Abstract

We deal with the vectorial equations of two-wave mixing without an external field (diffusion response) in Bi12SiO20 and Bi12TiO20 by splitting the vectorial amplitudes of signal and reference waves into a parallel part whose direction is determined by the optical activity rotation and into a perpendicular part. By doing so we obtain an approximation scheme that works particularly well after optimization with respect to the input polarization. Exploring the relevant crystal configurations [L, T, and D geometry of the (110) cut and T and D geometry of the (111) cut], we show that for common crystal thicknesses our approximate solution is almost as precise as the numeric solution.

© 2001 Optical Society of America

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  2. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).
  3. M. P. Georges and P. L. Lemaire, “Real-time holographic interferometry using sillenite photorefractive crystals. Study and optimization of a transportable set-up for quantified phase measurements on large objects,” Appl. Phys. B 68, 1073–1083 (1999), and references therein.
    [CrossRef]
  4. A. Marrakchi, R. V. Johnson, and J. A. R. Tanguay, “Polarization properties of photorefractive diffraction in electro-optic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321–336 (1986).
    [CrossRef]
  5. S. Mallick, D. Rouède, and A. G. Apostolidis, “Efficiency and polarization characteristics of photorefractive diffraction in a Bi12SiO20 crystal,” J. Opt. Soc. Am. B 4, 1247–1259 (1987).
    [CrossRef]
  6. S. Mallick and D. Rouède, “Influence of the polarization di-rection on two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B 43, 239–245 (1987).
    [CrossRef]
  7. E. Raita, A. A. Kamshilin, and T. Jaaskelainen, “Polarization properties of fanning light in fiberlike bismuth titanium oxide crystals,” Opt. Lett. 21, 1897–1899 (1996).
    [CrossRef] [PubMed]
  8. B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
    [CrossRef]
  9. V. V. Shepelevich, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, Yi Hu, K. H. Ringhofer, and E. Shamonina, “Gain optimization at two-wave mixing in cubic photorefractive piezocrystals of (111)-cut,” in Advances in Photorefractive Materials, Effects, and Devices, P. E. Andersen, P. M. Johansen, H. C. Pedersen, P. M. Petersen, and M. Saffman, eds., Vol. 27 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 353–360.
  10. V. P. Kamenov, Yi Hu, E. Shamonina, and K. H. Ringhofer, “(111)-cut: characterisation and comparision with the general cut,” Phys. Rev. E 62, 2863–2870 (2000).
    [CrossRef]
  11. E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
    [CrossRef]
  12. D. J. Webb, A. Kiessling, B. I. Sturman, E. Shamonina, and K. H. Ringhofer, “Verification of the standard model of the photorefractive nonlinearity in BSO crystal,” Opt. Commun. 108, 31–36 (1994).
    [CrossRef]
  13. S. M. Shandarov, A. Reshet’ko, A. A. Emelyanov, O. Kobozev, M. Krause, Y. F. Kargin, and V. V. Volkov, “Two-beam coupling in sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, Z. I. Alferov, Y. V. Gulyaev, and D. R. Pape, eds., Proc. SPIE 2969, 202–210 (1996).
    [CrossRef]
  14. S. Mallick, M. Miteva, and L. Nikolova, “Polarization properties of self-diffraction in sillenite crystals: reflection volume gratings,” J. Opt. Soc. Am. B 14, 1179–1186 (1997).
    [CrossRef]
  15. R. V. Litvinov, S. M. Shandarov, and S. G. Chistyakov, “Two-wave interaction on the photorefractive grating in cubic gyrotropic crystals at strong coupling,” Phys. Solid State 41, 568–572 (2000).
  16. E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, R. Kowarschik, and D. J. Webb, “Optical activity in photorefractive Bi12TiO20,” Opt. Commun. 146, 62–68 (1998).
    [CrossRef]
  17. A. A. Kamshilin, R. Ravattinen, H. Tuovinen, T. Jaaskelainen, and V. V. Prokofiev, “Double phase conjugation in Bi12TiO20 photorefractive fiber-like crystal,” Opt. Commun. 103, 221–226 (1993).
    [CrossRef]
  18. A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Opto-Electron. 2, 80–84 (1986).

2000 (3)

V. P. Kamenov, Yi Hu, E. Shamonina, and K. H. Ringhofer, “(111)-cut: characterisation and comparision with the general cut,” Phys. Rev. E 62, 2863–2870 (2000).
[CrossRef]

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

R. V. Litvinov, S. M. Shandarov, and S. G. Chistyakov, “Two-wave interaction on the photorefractive grating in cubic gyrotropic crystals at strong coupling,” Phys. Solid State 41, 568–572 (2000).

1999 (2)

M. P. Georges and P. L. Lemaire, “Real-time holographic interferometry using sillenite photorefractive crystals. Study and optimization of a transportable set-up for quantified phase measurements on large objects,” Appl. Phys. B 68, 1073–1083 (1999), and references therein.
[CrossRef]

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

1998 (1)

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, R. Kowarschik, and D. J. Webb, “Optical activity in photorefractive Bi12TiO20,” Opt. Commun. 146, 62–68 (1998).
[CrossRef]

1997 (1)

1996 (2)

E. Raita, A. A. Kamshilin, and T. Jaaskelainen, “Polarization properties of fanning light in fiberlike bismuth titanium oxide crystals,” Opt. Lett. 21, 1897–1899 (1996).
[CrossRef] [PubMed]

S. M. Shandarov, A. Reshet’ko, A. A. Emelyanov, O. Kobozev, M. Krause, Y. F. Kargin, and V. V. Volkov, “Two-beam coupling in sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, Z. I. Alferov, Y. V. Gulyaev, and D. R. Pape, eds., Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

1994 (1)

D. J. Webb, A. Kiessling, B. I. Sturman, E. Shamonina, and K. H. Ringhofer, “Verification of the standard model of the photorefractive nonlinearity in BSO crystal,” Opt. Commun. 108, 31–36 (1994).
[CrossRef]

1993 (1)

A. A. Kamshilin, R. Ravattinen, H. Tuovinen, T. Jaaskelainen, and V. V. Prokofiev, “Double phase conjugation in Bi12TiO20 photorefractive fiber-like crystal,” Opt. Commun. 103, 221–226 (1993).
[CrossRef]

1987 (2)

S. Mallick and D. Rouède, “Influence of the polarization di-rection on two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B 43, 239–245 (1987).
[CrossRef]

S. Mallick, D. Rouède, and A. G. Apostolidis, “Efficiency and polarization characteristics of photorefractive diffraction in a Bi12SiO20 crystal,” J. Opt. Soc. Am. B 4, 1247–1259 (1987).
[CrossRef]

1986 (2)

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Opto-Electron. 2, 80–84 (1986).

A. Marrakchi, R. V. Johnson, and J. A. R. Tanguay, “Polarization properties of photorefractive diffraction in electro-optic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321–336 (1986).
[CrossRef]

Apostolidis, A. G.

Cedilnik, G.

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, R. Kowarschik, and D. J. Webb, “Optical activity in photorefractive Bi12TiO20,” Opt. Commun. 146, 62–68 (1998).
[CrossRef]

Chistyakov, S. G.

R. V. Litvinov, S. M. Shandarov, and S. G. Chistyakov, “Two-wave interaction on the photorefractive grating in cubic gyrotropic crystals at strong coupling,” Phys. Solid State 41, 568–572 (2000).

Egorov, N. N.

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

Emelyanov, A. A.

S. M. Shandarov, A. Reshet’ko, A. A. Emelyanov, O. Kobozev, M. Krause, Y. F. Kargin, and V. V. Volkov, “Two-beam coupling in sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, Z. I. Alferov, Y. V. Gulyaev, and D. R. Pape, eds., Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Gayvoronsky, V. Y.

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

Georges, M. P.

M. P. Georges and P. L. Lemaire, “Real-time holographic interferometry using sillenite photorefractive crystals. Study and optimization of a transportable set-up for quantified phase measurements on large objects,” Appl. Phys. B 68, 1073–1083 (1999), and references therein.
[CrossRef]

Hu, Yi

V. P. Kamenov, Yi Hu, E. Shamonina, and K. H. Ringhofer, “(111)-cut: characterisation and comparision with the general cut,” Phys. Rev. E 62, 2863–2870 (2000).
[CrossRef]

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

Izvanov, A. A.

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Opto-Electron. 2, 80–84 (1986).

Jaaskelainen, T.

E. Raita, A. A. Kamshilin, and T. Jaaskelainen, “Polarization properties of fanning light in fiberlike bismuth titanium oxide crystals,” Opt. Lett. 21, 1897–1899 (1996).
[CrossRef] [PubMed]

A. A. Kamshilin, R. Ravattinen, H. Tuovinen, T. Jaaskelainen, and V. V. Prokofiev, “Double phase conjugation in Bi12TiO20 photorefractive fiber-like crystal,” Opt. Commun. 103, 221–226 (1993).
[CrossRef]

Johnson, R. V.

Kamenov, V.

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, R. Kowarschik, and D. J. Webb, “Optical activity in photorefractive Bi12TiO20,” Opt. Commun. 146, 62–68 (1998).
[CrossRef]

Kamenov, V. P.

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

V. P. Kamenov, Yi Hu, E. Shamonina, and K. H. Ringhofer, “(111)-cut: characterisation and comparision with the general cut,” Phys. Rev. E 62, 2863–2870 (2000).
[CrossRef]

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

Kamshilin, A. A.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

E. Raita, A. A. Kamshilin, and T. Jaaskelainen, “Polarization properties of fanning light in fiberlike bismuth titanium oxide crystals,” Opt. Lett. 21, 1897–1899 (1996).
[CrossRef] [PubMed]

A. A. Kamshilin, R. Ravattinen, H. Tuovinen, T. Jaaskelainen, and V. V. Prokofiev, “Double phase conjugation in Bi12TiO20 photorefractive fiber-like crystal,” Opt. Commun. 103, 221–226 (1993).
[CrossRef]

Kargin, Y. F.

S. M. Shandarov, A. Reshet’ko, A. A. Emelyanov, O. Kobozev, M. Krause, Y. F. Kargin, and V. V. Volkov, “Two-beam coupling in sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, Z. I. Alferov, Y. V. Gulyaev, and D. R. Pape, eds., Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Khat’kov, N. D.

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Opto-Electron. 2, 80–84 (1986).

Kiessling, A.

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, R. Kowarschik, and D. J. Webb, “Optical activity in photorefractive Bi12TiO20,” Opt. Commun. 146, 62–68 (1998).
[CrossRef]

D. J. Webb, A. Kiessling, B. I. Sturman, E. Shamonina, and K. H. Ringhofer, “Verification of the standard model of the photorefractive nonlinearity in BSO crystal,” Opt. Commun. 108, 31–36 (1994).
[CrossRef]

Kobozev, O.

S. M. Shandarov, A. Reshet’ko, A. A. Emelyanov, O. Kobozev, M. Krause, Y. F. Kargin, and V. V. Volkov, “Two-beam coupling in sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, Z. I. Alferov, Y. V. Gulyaev, and D. R. Pape, eds., Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Kowarschik, R.

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, R. Kowarschik, and D. J. Webb, “Optical activity in photorefractive Bi12TiO20,” Opt. Commun. 146, 62–68 (1998).
[CrossRef]

Krause, M.

S. M. Shandarov, A. Reshet’ko, A. A. Emelyanov, O. Kobozev, M. Krause, Y. F. Kargin, and V. V. Volkov, “Two-beam coupling in sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, Z. I. Alferov, Y. V. Gulyaev, and D. R. Pape, eds., Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Lemaire, P. L.

M. P. Georges and P. L. Lemaire, “Real-time holographic interferometry using sillenite photorefractive crystals. Study and optimization of a transportable set-up for quantified phase measurements on large objects,” Appl. Phys. B 68, 1073–1083 (1999), and references therein.
[CrossRef]

Litvinov, R. V.

R. V. Litvinov, S. M. Shandarov, and S. G. Chistyakov, “Two-wave interaction on the photorefractive grating in cubic gyrotropic crystals at strong coupling,” Phys. Solid State 41, 568–572 (2000).

Mallick, S.

Mandel, A. E.

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Opto-Electron. 2, 80–84 (1986).

Marrakchi, A.

Miteva, M.

Nichiporko, S. F.

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

Nikolova, L.

Nippolainen, E.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

Podivilov, E. V.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

Prokofiev, V. V.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

A. A. Kamshilin, R. Ravattinen, H. Tuovinen, T. Jaaskelainen, and V. V. Prokofiev, “Double phase conjugation in Bi12TiO20 photorefractive fiber-like crystal,” Opt. Commun. 103, 221–226 (1993).
[CrossRef]

Raita, E.

Ravattinen, R.

A. A. Kamshilin, R. Ravattinen, H. Tuovinen, T. Jaaskelainen, and V. V. Prokofiev, “Double phase conjugation in Bi12TiO20 photorefractive fiber-like crystal,” Opt. Commun. 103, 221–226 (1993).
[CrossRef]

Reshet’ko, A.

S. M. Shandarov, A. Reshet’ko, A. A. Emelyanov, O. Kobozev, M. Krause, Y. F. Kargin, and V. V. Volkov, “Two-beam coupling in sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, Z. I. Alferov, Y. V. Gulyaev, and D. R. Pape, eds., Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Ringhofer, K. H.

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

V. P. Kamenov, Yi Hu, E. Shamonina, and K. H. Ringhofer, “(111)-cut: characterisation and comparision with the general cut,” Phys. Rev. E 62, 2863–2870 (2000).
[CrossRef]

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, R. Kowarschik, and D. J. Webb, “Optical activity in photorefractive Bi12TiO20,” Opt. Commun. 146, 62–68 (1998).
[CrossRef]

D. J. Webb, A. Kiessling, B. I. Sturman, E. Shamonina, and K. H. Ringhofer, “Verification of the standard model of the photorefractive nonlinearity in BSO crystal,” Opt. Commun. 108, 31–36 (1994).
[CrossRef]

Rouède, D.

S. Mallick, D. Rouède, and A. G. Apostolidis, “Efficiency and polarization characteristics of photorefractive diffraction in a Bi12SiO20 crystal,” J. Opt. Soc. Am. B 4, 1247–1259 (1987).
[CrossRef]

S. Mallick and D. Rouède, “Influence of the polarization di-rection on two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B 43, 239–245 (1987).
[CrossRef]

Shamonina, E.

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

V. P. Kamenov, Yi Hu, E. Shamonina, and K. H. Ringhofer, “(111)-cut: characterisation and comparision with the general cut,” Phys. Rev. E 62, 2863–2870 (2000).
[CrossRef]

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, R. Kowarschik, and D. J. Webb, “Optical activity in photorefractive Bi12TiO20,” Opt. Commun. 146, 62–68 (1998).
[CrossRef]

D. J. Webb, A. Kiessling, B. I. Sturman, E. Shamonina, and K. H. Ringhofer, “Verification of the standard model of the photorefractive nonlinearity in BSO crystal,” Opt. Commun. 108, 31–36 (1994).
[CrossRef]

Shandarov, S. M.

R. V. Litvinov, S. M. Shandarov, and S. G. Chistyakov, “Two-wave interaction on the photorefractive grating in cubic gyrotropic crystals at strong coupling,” Phys. Solid State 41, 568–572 (2000).

S. M. Shandarov, A. Reshet’ko, A. A. Emelyanov, O. Kobozev, M. Krause, Y. F. Kargin, and V. V. Volkov, “Two-beam coupling in sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, Z. I. Alferov, Y. V. Gulyaev, and D. R. Pape, eds., Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Opto-Electron. 2, 80–84 (1986).

Shepelevich, V. V.

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

Sturman, B. I.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

D. J. Webb, A. Kiessling, B. I. Sturman, E. Shamonina, and K. H. Ringhofer, “Verification of the standard model of the photorefractive nonlinearity in BSO crystal,” Opt. Commun. 108, 31–36 (1994).
[CrossRef]

Tanguay, J. A. R.

Tuovinen, H.

A. A. Kamshilin, R. Ravattinen, H. Tuovinen, T. Jaaskelainen, and V. V. Prokofiev, “Double phase conjugation in Bi12TiO20 photorefractive fiber-like crystal,” Opt. Commun. 103, 221–226 (1993).
[CrossRef]

Volkov, V. V.

S. M. Shandarov, A. Reshet’ko, A. A. Emelyanov, O. Kobozev, M. Krause, Y. F. Kargin, and V. V. Volkov, “Two-beam coupling in sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, Z. I. Alferov, Y. V. Gulyaev, and D. R. Pape, eds., Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Webb, D. J.

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, R. Kowarschik, and D. J. Webb, “Optical activity in photorefractive Bi12TiO20,” Opt. Commun. 146, 62–68 (1998).
[CrossRef]

D. J. Webb, A. Kiessling, B. I. Sturman, E. Shamonina, and K. H. Ringhofer, “Verification of the standard model of the photorefractive nonlinearity in BSO crystal,” Opt. Commun. 108, 31–36 (1994).
[CrossRef]

Zagorskiy, A. E.

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

Appl. Phys. B (2)

M. P. Georges and P. L. Lemaire, “Real-time holographic interferometry using sillenite photorefractive crystals. Study and optimization of a transportable set-up for quantified phase measurements on large objects,” Appl. Phys. B 68, 1073–1083 (1999), and references therein.
[CrossRef]

S. Mallick and D. Rouède, “Influence of the polarization di-rection on two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B 43, 239–245 (1987).
[CrossRef]

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

Opt. Commun. (4)

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kiessling, R. Kowarschik, and D. J. Webb, “Optical activity in photorefractive Bi12TiO20,” Opt. Commun. 146, 62–68 (1998).
[CrossRef]

A. A. Kamshilin, R. Ravattinen, H. Tuovinen, T. Jaaskelainen, and V. V. Prokofiev, “Double phase conjugation in Bi12TiO20 photorefractive fiber-like crystal,” Opt. Commun. 103, 221–226 (1993).
[CrossRef]

E. Shamonina, Yi Hu, V. P. Kamenov, K. H. Ringhofer, V. Y. Gayvoronsky, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, and V. V. Shepelevich, “Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes,” Opt. Commun. 180, 183–190 (2000).
[CrossRef]

D. J. Webb, A. Kiessling, B. I. Sturman, E. Shamonina, and K. H. Ringhofer, “Verification of the standard model of the photorefractive nonlinearity in BSO crystal,” Opt. Commun. 108, 31–36 (1994).
[CrossRef]

Opt. Lett. (1)

Opto-Electron. (1)

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Opto-Electron. 2, 80–84 (1986).

Phys. Rev. E (2)

V. P. Kamenov, Yi Hu, E. Shamonina, and K. H. Ringhofer, “(111)-cut: characterisation and comparision with the general cut,” Phys. Rev. E 62, 2863–2870 (2000).
[CrossRef]

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

Phys. Solid State (1)

R. V. Litvinov, S. M. Shandarov, and S. G. Chistyakov, “Two-wave interaction on the photorefractive grating in cubic gyrotropic crystals at strong coupling,” Phys. Solid State 41, 568–572 (2000).

Proc. SPIE (1)

S. M. Shandarov, A. Reshet’ko, A. A. Emelyanov, O. Kobozev, M. Krause, Y. F. Kargin, and V. V. Volkov, “Two-beam coupling in sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, Z. I. Alferov, Y. V. Gulyaev, and D. R. Pape, eds., Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Other (3)

V. V. Shepelevich, S. F. Nichiporko, A. E. Zagorskiy, N. N. Egorov, Yi Hu, K. H. Ringhofer, and E. Shamonina, “Gain optimization at two-wave mixing in cubic photorefractive piezocrystals of (111)-cut,” in Advances in Photorefractive Materials, Effects, and Devices, P. E. Andersen, P. M. Johansen, H. C. Pedersen, P. M. Petersen, and M. Saffman, eds., Vol. 27 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 353–360.

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Heidelberg, 1991).

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

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Figures (4)

Fig. 1
Fig. 1

Optical configuration of (110)- and (111)-cut crystals: (a) (110) cut. L geometry, (K ‖ [001]), T geometry, (K ‖ [110]), D geometry, (K ‖ [111]); (b) (111) cut. T geometry, (K ‖ [110]), D geometry, (K ‖ [112]).

Fig. 2
Fig. 2

G(d) for L geometry. KrD=1, providing the maximum coupling coefficient. Nt=1022 m-3; λ=633 nm for BTO and λ=515 nm for BSO; the other parameters are as in Refs. 9 and 11. The UPA (dotted curves), the CGA (dashed curves), the combined solution (solid curves), and numeric data (points) are shown. There are two curves of each type, for initial polarization angles ±45° against grating vector K.

Fig. 3
Fig. 3

G(β) for BTO; d=10 mm. (a) φ=(ϱd+ϕ0)/2, providing the maximum parallel component, and (b) φ=(ϱd+ϕ0-90°)/2, providing the maximum perpendicular component. The other parameters are as in Fig. 2. The UPA, the CGA, (a) the combined solution, and (b) the combined solutions that take into account second- and third-order gains of perpendicular components, and numeric data (points) are shown.

Fig. 4
Fig. 4

G(d) for D geometry; β=10. The other parameters are as in Fig. 2. The UPA, (dotted lines), the CGA, the first order approximation, the second-order approximation, the combined solution, and numerical data are shown.

Equations (41)

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dSdz=iϱσ2S+12Γm*Hˆ(n)R,
dRdz=iϱσ2R-12ΓmHˆ(n)S,
Γ=πn3r41Sλ KkBT/e1+(KrD)2,m=2S*·R|S|2+|R|2.
Hˆ(n)=1r41S|Esc| eˆx|ΔBˆ|eˆxeˆx|ΔBˆ|eˆyeˆy|ΔBˆ|eˆxeˆy|ΔBˆ|eˆy,
ΔBmn=(rmnpSnp+pmnklEnlγkiepijnpnj)Esc
Γik=cijklEnjnl,
σ1=0110,σ2=0-ii0,σ3=100-1,
Hˆ=H01ˆ+H·σ,
G=|S(z)|2-|S(0)|2|S(0)|2,
eˆ=cos φsin φ,eˆ=-sin φcos φ.
ddz ss=Γ(rs+rs)HH×H×Hrr,
ddz rr=-Γ(rs+rs)HH×H×Hss,
H=H0+H3 cos(2φ-2ϱz)+H1 sin(2φ-2ϱz),
H=H0-H3 cos(2φ-2ϱz)-H1 sin(2φ-2ϱz),
H×=H1 cos(2φ-2ϱz)-H3 sin(2φ-2ϱz)
H1=H sin ϕ0,H3=H cos ϕ0,
H=H0+H cos(2φ-2ϱz-ϕ0),
H=H0-H cos(2φ-2ϱz-ϕ0),
H×=-H sin(2φ-2ϱz-ϕ0).
s(1)(z)s(0)=Γzr(0)2(H0+Hτ cos ϑ),
s(1)(z)s(0)=-Γzr(0)2(Hτ sin ϑ),
s(2)(z)s(0)=Γ2z22r(0)2{[1-3s(0)2](H0+Hτ cos ϑ)2-s(0)2(Hτ sin ϑ)2},
s(2)(z)s(0)=Γ2z2H8r(0)2[1-2s(0)2]×H2ϱz-sin 2ϱzϱ2z2-2r2 sin 2ϑ+4H0 sin ϱz cos ϑ-ϱz cos(ϱz-ϑ)ϱ2z2-2s(0)2H 2ϱz-sin 2ϱzϱ2z2-4H0τ sin ϑ.
sp(z)s(0)={s(0)2+r(0)2 exp[-2Γz(H0+Hτ cos ϑ)]}-1/2.
s(z)s(0)=sp(z)s(0)-Γ2z22r(0)2s(0)2(Hτ sin ϑ)2.
G(1)=2ββ+1Γz(H0+Hτ cos ϑ),
G(2)=β(β-1)(β+1)2(Γz)2[2(H0+Hτ cos ϑ)2+(Hτ sin θ)2],
G=β{1-exp[-2Γz(H0+Hτ cos ϑ)]}1+β exp[-2Γz(H0+Hτ cos ϑ)]+β(β-1)(β+1)2(Γz)2(Hτ sin ϑ)2,
Giso=β{1-exp[-2Γz(H0+Hτ)]}1+β exp[-2Γz(H0+Hτ)]
Ganiso=β[1-exp(-2ΓH0z)1+β exp(-2ΓH0z)+β(β-1)(β+1)2(ΓHzτ)2
Ganiso(3)=β2(β-3)(β+1)3(Γz)3(Hτ)3×H0±H 2ϱz-sin 2ϱz4ϱz sin ϱz,
dT±dz=-i(ν±01ˆ+ν±·σ)T±,
T±=exp(-iν±0z)(cos νz1ˆ-i sin νzν ν±·σ)T±(0),
S(z)R(z)=Xˆ+Xˆ--Xˆ-Xˆ+S(0)R(0),
Xˆ+Xˆ-=cos ν0z-sin ν0zsin ν0zcos ν0z×cos νz1ˆ+sin νzνiϱσ2sin νzν(ν1σ1+ν3σ3),
Gh=f(ν0)2cos2 νz+ϱ2ν2 sin2 νz+g(ν0)2 sin2 νz×1-ϱ2ν2+2 f(ν0)g(ν0) sin νzν×ν3cos νz cos 2φ+ϱν sin νz sin 2φ+ν1cos νz sin 2φ-ϱν sin νz cos 2φ-1,
Gh(1)=2ββ+1Γz(H0+Hτh cos ϑh),
Gh(2)=β(β-1)(β+1)2(Γz)2[(H0+Hτh cos ϑh)2+(Hτh sin ϑh)2].
ddz ss=ΓHH×s.
ss(0)=exp[Γz(H0+Hτ cos ϑ)],
ss(0)=-H 0z sin(ϑ(ς)-ϱς)×exp{Γς[H0+Hτ(ς)cos ϑ(ς)]}dς,

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