Abstract

We present a theory of resonant photorefractive wave coupling in cubic photorefractive crystals that are in general optically active. This theory includes the resonance enhancement of the photorefractive response in a constant applied electric field, the influence of photoelasticity, and the spatial inhomogeneity of the light intensity. In a unified manner, it allows one to describe the polarization and energy properties of two-wave coupling for the optical configurations relevant to experiment. Applications of the theory are given to photorefractive crystals of the sillenite family.

© 2000 Optical Society of America

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    [CrossRef]
  7. E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kießling, and R. Kowarschik, “Optimum orientation of phase volume gratings in photorefractive sillenites: is it always [111]?,” J. Opt. Soc. Am. B 15, 2552–2559 (1998).
    [CrossRef]
  8. Y. Ding and H. J. Eichler, “Crystal orientation dependence of the photorefractive four-wave mixing in compound semiconductors of symmetry group 4¯3m,” Opt. Commun. 110, 456–464 (1994).
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    [CrossRef]
  13. P. Refregier, 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).
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  26. H. C. Ellin and L. Solymar, “Light scattering in bismuth silicate: matching of experimental results,” Opt. Commun. 130, 85–88 (1996).
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  30. 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]
  31. T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
    [CrossRef]
  32. B. I. Sturman, A. I. Chernykh, E. Shamonina, V. P. Kamenov, and K. H. Ringhofer, “Rigorous three-dimensional theory of the subharmonic instability in sillenite,” J. Opt. Soc. Am. B 16, 1099–1103 (1999).
    [CrossRef]
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    [CrossRef]

1999 (2)

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 6, 3332–3352 (1999).
[CrossRef]

B. I. Sturman, A. I. Chernykh, E. Shamonina, V. P. Kamenov, and K. H. Ringhofer, “Rigorous three-dimensional theory of the subharmonic instability in sillenite,” J. Opt. Soc. Am. B 16, 1099–1103 (1999).
[CrossRef]

1998 (4)

1997 (2)

1996 (4)

H. C. Ellin and L. Solymar, “Light scattering in bismuth silicate: matching of experimental results,” Opt. Commun. 130, 85–88 (1996).
[CrossRef]

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,” Proc. SPIE 2969, 202–210 (1996).
[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]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

1995 (3)

1994 (2)

Y. Ding and H. J. Eichler, “Crystal orientation dependence of the photorefractive four-wave mixing in compound semiconductors of symmetry group 4¯3m,” Opt. Commun. 110, 456–464 (1994).
[CrossRef]

V. V. Shepelevich, N. N. Egorov, and V. Shepelevich, “Orientation and polarization effects of two-beam coupling in a cubic optically active photorefractive piezoelectric BSO crystal,” J. Opt. Soc. Am. B 11, 1394–1402 (1994).
[CrossRef]

1993 (1)

1991 (3)

D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[CrossRef]

J. Takacs, D. J. Webb, K. H. Ringhofer, and L. Solymar, “Two-wave mixing in BTO crystals in the presence of detuning,” Opt. Commun. 84, 90–94 (1991).
[CrossRef]

G. Pauliat, P. Mathey, and G. Roosen, “Influence of piezoelectricity on the photorefractive effect,” J. Opt. Soc. Am. B 8, 1942–1946 (1991).
[CrossRef]

1990 (3)

V. V. Shepelevich, S. M. Shandarov, and A. E. Mandel, “Light diffraction by holographic gratings in optically active photorefractive piezocrystal,” Ferroelectrics 110, 235–249 (1990).
[CrossRef]

K. Walsh, A. K. Powell, C. Stace, and T. J. Hall, “Techniques for the enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 288–303 (1990).
[CrossRef]

T. J. Hall, A. K. Powell, and C. Stace, “Vector four-wave mixing in cubic, optically active photorefractive media,” Opt. Commun. 75, 159–164 (1990).
[CrossRef]

1989 (1)

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

1987 (1)

S. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

1986 (1)

1985 (2)

P. Refregier, 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]

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[CrossRef]

1979 (1)

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

Andersen, P. E.

Buchhave, P.

S. Lyukslyutov, P. Buchhave, and M. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67 (1997).
[CrossRef]

Cedilnik, G.

Chernykh, A. I.

Ding, Y.

Y. Ding and H. J. Eichler, “Crystal orientation dependence of the photorefractive four-wave mixing in compound semiconductors of symmetry group 4¯3m,” Opt. Commun. 110, 456–464 (1994).
[CrossRef]

Egorov, N. N.

Eichler, H. J.

Y. Ding and H. J. Eichler, “Crystal orientation dependence of the photorefractive four-wave mixing in compound semiconductors of symmetry group 4¯3m,” Opt. Commun. 110, 456–464 (1994).
[CrossRef]

Ellin, H. C.

H. C. Ellin and L. Solymar, “Light scattering in bismuth silicate: matching of experimental results,” Opt. Commun. 130, 85–88 (1996).
[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,” Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Hall, T. J.

K. Walsh, A. K. Powell, C. Stace, and T. J. Hall, “Techniques for the enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 288–303 (1990).
[CrossRef]

T. J. Hall, A. K. Powell, and C. Stace, “Vector four-wave mixing in cubic, optically active photorefractive media,” Opt. Commun. 75, 159–164 (1990).
[CrossRef]

Huignard, J. P.

P. Refregier, 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]

Jaaskelainen, T.

Johansen, P. M.

Johnson, R. V.

Kamenov, V.

Kamenov, V. P.

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 6, 3332–3352 (1999).
[CrossRef]

B. I. Sturman, A. I. Chernykh, E. Shamonina, V. P. Kamenov, and K. H. Ringhofer, “Rigorous three-dimensional theory of the subharmonic instability in sillenite,” J. Opt. Soc. Am. B 16, 1099–1103 (1999).
[CrossRef]

Kamshilin, A. A.

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,” Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Khat’kov, N. D.

S. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

Kießling, A.

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,” Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Kowarschik, R.

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,” Proc. SPIE 2969, 202–210 (1996).
[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, 949–964 (1979).
[CrossRef]

Lyukslyutov, S.

S. Lyukslyutov, P. Buchhave, and M. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67 (1997).
[CrossRef]

Mandel, A. E.

V. V. Shepelevich, S. M. Shandarov, and A. E. Mandel, “Light diffraction by holographic gratings in optically active photorefractive piezocrystal,” Ferroelectrics 110, 235–249 (1990).
[CrossRef]

Mann, M.

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[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]

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]

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, 949–964 (1979).
[CrossRef]

Marrakchi, A.

Mathey, P.

McClelland, T. E.

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[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]

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 6, 3332–3352 (1999).
[CrossRef]

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, 949–964 (1979).
[CrossRef]

Otten, J.

Pauliat, G.

Pedersen, H. C.

Petrov, M. P.

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[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 6, 3332–3352 (1999).
[CrossRef]

Powell, A. K.

T. J. Hall, A. K. Powell, and C. Stace, “Vector four-wave mixing in cubic, optically active photorefractive media,” Opt. Commun. 75, 159–164 (1990).
[CrossRef]

K. Walsh, A. K. Powell, C. Stace, and T. J. Hall, “Techniques for the enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 288–303 (1990).
[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 6, 3332–3352 (1999).
[CrossRef]

Raita, E.

Rajbenbach, H.

P. Refregier, 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]

Refregier, P.

P. Refregier, 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]

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,” Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Ringhofer, K. H.

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 6, 3332–3352 (1999).
[CrossRef]

B. I. Sturman, A. I. Chernykh, E. Shamonina, V. P. Kamenov, and K. H. Ringhofer, “Rigorous three-dimensional theory of the subharmonic instability in sillenite,” J. Opt. Soc. Am. B 16, 1099–1103 (1999).
[CrossRef]

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kießling, and R. Kowarschik, “Optimum orientation of phase volume gratings in photorefractive sillenites: is it always [111]?,” J. Opt. Soc. Am. B 15, 2552–2559 (1998).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[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]

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]

J. Takacs, D. J. Webb, K. H. Ringhofer, and L. Solymar, “Two-wave mixing in BTO crystals in the presence of detuning,” Opt. Commun. 84, 90–94 (1991).
[CrossRef]

Roosen, G.

Shamonina, 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 6, 3332–3352 (1999).
[CrossRef]

B. I. Sturman, A. I. Chernykh, E. Shamonina, V. P. Kamenov, and K. H. Ringhofer, “Rigorous three-dimensional theory of the subharmonic instability in sillenite,” J. Opt. Soc. Am. B 16, 1099–1103 (1999).
[CrossRef]

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kießling, and R. Kowarschik, “Optimum orientation of phase volume gratings in photorefractive sillenites: is it always [111]?,” J. Opt. Soc. Am. B 15, 2552–2559 (1998).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

Shandarov, S. 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,” Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

V. V. Shepelevich, S. M. Shandarov, and A. E. Mandel, “Light diffraction by holographic gratings in optically active photorefractive piezocrystal,” Ferroelectrics 110, 235–249 (1990).
[CrossRef]

S. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

Shepelevich, V.

Shepelevich, V. V.

V. V. Shepelevich, N. N. Egorov, and V. Shepelevich, “Orientation and polarization effects of two-beam coupling in a cubic optically active photorefractive piezoelectric BSO crystal,” J. Opt. Soc. Am. B 11, 1394–1402 (1994).
[CrossRef]

V. V. Shepelevich, S. M. Shandarov, and A. E. Mandel, “Light diffraction by holographic gratings in optically active photorefractive piezocrystal,” Ferroelectrics 110, 235–249 (1990).
[CrossRef]

Solymar, L.

H. C. Ellin and L. Solymar, “Light scattering in bismuth silicate: matching of experimental results,” Opt. Commun. 130, 85–88 (1996).
[CrossRef]

J. Takacs, D. J. Webb, K. H. Ringhofer, and L. Solymar, “Two-wave mixing in BTO crystals in the presence of detuning,” Opt. Commun. 84, 90–94 (1991).
[CrossRef]

D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[CrossRef]

P. Refregier, 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]

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, 949–964 (1979).
[CrossRef]

Stace, C.

T. J. Hall, A. K. Powell, and C. Stace, “Vector four-wave mixing in cubic, optically active photorefractive media,” Opt. Commun. 75, 159–164 (1990).
[CrossRef]

K. Walsh, A. K. Powell, C. Stace, and T. J. Hall, “Techniques for the enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 288–303 (1990).
[CrossRef]

Stepanov, S.

S. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

Stepanov, S. I.

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[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 6, 3332–3352 (1999).
[CrossRef]

B. I. Sturman, A. I. Chernykh, E. Shamonina, V. P. Kamenov, and K. H. Ringhofer, “Rigorous three-dimensional theory of the subharmonic instability in sillenite,” J. Opt. Soc. Am. B 16, 1099–1103 (1999).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[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]

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]

Takacs, J.

J. Takacs, D. J. Webb, K. H. Ringhofer, and L. Solymar, “Two-wave mixing in BTO crystals in the presence of detuning,” Opt. Commun. 84, 90–94 (1991).
[CrossRef]

Tanguay, J. A. R.

Tuovinen, H.

Vasnetsov, M.

S. Lyukslyutov, P. Buchhave, and M. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67 (1997).
[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, 949–964 (1979).
[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,” Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Walsh, K.

Webb, D. J.

H. C. Pedersen, D. J. Webb, and P. M. Johansen, “Fundamental characteristics of space-charge waves in photorefractive sillenite crystals,” J. Opt. Soc. Am. B 15, 2573–2580 (1998).
[CrossRef]

H. C. Pedersen, D. J. Webb, and P. M. Johansen, “Influence of beam-coupling on photorefractive parametric oscillation in a dc-field-biased Bi12SiO20,” J. Opt. Soc. Am. B 15, 2439–2445 (1998).
[CrossRef]

H. C. Pedersen, P. M. Johansen, and D. J. Webb, “Photorefractive subharmonics: a beam coupling effect?,” J. Opt. Soc. Am. B 15, 1528–1532 (1998).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[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]

D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[CrossRef]

J. Takacs, D. J. Webb, K. H. Ringhofer, and L. Solymar, “Two-wave mixing in BTO crystals in the presence of detuning,” Opt. Commun. 84, 90–94 (1991).
[CrossRef]

Yeh, P.

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

Ferroelectrics (2)

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

V. V. Shepelevich, S. M. Shandarov, and A. E. Mandel, “Light diffraction by holographic gratings in optically active photorefractive piezocrystal,” Ferroelectrics 110, 235–249 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

J. Appl. Phys. (1)

P. Refregier, 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 (12)

K. Walsh, A. K. Powell, C. Stace, and T. J. Hall, “Techniques for the enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 288–303 (1990).
[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]

H. C. Pedersen, D. J. Webb, and P. M. Johansen, “Fundamental characteristics of space-charge waves in photorefractive sillenite crystals,” J. Opt. Soc. Am. B 15, 2573–2580 (1998).
[CrossRef]

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

V. V. Shepelevich, N. N. Egorov, and V. Shepelevich, “Orientation and polarization effects of two-beam coupling in a cubic optically active photorefractive piezoelectric BSO crystal,” J. Opt. Soc. Am. B 11, 1394–1402 (1994).
[CrossRef]

E. Shamonina, V. Kamenov, K. H. Ringhofer, G. Cedilnik, A. Kießling, and R. Kowarschik, “Optimum orientation of phase volume gratings in photorefractive sillenites: is it always [111]?,” J. Opt. Soc. Am. B 15, 2552–2559 (1998).
[CrossRef]

H. C. Pedersen and P. M. Johansen, “Analysis of wave coupling in photorefractive cubic media far from the paraxial limit,” J. Opt. Soc. Am. B 12, 592–599 (1995).
[CrossRef]

H. Tuovinen, A. A. Kamshilin, and T. Jaaskelainen, “Asymmetry of two-wave coupling in cubic photorefractive crystals,” J. Opt. Soc. Am. B 14, 3383–3392 (1997).
[CrossRef]

G. Pauliat, P. Mathey, and G. Roosen, “Influence of piezoelectricity on the photorefractive effect,” J. Opt. Soc. Am. B 8, 1942–1946 (1991).
[CrossRef]

H. C. Pedersen, D. J. Webb, and P. M. Johansen, “Influence of beam-coupling on photorefractive parametric oscillation in a dc-field-biased Bi12SiO20,” J. Opt. Soc. Am. B 15, 2439–2445 (1998).
[CrossRef]

B. I. Sturman, A. I. Chernykh, E. Shamonina, V. P. Kamenov, and K. H. Ringhofer, “Rigorous three-dimensional theory of the subharmonic instability in sillenite,” J. Opt. Soc. Am. B 16, 1099–1103 (1999).
[CrossRef]

H. C. Pedersen, P. M. Johansen, and D. J. Webb, “Photorefractive subharmonics: a beam coupling effect?,” J. Opt. Soc. Am. B 15, 1528–1532 (1998).
[CrossRef]

Opt. Commun. (8)

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, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

H. C. Ellin and L. Solymar, “Light scattering in bismuth silicate: matching of experimental results,” Opt. Commun. 130, 85–88 (1996).
[CrossRef]

D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[CrossRef]

J. Takacs, D. J. Webb, K. H. Ringhofer, and L. Solymar, “Two-wave mixing in BTO crystals in the presence of detuning,” Opt. Commun. 84, 90–94 (1991).
[CrossRef]

Y. Ding and H. J. Eichler, “Crystal orientation dependence of the photorefractive four-wave mixing in compound semiconductors of symmetry group 4¯3m,” Opt. Commun. 110, 456–464 (1994).
[CrossRef]

T. J. Hall, A. K. Powell, and C. Stace, “Vector four-wave mixing in cubic, optically active photorefractive media,” Opt. Commun. 75, 159–164 (1990).
[CrossRef]

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. E (1)

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 6, 3332–3352 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

S. Lyukslyutov, P. Buchhave, and M. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67 (1997).
[CrossRef]

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,” Proc. SPIE 2969, 202–210 (1996).
[CrossRef]

Sov. Phys. Solid State (1)

S. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

Other (4)

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, 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).

W. M. Yen and P. M. Selzer, Laser Spectroscopy of Solids (Springer-Verlag, Berlin, 1981), p. 19.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1969).

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Figures (12)

Fig. 1
Fig. 1

Scheme of a photorefractive resonance dc experiment.

Fig. 2
Fig. 2

Geometrical scheme.

Fig. 3
Fig. 3

Contour lines of the quality factor, Q(E0, Λ)=const, for (a) BSO and (b) BTO parameters.

Fig. 4
Fig. 4

Dependences ν0,1,3(ζ) for (a) BSO and (b) BTO crystals. For the dotted curves the elasto-optic contributions are omitted.

Fig. 5
Fig. 5

Dependences Φ(δ) for (a) α=0.75 cm-1 and (b) α=1.5 cm-1. Quality factor Q=6. Curves 1, 2, 3, and 4 correspond to l=2, 4, 8, and 16 mm. The dotted curves correspond to αl=0.

Fig. 6
Fig. 6

lΦmax versus l for Q=6 and different values of α. Solid curves 1, 2, 3, and 4 correspond to α=0.5, 1, 1.5, and 2.5 cm-1, respectively. The dashed line is plotted for α=0.

Fig. 7
Fig. 7

Dependences of [g(Ω)]max on the crystal thickness for the diagonal optical configuration. Curves 1 and 2 are plotted for E0=10 kV/cm, Λ=5 µm, and α=0.5 cm-1, whereas curves 3 and 4 are obtained for E0=20 kV/cm, Λ=10 µm, and α=1 cm-1. The dashed curves correspond to the simplified model.

Fig. 8
Fig. 8

Positive contour lines of lng(θ, ψ) for the D configuration optimized with respect to the frequency detuning Ω at each set of the arguments. The material parameters correspond to Table 1. (a) E0=10 kV/cm, l=4 mm, and α=0.5 cm-1. (b) E0=20 kV/cm, l=2 mm, and α=1 cm-1. The polarization vectors are directed along E0.

Fig. 9
Fig. 9

Dependences g(δ) for (a) E0  K[1¯1¯1] and (b) E0K[001]. Solid curves 1 and 2 are plotted for ep  E0 and epE0, respectively, on the basis of Eqs. (3) and (6). The dotted curves correspond to the simplified model; they are independent of the polarization state. The relevant parameters are E0=6 kV/cm, Λ=20 µm, l=8 mm, and α=1 cm-1.

Fig. 10
Fig. 10

Contour lines of lng(θ, ψ) for E0  [001], α=1.5 cm-1, and E0=6 kV/cm: (a) l=4 mm and (b) l=8 mm. In case (a) the maximum value of ln g, shown by a dot, is approximately 3.85, whereas in case (b) it equals 4.2.

Fig. 11
Fig. 11

Dependence lng(θ,ψ) for E0[1¯1¯1], α=1.5 cm-1, E0=6 kV/cm, and l=8mm: (a) A1,2 ‖ [1̅1̅1] and (b) A1,2[1¯1¯1]. The maximum values of ln g are approximately 5.35 and 4.4.

Fig. 12
Fig. 12

Dependence lng(θ, ψ) for E0[001], α=1.5 cm-1, E0=6 kV/cm, l=4 mm, and two different input polarizations: (a) left circular and (b) right circular. The maximum values of ln g are approximately 4.23 and 4.25.

Tables (1)

Tables Icon

Table 1 Representative Parameters for BSO and BTO Crystals

Equations (27)

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Elight=[A1 exp(ik1·r-iΩt)+A2 exp(ik2·r)]exp(-iωt)+c.c.,
Esc=nE0eK exp[i(K·r-Ωt)]+c.c.,
ddz+α2A1-iGˆA1=ieKVˆA2,
ddz+α2A2-iGˆA2=ieK*VˆA1.
Gij=sHij(0)+iρδijz,
Vij=sHij,
Hˆ(0)=0sin ζ0sin ζ0cos ζ0.
eK=ω0Eq(1+iED/E0)Ω(E0+iED+iEM)+iω0(E0+iED+iEq)×A1·A2*I0.
eKωKΩ-ωK+iγKA1·A2*I0,
ωK=ω0 EqE0I0KE0γK=ω01+EqEDE02EqEME02.
σˆ1=0110,σˆ2=0-ii0,σˆ3=100-1,
Gˆ=κ·σ;Vˆ=ν01ˆ+ν·σ,
ν0=s(Hxx+Hyy)/2,
ν1=sHxy,ν2=0,ν3=s(Hxx-Hyy)/2,
κ1=sHxy(0),κ2=-ρ,κ3=s(Hxx(0)-Hyy(0))/2.
ddz+α2-iκ·σˆA1=ieK(ν0+ν·σˆ)A2,
ddz+α2-iκ·σˆA2=ieK*(ν0+ν·σˆ)A1.
A1,2(z)=exp(-αz/2)exp[i(κ·σˆ)z]A1,2(0),
exp[i(κ·σ)z]=cos κz1ˆ+iκsin κz(κ·σˆ),
A1,2(z)=I0(0) exp(-αz/2)exp[i(κ·σˆ)z]b1,2.
db1dz=F(b1·ep*)(ν0+q·σˆ)ep,
F={Q-1+i[1-δ exp(αz)]}-1,
q=κ (ν·κ)κ2+ν-κ (ν·κ)κ2×cos 2κz-(ν×κ)κsin 2κz,
(b1·ep*)=(b1·ep*)0 exp0zF[ν0+ep*(q·σˆ)ep]dz,
ln g=2Ql[ν0+ep*(q0·σˆ)ep]Φ,
Φ=1l0l{1+Q-2[1-δ exp(-αz)]2}-1dz.
ln gmax[cm-1]0.8QE0[kV/cm]l[cm]Φmax.

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