef]

Whitham, G. B.

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).

Zha, M. Z.

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146–149 (1984).
[CrossRef]

Appl. Phys. A

B. I. Sturman, M. Mann, and K. H. Ringhofer, "Instability of moving gratings in photorefractive crystals," Appl. Phys. A 55, 235–241 (1992).
[CrossRef]

Appl. Phys. Lett.

E. Serrano, M. Carrascosa, F. A. López, and L. Solymar, "Subharmonic instability taking into account higher harmonics," Appl. Phys. Lett. 64, 658–660 (1994).
[CrossRef]

Ferroelectrics

E. Krätzig and R. Orlowski, "Light induced charge transport in doped LiNbO3 and LiTaO3," Ferroelectrics 27, 241–244 (1980).
[CrossRef]

A. Furman, "Photovoltaic instabilities," Ferroelectrics 83, 41–52 (1988).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–960, 961–964 (1979).
[CrossRef]

J. Appl. Phys.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660–5663 (1988).
[CrossRef]

C. Medrano, E. Voit, P. Amrhein, and P. Günter, "Optimization of the photorefractive properties of KNbO3 crystals," J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium-barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, "Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments," J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

J. Opt. Soc. Am. B

R. A. Vasquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416–1427 (1992).
[CrossRef]

N. Bary, L. Duffault, R. Troth, R. Ramos-Garsia, and M. J. Damzen, "Comparison between continuous-wave and pulsed photorefraction in barium titanate," J. Opt. Soc. Am. B 11, 1758–1763 (1994).
[CrossRef]

M. C. Bashaw, M. Jeganathan, and L. Hesselink, "Theory of two-center transport in photorefractive media for low-intensity, continuous-wave illumination in the quasi-steady-state limit," J. Opt. Soc. Am. B 11, 1743–1757 (1994).
[CrossRef]

G. A. Brost, K. M. Madge, J. J. Larkin, and T. Harris, "Modulation dependence of the photorefractive response with moving gratings: numerical analysis and experiment," J. Opt. Soc. Am. B 11, 1764–1772 (1994).
[CrossRef]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, "Space-charge waves and their parametric excitation," J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

A. Grunnet-Jepsen, I. Richter, M. Shamonin, and L. Solymar, "Subharmonic instabilities in photorefractive crystals for an applied alternating electric field: theoretical analysis," J. Opt. Soc. Am. B 11, 132–135 (1994).
[CrossRef]

O. P. Nestiorkin and Y. P. Shershakov, "Parametric generation of a spatial subharmonic grating in photorefractive crystals: theory," J. Opt. Soc. Am. B 10, 1909–1918 (1993).
[CrossRef]

G. A. Brost, R. A. Motes, and J. R. Rotge, "Intensity-dependent absorption and photorefractive effects in barium titanate," J. Opt. Soc. Am. B 5, 1879–1885 (1988).
[CrossRef]

B. Sturman, A. Bledowski, J. Otten, and K. H. Ringhofer, "Spatial subharmonics in photorefractive crystals," J. Opt. Soc. Am. B 9, 672–681 (1992).
[CrossRef]

Opt. Commun.

S. Stepanov, V. V. Kulikov, and M. P. Petrov, "'Running' holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19–23 (1982).
[CrossRef]

D. J. Webb and L. Solymar, "Observation of spatial subharmonics arising during two-wave mixing in BSO," Opt. Commun. 74, 386–389 (1990).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, "Low frequency peculiarities of the photorefractive response in sillenites," Opt. Commun. 113, 371–377 (1995).
[CrossRef]

R. A. Vasquez, M. D. Ewbank, and R. R. Neurgaonkar, "Photorefractive properties of doped strontium-barium niobate," Opt. Commun. 80, 253–258 (1991).
[CrossRef]

S. Sochava, K. Buse, and E. Krätzig, "Non-steady state photocurrent technique for the characterization of photorefractive BaTiO3," Opt. Commun. 98, 265–268 (1993).
[CrossRef]

K. R. MacDonald, J. Feinberg, M. Z. Zha, and P. Günter, "Asymmetric transmission through a photorefractive crystal of barium titanate," Opt. Commun. 50, 146–149 (1984).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, "Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling," Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

D. Mahgereften and J. Feinberg, "Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate," Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef]

Sov. Phys. Semicond.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480–485 (1973).

Sov. Phys.-JETP

I. F. Kanaev, V. K. Malinovski, and B. I. Sturman, "Induced reflection and bleaching effects in electro-optic crystals," Sov. Phys.-JETP 47, 834–837 (1978).

Sov. Tech. Phys. Lett.

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

Other

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

M. Klein, "Photorefractive properties of BaTiO3," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 195–236.
[CrossRef]

O. P. Nestiorkin and Y. P. Shershakov, "Parametric generation of a spatial subharmonic photorefractive grating in an external dc field with a small electron drift length," presented at the meeting on Photorefractive Materials, Effects, and Devices, PRM'93, August 11–14, 1993. Theophania, Kiev, Ukraine.

G. C. Valley and J. F. Lam, "Theory of photorefractive effects in electro-optic crystals," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., volume 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 75–98.
[CrossRef]

R. Sommerfeldt, "The influence of further impurities on the photorefractive properties of Fe-doped LiNbO3 crystals," Ph.D. dissertation (University of Osnabrück, Osnabrück, Germany, 1989).

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).

In crystals with small μτ the frequency shift between the pump beams probably can be replaced by the application of an alternating external field.

D. A. Temple, R. S. Hathcock, and C. Warde, "Holographic light scattering in photorefractive materials," in Digest of Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), paper ThB1, p. 122.

We have no information on the anisotropy of the electron mobility.

E. Krätzig and O. F. Schirmer, "Photorefractive centers in electro-optic crystals," in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 131–163.
[CrossRef]

H.-J. Eichler, P. Günter, and D. W. Pohl, eds., Laser-Induced Dynamic Gratings, Vol. 50 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of a charge transfer for a photorefractive crystal.

Fig. 2
Fig. 2

(a) Contour lines of the quality factor Q(k, E0) = constant for NE = 2 × 1016 cm−3, μτ = 10−11 cm2 V−1, and = 3700. (b) The same for NE = 0.4 × 1016 cm−3, μτ = 5 × 10−10 cm2 V−1, and = 3400.

Fig. 3
Fig. 3

Frequency dependence of the amplitude of the fundamental grating for E0 = 6 kV cm−1, 2π/K = 5 μm, and m = 0.05, 0.2, 0.4, 0.7, 1.0. The crystal parameters correspond to Fig. 2.

Fig. 4
Fig. 4

Spatial distribution of the space-charge field for Ω = −15.5 s−1 and m = 0.1, 1.0.

Fig. 5
Fig. 5

Schematic of the decay processes with participation of the second spatial harmonic of the fundamental grating.

Fig. 6
Fig. 6

(a) Temporal evolution of the amplitudes EK/2, EK, E3K/2, E2K, and E3K with six harmonics taken into account. (b) The same with 10 harmonics. The half-integer harmonics are too small to be seen.

Tables (2)

Tables Icon

Table 1 Expected Characteristics of Space-Charge Waves for a Number of Photorefractive Crystals

Tables Icon

Table 2 Values of Absorption Coefficient a, Concentrations of Fe2+ and Fe3+, Specific Photoconductivity σph/I0, Photovoltaic Constant jph/I0, Lifetime–Mobility Product μτ, and Maximum Quality Factor Qmax for Several Samples of LiNbO3:Fe

Equations (23)

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

N + t = s e N I - γ e N + n , s e N I - γ e N + n + div j e = 0 , 0 div E = e δ N + j e = μ e n ( E 0 + E ) + D e n + β N I z ^ .
α e = s e N ω ,             γ e N + = 1 / τ ,             β = - s e μ e τ e E ph ,
ω k - i γ k = ω 0 e E q + E D - i ( E 0 - N + E ph N 0 - 1 ) E 0 + i ( E D + E M e ) ,
ω 0 e = s e N 0 N + I 0 ,             E q = e N E 0 k z ,             E D = k 2 k B T e k z , E M e = 1 k z μ e τ e ,
| E 0 - N + N 0 E ph | E q , E D ,             E M e E 0 .
ω k = - ω 0 e l 0 * k z ,         γ k = t d - 1 + ω 0 e ( l 0 l 0 * k z 2 + k 2 l D 2 ) ,
l 0 = μ e τ e E 0 ,             l 0 * = μ e τ e ( E 0 - N + N 0 E ph ) , l D = D e τ e .
ω k - i γ k = ω 0 e E q + E D - i E 0 E 0 + i ( E D + E M e ) + ω 0 h E q + E D - i E 0 - E 0 + i ( E D + E M h ) ,
Q k = ( | E 0 E M | + | E q E 0 | + | E D E 0 | ) - 1 .
k 0 2 = 1 ( l 0 2 + l D 2 ) ω 0 t d ,             Q 0 = l 0 2 ( ω 0 t d l 0 2 + l D 2 ) 1 / 2 .
k 0 1 r d = ( N E e 2 0 k B T ) 1 / 2 ,             Q 0 E 0 2 ( 0 N E k B T ) 1 / 2 ,
Q max = ( 0 4 e N E μ τ ) 1 / 2 .
( μ h s h γ e μ e s e γ h ) 1 / 2 N N + ,
1 E 0 E M h s e s h N N + .
μ h 0 γ h e N N + .
ω k = ω 0 l ph k z N + N 0 ,             γ k = 1 t d ( 1 + k 2 r d 2 ) .
Q max = N + 2 N 0 r d l ph l D 2 = E ph 2 N + N 0 ( 0 N E k B T ) 1 / 2 .
I = I 0 [ 1 + m cos ( K z - Ω t ) ] ,
E = E K exp ( i K z - i Ω t ) + c . c .
E K i m 2 E q ω K Ω - ω K + i γ K ,
E K max m 2 E q Q K .
K = k + k , Ω = ω k + ω k .
u t + u u z = 0

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