Abstract

We study the simultaneous influence of optical activity, piezoelectric effect, and elasto-optic effect on two-wave mixing (TWM) under diffusion recording in photorefractive Bi12TiO20 and Bi12SiO20 crystals and find numerically the maximum of the TWM gain as a function of the orientation of the grating vector. Contrary to widespread belief, the grating orientation K[111] is the optimum orientation only if optical activity is negligibly small. Nonzero optical activity results in a strong dependence of the optimum grating orientation on the crystal thickness. The strongest deviation of the optimum from the [111] direction is achieved for ϱd=180°, where ϱ is the rotatory power and d is the crystal thickness. Our theory explains well prior results for crystals of moderate thickness and predicts new effects for thick (e.g., fiberlike) crystals.

© 1998 Optical Society of America

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  7. N. V. Kukhtarev, T. I. Semenec, and P. Hribek, “The influence of photoelasticity on the self-diffraction of light in cubic photorefractive crystals,” Ferroelectr. Lett. Sect. 13, 29–35 (1991).
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  22. G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Günter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).
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  23. P. Mathey, “Photorefractive-gain dependence on piezoelectric and photoelastic effects in barium titanate,” Phys. Rev. E 55, 7782–7784 (1997).
    [CrossRef]
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    [CrossRef]
  25. A. Kiessling and L. Wenke, “Real-time holographic interferometry using degenerated four-wave mixing in Bi12TiO20,” Int. J. Optoelectron. 8, 617–627 (1993).
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    [CrossRef]
  33. A. Marrakchi, R. V. Johnson, and A. R. Tanguay, Jr., “Polarization properties of photorefractive diffraction in electrooptic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321–336 (1986).
    [CrossRef]
  34. F. Vachss and L. Hesselink, “Measurements of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
    [CrossRef]
  35. C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
    [CrossRef]
  36. A. Yariv and P. Yeh, Optical Waves in Crystals, Wiley Series in Pure and Applied Optics (Wiley, New York, 1984), pp. 223–237.
  37. E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
    [CrossRef]
  38. A. A. Kamshilin, V. Prokofiev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).
    [CrossRef]
  39. A. A. Kamshilin, E. Raita, and A. V. Khomenko, “Intensity redistribution in a thin photorefractive crystal caused by strong fanning effect and internal reflections,” J. Opt. Soc. Am. B 13, 2536–2543 (1996).
    [CrossRef]

1997 (5)

V. V. Shepelevich, N. N. Egorov, P. I. Ropot, and P. P. Khomutovskiy, “Extremal conditions of diffraction and two-wave mixing in cubic gyrotropic photorefractive piezocrystals,” in Optical Organic and Semiconductor Inorganic Materials, E. A. Siliush, A. Medvids, A. R. Lusis, and A. O. Ozols, eds., Proc. SPIE 2968, 301–306 (1997).
[CrossRef]

V. V. Shepelevich, “Diffraction and two-wave coupling in cubic gyrotropic piezoelectric crystals of an arbitrary cut: general relations,” Opt. Spectrosc. 83, 161–165 (1997).

P. Mathey, “Photorefractive-gain dependence on piezoelectric and photoelastic effects in barium titanate,” Phys. Rev. E 55, 7782–7784 (1997).
[CrossRef]

D. Dirksen, F. Matthes, S. Riehemann, and G. von Bally, “Phase shifting holographic double expose interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310 (1997).
[CrossRef]

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

1996 (3)

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. Emelyanov, O. Kobozev, A. Reshet’ko, V. V. Volkov, and Yu. F. Kargin, “Photorefractive properties of doped sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, V. I. Emelýanov and V. Y. Panchenko, eds., Proc. SPIE 2801, 221–230 (1996).
[CrossRef]

A. A. Kamshilin, E. Raita, and A. V. Khomenko, “Intensity redistribution in a thin photorefractive crystal caused by strong fanning effect and internal reflections,” J. Opt. Soc. Am. B 13, 2536–2543 (1996).
[CrossRef]

1995 (4)

M. Zgonik, K. Nakagawa, and P. Günter, “Electro-optic and dielectric properties of photorefractive BaTiO3 and KNbO3,” J. Opt. Soc. Am. B 12, 1416–1421 (1995).
[CrossRef]

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Günter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).
[CrossRef] [PubMed]

A. A. Kamshilin, V. Prokofiev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).
[CrossRef]

H. J. Eichler, Y. Ding, and B. Smandek, “Photorefractive two-wave mixing in semiconductors of the 4¯3m space group in general spatial orientation,” Phys. Rev. A 52, 2411–2418 (1995).
[CrossRef] [PubMed]

1994 (3)

1993 (2)

A. Kiessling and L. Wenke, “Real-time holographic interferometry using degenerated four-wave mixing in Bi12TiO20,” Int. J. Optoelectron. 8, 617–627 (1993).

E. Anastassakis, “Photorefractive effects in cubic crystals: explicit treatment of the piezoelectric contribution,” IEEE J. Quantum Electron. 29, 2239–2244 (1993).
[CrossRef]

1992 (1)

S. M. Shandarov, “Influence of piezoelectric effect on photorefractive gratings in electro-optic crystals,” Appl. Phys. A 55, 91–96 (1992).
[CrossRef]

1991 (5)

P. Günter and M. Zgonik, “Clamped–unclamped electro-optic coefficient dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
[CrossRef]

S. M. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. 70, 627–630 (1991).

V. V. Shepelevich and N. N. Egorov, “Light diffraction on holographic gratings in gyrotropic cubic photorefractive crystals,” Opt. Spectrosc. 71, 600–603 (1991).

N. V. Kukhtarev, T. I. Semenec, and P. Hribek, “The influence of photoelasticity on the self-diffraction of light in cubic photorefractive crystals,” Ferroelectr. Lett. Sect. 13, 29–35 (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 (1)

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

1989 (2)

A. E. Mandel, S. M. Shandarov, and V. V. Shepelevich, “Influence of piezoelectric effect and gyrotropy on light diffraction in cubic photorefractive crystals,” Opt. Spectrosc. 67, 481–484 (1989).

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[CrossRef]

1988 (1)

A. Mandel, N. Khatkov, and S. Shandarov, “Light diffraction in holographic arrays—different mechanisms of photorefractive effect in ferroelectrics,” Ferroelectrics 83, 215–220 (1988).
[CrossRef]

1987 (2)

F. Vachss and L. Hesselink, “Measurements of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
[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).

1986 (2)

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

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

1975 (1)

A. J. Fox and T. M. Bruton, “Electro-optic effects in the optically active compounds Bi12TiO20 and Bi40Ga2O63,” Appl. Phys. Lett. 27, 360–362 (1975).
[CrossRef]

1966 (1)

Anastassakis, E.

E. Anastassakis, “Photorefractive effects in cubic crystals: explicit treatment of the piezoelectric contribution,” IEEE J. Quantum Electron. 29, 2239–2244 (1993).
[CrossRef]

Anderson, D. Z.

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Günter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).
[CrossRef] [PubMed]

Ballman, A. A.

Bruton, T. M.

A. J. Fox and T. M. Bruton, “Electro-optic effects in the optically active compounds Bi12TiO20 and Bi40Ga2O63,” Appl. Phys. Lett. 27, 360–362 (1975).
[CrossRef]

Cedilnik, G.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Czaia, L.

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Günter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).
[CrossRef] [PubMed]

Ding, Y.

H. J. Eichler, Y. Ding, and B. Smandek, “Photorefractive two-wave mixing in semiconductors of the 4¯3m space group in general spatial orientation,” Phys. Rev. A 52, 2411–2418 (1995).
[CrossRef] [PubMed]

Dirksen, D.

D. Dirksen, F. Matthes, S. Riehemann, and G. von Bally, “Phase shifting holographic double expose interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310 (1997).
[CrossRef]

Egorov, N. N.

V. V. Shepelevich, N. N. Egorov, P. I. Ropot, and P. P. Khomutovskiy, “Extremal conditions of diffraction and two-wave mixing in cubic gyrotropic photorefractive piezocrystals,” in Optical Organic and Semiconductor Inorganic Materials, E. A. Siliush, A. Medvids, A. R. Lusis, and A. O. Ozols, eds., Proc. SPIE 2968, 301–306 (1997).
[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]

V. V. Shepelevich and N. N. Egorov, “Light diffraction on holographic gratings in gyrotropic cubic photorefractive crystals,” Opt. Spectrosc. 71, 600–603 (1991).

Eichler, H. J.

H. J. Eichler, Y. Ding, and B. Smandek, “Photorefractive two-wave mixing in semiconductors of the 4¯3m space group in general spatial orientation,” Phys. Rev. A 52, 2411–2418 (1995).
[CrossRef] [PubMed]

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.

S. M. Shandarov, A. Emelyanov, O. Kobozev, A. Reshet’ko, V. V. Volkov, and Yu. F. Kargin, “Photorefractive properties of doped sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, V. I. Emelýanov and V. Y. Panchenko, eds., Proc. SPIE 2801, 221–230 (1996).
[CrossRef]

Fox, A. J.

A. J. Fox and T. M. Bruton, “Electro-optic effects in the optically active compounds Bi12TiO20 and Bi40Ga2O63,” Appl. Phys. Lett. 27, 360–362 (1975).
[CrossRef]

Günter, P.

Hall, T. J.

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[CrossRef]

Hesselink, L.

F. Vachss and L. Hesselink, “Measurements of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
[CrossRef]

Hribek, P.

N. V. Kukhtarev, T. I. Semenec, and P. Hribek, “The influence of photoelasticity on the self-diffraction of light in cubic photorefractive crystals,” Ferroelectr. Lett. Sect. 13, 29–35 (1991).
[CrossRef]

Izvanov, A. A.

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

Jaaskelainen, T.

A. A. Kamshilin, V. Prokofiev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).
[CrossRef]

Johnson, R. V.

Kamshilin, A. A.

A. A. Kamshilin, E. Raita, and A. V. Khomenko, “Intensity redistribution in a thin photorefractive crystal caused by strong fanning effect and internal reflections,” J. Opt. Soc. Am. B 13, 2536–2543 (1996).
[CrossRef]

A. A. Kamshilin, V. Prokofiev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).
[CrossRef]

Kargin, Yu. F.

S. M. Shandarov, A. Emelyanov, O. Kobozev, A. Reshet’ko, V. V. Volkov, and Yu. F. Kargin, “Photorefractive properties of doped sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, V. I. Emelýanov and V. Y. Panchenko, eds., Proc. SPIE 2801, 221–230 (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).

Khatkov, N.

A. Mandel, N. Khatkov, and S. Shandarov, “Light diffraction in holographic arrays—different mechanisms of photorefractive effect in ferroelectrics,” Ferroelectrics 83, 215–220 (1988).
[CrossRef]

Khatkov, N. D.

S. M. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. 70, 627–630 (1991).

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

Khomenko, A. V.

Khomutovskiy, P. P.

V. V. Shepelevich, N. N. Egorov, P. I. Ropot, and P. P. Khomutovskiy, “Extremal conditions of diffraction and two-wave mixing in cubic gyrotropic photorefractive piezocrystals,” in Optical Organic and Semiconductor Inorganic Materials, E. A. Siliush, A. Medvids, A. R. Lusis, and A. O. Ozols, eds., Proc. SPIE 2968, 301–306 (1997).
[CrossRef]

Kiessling, A.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

A. Kiessling and L. Wenke, “Real-time holographic interferometry using degenerated four-wave mixing in Bi12TiO20,” Int. J. Optoelectron. 8, 617–627 (1993).

Kobozev, O.

S. M. Shandarov, A. Emelyanov, O. Kobozev, A. Reshet’ko, V. V. Volkov, and Yu. F. Kargin, “Photorefractive properties of doped sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, V. I. Emelýanov and V. Y. Panchenko, eds., Proc. SPIE 2801, 221–230 (1996).
[CrossRef]

Kowarschik, R.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, T. I. Semenec, and P. Hribek, “The influence of photoelasticity on the self-diffraction of light in cubic photorefractive crystals,” Ferroelectr. Lett. Sect. 13, 29–35 (1991).
[CrossRef]

Lenzo, P. V.

Litvinov, R.

Mandel, A.

A. Mandel, N. Khatkov, and S. Shandarov, “Light diffraction in holographic arrays—different mechanisms of photorefractive effect in ferroelectrics,” Ferroelectrics 83, 215–220 (1988).
[CrossRef]

Mandel, A. E.

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

A. E. Mandel, S. M. Shandarov, and V. V. Shepelevich, “Influence of piezoelectric effect and gyrotropy on light diffraction in cubic photorefractive crystals,” Opt. Spectrosc. 67, 481–484 (1989).

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

Mann, M.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Marrakchi, A.

Mathey, P.

P. Mathey, “Photorefractive-gain dependence on piezoelectric and photoelastic effects in barium titanate,” Phys. Rev. E 55, 7782–7784 (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]

Matthes, F.

D. Dirksen, F. Matthes, S. Riehemann, and G. von Bally, “Phase shifting holographic double expose interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310 (1997).
[CrossRef]

Montemezzani, G.

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Günter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).
[CrossRef] [PubMed]

Nakagawa, K.

Pauliat, G.

Powell, A. K.

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[CrossRef]

Prokofiev, V.

A. A. Kamshilin, V. Prokofiev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).
[CrossRef]

Raita, E.

Reshet’ko, A.

S. M. Shandarov, A. Emelyanov, O. Kobozev, A. Reshet’ko, V. V. Volkov, and Yu. F. Kargin, “Photorefractive properties of doped sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, V. I. Emelýanov and V. Y. Panchenko, eds., Proc. SPIE 2801, 221–230 (1996).
[CrossRef]

Riehemann, S.

D. Dirksen, F. Matthes, S. Riehemann, and G. von Bally, “Phase shifting holographic double expose interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310 (1997).
[CrossRef]

Ringhofer, K. H.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Roosen, G.

Ropot, P. I.

V. V. Shepelevich, N. N. Egorov, P. I. Ropot, and P. P. Khomutovskiy, “Extremal conditions of diffraction and two-wave mixing in cubic gyrotropic photorefractive piezocrystals,” in Optical Organic and Semiconductor Inorganic Materials, E. A. Siliush, A. Medvids, A. R. Lusis, and A. O. Ozols, eds., Proc. SPIE 2968, 301–306 (1997).
[CrossRef]

Semenec, T. I.

N. V. Kukhtarev, T. I. Semenec, and P. Hribek, “The influence of photoelasticity on the self-diffraction of light in cubic photorefractive crystals,” Ferroelectr. Lett. Sect. 13, 29–35 (1991).
[CrossRef]

Shamonina, E.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Shandarov, S.

R. Litvinov and S. Shandarov, “Influence of piezoelectric and photoelastic effects on pulse hologram recording in photorefractive crystals,” J. Opt. Soc. Am. B 11, 1204–1210 (1994).
[CrossRef]

A. Mandel, N. Khatkov, and S. Shandarov, “Light diffraction in holographic arrays—different mechanisms of photorefractive effect in ferroelectrics,” Ferroelectrics 83, 215–220 (1988).
[CrossRef]

Shandarov, S. M.

S. M. Shandarov, A. Emelyanov, O. Kobozev, A. Reshet’ko, V. V. Volkov, and Yu. F. Kargin, “Photorefractive properties of doped sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, V. I. Emelýanov and V. Y. Panchenko, eds., Proc. SPIE 2801, 221–230 (1996).
[CrossRef]

S. M. Shandarov, “Influence of piezoelectric effect on photorefractive gratings in electro-optic crystals,” Appl. Phys. A 55, 91–96 (1992).
[CrossRef]

S. M. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. 70, 627–630 (1991).

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

A. E. Mandel, S. M. Shandarov, and V. V. Shepelevich, “Influence of piezoelectric effect and gyrotropy on light diffraction in cubic photorefractive crystals,” Opt. Spectrosc. 67, 481–484 (1989).

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).

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

Shepelevich, V.

Shepelevich, V. V.

V. V. Shepelevich, N. N. Egorov, P. I. Ropot, and P. P. Khomutovskiy, “Extremal conditions of diffraction and two-wave mixing in cubic gyrotropic photorefractive piezocrystals,” in Optical Organic and Semiconductor Inorganic Materials, E. A. Siliush, A. Medvids, A. R. Lusis, and A. O. Ozols, eds., Proc. SPIE 2968, 301–306 (1997).
[CrossRef]

V. V. Shepelevich, “Diffraction and two-wave coupling in cubic gyrotropic piezoelectric crystals of an arbitrary cut: general relations,” Opt. Spectrosc. 83, 161–165 (1997).

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]

S. M. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. 70, 627–630 (1991).

V. V. Shepelevich and N. N. Egorov, “Light diffraction on holographic gratings in gyrotropic cubic photorefractive crystals,” Opt. Spectrosc. 71, 600–603 (1991).

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

A. E. Mandel, S. M. Shandarov, and V. V. Shepelevich, “Influence of piezoelectric effect and gyrotropy on light diffraction in cubic photorefractive crystals,” Opt. Spectrosc. 67, 481–484 (1989).

Smandek, B.

H. J. Eichler, Y. Ding, and B. Smandek, “Photorefractive two-wave mixing in semiconductors of the 4¯3m space group in general spatial orientation,” Phys. Rev. A 52, 2411–2418 (1995).
[CrossRef] [PubMed]

Solymar, L.

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

Spencer, E. G.

Stace, C.

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[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, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39–116 (1994), and references cited therein.
[CrossRef]

Tanguay, Jr., A. R.

Vachss, F.

F. Vachss and L. Hesselink, “Measurements of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
[CrossRef]

Volkov, V. V.

S. M. Shandarov, A. Emelyanov, O. Kobozev, A. Reshet’ko, V. V. Volkov, and Yu. F. Kargin, “Photorefractive properties of doped sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, V. I. Emelýanov and V. Y. Panchenko, eds., Proc. SPIE 2801, 221–230 (1996).
[CrossRef]

von Bally, G.

D. Dirksen, F. Matthes, S. Riehemann, and G. von Bally, “Phase shifting holographic double expose interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310 (1997).
[CrossRef]

Walsh, K.

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[CrossRef]

Webb, D. J.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Wenke, L.

A. Kiessling and L. Wenke, “Real-time holographic interferometry using degenerated four-wave mixing in Bi12TiO20,” Int. J. Optoelectron. 8, 617–627 (1993).

Zgonik, M.

Zozulya, A. A.

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Günter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. A (1)

S. M. Shandarov, “Influence of piezoelectric effect on photorefractive gratings in electro-optic crystals,” Appl. Phys. A 55, 91–96 (1992).
[CrossRef]

Appl. Phys. B (1)

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, and K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

A. J. Fox and T. M. Bruton, “Electro-optic effects in the optically active compounds Bi12TiO20 and Bi40Ga2O63,” Appl. Phys. Lett. 27, 360–362 (1975).
[CrossRef]

Ferroelectr. Lett. Sect. (1)

N. V. Kukhtarev, T. I. Semenec, and P. Hribek, “The influence of photoelasticity on the self-diffraction of light in cubic photorefractive crystals,” Ferroelectr. Lett. Sect. 13, 29–35 (1991).
[CrossRef]

Ferroelectrics (2)

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

A. Mandel, N. Khatkov, and S. Shandarov, “Light diffraction in holographic arrays—different mechanisms of photorefractive effect in ferroelectrics,” Ferroelectrics 83, 215–220 (1988).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. A. Kamshilin, V. Prokofiev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).
[CrossRef]

E. Anastassakis, “Photorefractive effects in cubic crystals: explicit treatment of the piezoelectric contribution,” IEEE J. Quantum Electron. 29, 2239–2244 (1993).
[CrossRef]

Int. J. Optoelectron. (1)

A. Kiessling and L. Wenke, “Real-time holographic interferometry using degenerated four-wave mixing in Bi12TiO20,” Int. J. Optoelectron. 8, 617–627 (1993).

J. Opt. Soc. Am. B (6)

Opt. Commun. (4)

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

F. Vachss and L. Hesselink, “Measurements of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
[CrossRef]

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[CrossRef]

D. Dirksen, F. Matthes, S. Riehemann, and G. von Bally, “Phase shifting holographic double expose interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310 (1997).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (4)

A. E. Mandel, S. M. Shandarov, and V. V. Shepelevich, “Influence of piezoelectric effect and gyrotropy on light diffraction in cubic photorefractive crystals,” Opt. Spectrosc. 67, 481–484 (1989).

V. V. Shepelevich, “Diffraction and two-wave coupling in cubic gyrotropic piezoelectric crystals of an arbitrary cut: general relations,” Opt. Spectrosc. 83, 161–165 (1997).

S. M. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. 70, 627–630 (1991).

V. V. Shepelevich and N. N. Egorov, “Light diffraction on holographic gratings in gyrotropic cubic photorefractive crystals,” Opt. Spectrosc. 71, 600–603 (1991).

Optoelectronics (1)

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

Phys. Rev. A (2)

H. J. Eichler, Y. Ding, and B. Smandek, “Photorefractive two-wave mixing in semiconductors of the 4¯3m space group in general spatial orientation,” Phys. Rev. A 52, 2411–2418 (1995).
[CrossRef] [PubMed]

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Günter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

P. Mathey, “Photorefractive-gain dependence on piezoelectric and photoelastic effects in barium titanate,” Phys. Rev. E 55, 7782–7784 (1997).
[CrossRef]

Proc. SPIE (2)

S. M. Shandarov, A. Emelyanov, O. Kobozev, A. Reshet’ko, V. V. Volkov, and Yu. F. Kargin, “Photorefractive properties of doped sillenite crystals,” in Nonlinear Optics of Low-Dimensional Structures and New Materials, V. I. Emelýanov and V. Y. Panchenko, eds., Proc. SPIE 2801, 221–230 (1996).
[CrossRef]

V. V. Shepelevich, N. N. Egorov, P. I. Ropot, and P. P. Khomutovskiy, “Extremal conditions of diffraction and two-wave mixing in cubic gyrotropic photorefractive piezocrystals,” in Optical Organic and Semiconductor Inorganic Materials, E. A. Siliush, A. Medvids, A. R. Lusis, and A. O. Ozols, eds., Proc. SPIE 2968, 301–306 (1997).
[CrossRef]

Rep. Prog. Phys. (1)

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39–116 (1994), and references cited therein.
[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 (6)

V. V. Shepelevich, “Optimization of the energy transfer in cubic photorefractive piezocrystals,” in Technical Digest on Topical Meeting on Photorefractive Materials, Effects, and Devices (Ukrainian Academy of Sciences, Theophania, Kiev, Ukraine, 1993), pp. 128–131.

V. V. Shepelevich, N. N. Egorov, G. von Bally, S. G. Odoulov, and P. P. Khomutovskiy, “Optimization of energy exchange of light waves in crystal BTO by selection of grating vector orientation and thickness of crystal,” in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of Japan, Tokyo, Japan, 1997), pp. 319–321.

M. P. Georges and P. C. Lemaire, “Real-time holographic interferometry with sillenite crystals: a breadboard system for industrial applications, I and II,” in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of Japan, Tokyo, Japan, 1997), pp. 495–498 and 637–640 and references cited therein.

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, Germany, 1991), pp. 233–239.

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

A. Yariv and P. Yeh, Optical Waves in Crystals, Wiley Series in Pure and Applied Optics (Wiley, New York, 1984), pp. 223–237.

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Figures (5)

Fig. 1
Fig. 1

Dependences S|φmax(ξ) (dashed curves), S|φmin(ξ) (dotted curves), and 〈S(ξ)〉 (solid curves) for various sets of parameters (Ref. 2): (a) no elasto-optic contribution, (b) BTO (r41S=4.75×10-12 m/V, e14=1.1 C/m2, p{1,2,4}={0.173, -0.0015,-0.005}, c{1,2,4}={13.7, 2.8, 2.6}×1010 N/m2), (c) BSO (r41S =5.0×10-12 m/V, e14=1.12 C/m2, p{1,2,4}={0.16, 0.125,0.015}, c{1,2,4}={12.96, 2.99, 2.45}×1010 N/m2). Note that the curves in (a) coincide for BTO and BSO parameters.

Fig. 2
Fig. 2

Dependence of the normalized maximum gain on the grating orientation and the crystal thickness: (a) BTO without and (b) BTO with elasto-optic contribution [λ=633 nm, n=2.58, ¯=47, ϱ=6.3°/mm (Refs. 2, 29, and 32)]; (c) BSO with elasto-optic contribution [λ=514.5 nm, n=2.615, ¯=56, ϱ=38.6°/mm (Refs. 29 and 33)]. Nt=1022 m-3 (Ref. 29), K=2×106 m-1, and β=100. The other parameters are as in Fig. 1.

Fig. 3
Fig. 3

Thickness dependence of (a) the optimum grating orientation, (b) the optimum polarization angle, and (c) the maximum gain for the three cases of Fig. 2. The initial value for all three curves, ξmax(ϱd=0°)125.5°, corresponds to the grating orientation K[111]. This grating orientation is the optimum one when optical activity is neglected. The vertical lines at ϱd=180° and 360° in (b) indicate gain independence of the polarization angle.

Fig. 4
Fig. 4

Thickness dependence of (a) the envelope functions for the gain at the optimum grating orientation, G|φmax(ξmax) (solid curve) and G|φmin(ξmax) (dashed curve), and (b) the corresponding polarization angles φmax (solid curves) and φmin (dashed curves). The vertical lines at ϱd=180° and 360° in (b) indicate gain independence of the polarization angle. BTO parameters are used [as in Fig. 2(b)].

Fig. 5
Fig. 5

Thickness dependence of the increase of the maximum gain Δmax by choosing the optimum grating orientation rather than K[111] in BTO (solid curve) and BSO (dotted–dashed curve). Parameters are as in Figs. 2(b) and 2(c).

Equations (24)

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

Es=iϱσ2Es+ig*Σ(K/K)Ep,
Ep=iϱσ2Ep+igΣ(K/K)Es,
g=iΓ m2=-πn3r41Sλ Esc,
Γ=πn3r41Sλ KkBT/e1+(KrD)2,m=2Es*Ep|Es|2+|Ep|2.
Σ11=-e14r41S cos ξ sin2 ξ-Ap1+2Bp2C,
Σ22=-(cos ξ)1+e14r41S sin2 ξ×-Ap2+B(p1+p2+2p4)C,
Σ12=-(sin ξ)1+e14p4r41S×-A sin2 ξ+2B cos2 ξC.
A=4(c2+c4)cos2 ξ-(c1+c2)sin2 ξ-2c4,
B=2c1 cos2 ξ-(c2-c4)sin2 ξ,
C=(c1 cos2 ξ+c4 sin2 ξ)[(c1+c2)sin2 ξ+2c4]-2(c2+c4)2 sin2 ξ cos2 ξ.
Σ11=0,Σ22=-cos ξ,Σ12=-sin ξ.
S(ξ)=es|Σ(ξ)|ep,
ep=es=[cos ψ, sin ψ exp(iδ)],
S(ξ)=Σ11(ξ)cos2 ψ+Σ22(ξ)sin2 ψ+Σ12(ξ)sin 2ψ cos δ.
S(ξ)|δextrem=Σ11(ξ)cos2 ψ+Σ22(ξ)sin2 ψ±Σ12(ξ)sin 2ψ.
S(ξ)=Σ11(ξ)+Σ22(ξ)2.
S(90°+ξ)|φmax =-S(90°-ξ)|φmin.
S(90°+ξ)=-S(90°-ξ).
G=Γd ββ+1 [(Σ11+Σ22)+(Σ11-Σ22)×τ cos(2φ-ϱd)+2Σ12τ sin(2φ-ϱd)],
G=-Γd ββ+1 {2τ sin ξ sin(2φ-ϱd)+(cos ξ)[1-τ cos(2φ-ϱd)]}.
ξ1,2max =180°±arctan9τ2-12
2φ1,2max-ϱd=180°arccos 13τ.
ξmax=180°,
2φmax-ϱd=180°forτ>00forτ<0anyforτ=0.

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