Abstract

A simple optical method for determination of crystallographic orientations ±x, ±y, and ±z in photorefractive crystals based on light amplification via backward two-wave mixing (TWM) is presented. We consider a photorefractive Fe-doped lithium niobate crystal (LiNbO3:Fe) with a standard xyz cut as an example to illustrate the principle, manipulation, and experimental results of this method in detail. Also we see that the direction of the light amplification, namely, the direction of the nonreciprocal steady-state energy transfer, strongly depends on the direction of the grating vector with respect to the corresponding crystallographic axes mainly under the diffusion mechanism. Finally, a way of determining the sign of the charge carriers in photorefractive materials is proposed.

© 2006 Optical Society of America

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  1. A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72-74 (1966).
    [CrossRef]
  2. Haiying Xu, Yang Yuan, Kebin Xu, and Yueguang Lu, "Real-time parallel optical logic operation using photorefractive two-wave mixing and fringe-shifting techniques," Appl. Opt. 31, 1769-1773 (1992).
    [CrossRef] [PubMed]
  3. J. Joseph, K. Kamra, K. Singh, and P. K. C. Pillai, "Real-time image processing using selective erasure in photorefractive two-wave mixing," Appl. Opt. 31, 4769-4772 (1992).
    [CrossRef] [PubMed]
  4. G. Cedilnik, M. Esselbach, A. Kiessling, and R. Kowarschik, "Real-time holographic interferometry with double two-wave mixing in photorefractive crystals," Appl. Opt. 39, 2091-2100 (2000).
    [CrossRef]
  5. W. L. Bond, Crystal Technology (Wiley, 1976).
  6. 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]
  7. Simin Liu, Guangyin Zhang, Jinlong Wang, Xiaoyan Ma, and Yuanfen Fu, "Quasi-periodic oscillations in photoinduced conical light scattering from LiNbO3:Fe crystals," Opt. Commun. 70, 185-189 (1989).
    [CrossRef]
  8. M. Chauvet, "Temporal analysis of open-circuit dark photovoltaic spatial solitons," J. Opt. Soc. Am. B 20, 2515-2522 (2003).
    [CrossRef]
  9. P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484-519 (1989).
    [CrossRef]
  10. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).
  11. P. Gunter and J.-P. Huignard, Photorefractive Materials and Their Applications (Springer-Verlag, 1989).
  12. M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, 1991).
  13. F. S. Chen, "Optically induced change of refractive indices in LiNbO3 and LiTaO3," J. Appl. Phys. 40, 3389-3396 (1969).
    [CrossRef]
  14. D. L. Staebler and J. J. Amodei, "Coupled-wave analysis of holographic storage in LiNbO3," J. Appl. Phys. 43, 1042-1049 (1972).
    [CrossRef]
  15. J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297-1305 (1980).
    [CrossRef]

2003 (1)

2000 (1)

1997 (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]

1992 (2)

1989 (2)

Simin Liu, Guangyin Zhang, Jinlong Wang, Xiaoyan Ma, and Yuanfen Fu, "Quasi-periodic oscillations in photoinduced conical light scattering from LiNbO3:Fe crystals," Opt. Commun. 70, 185-189 (1989).
[CrossRef]

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

1980 (1)

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

1972 (1)

D. L. Staebler and J. J. Amodei, "Coupled-wave analysis of holographic storage in LiNbO3," J. Appl. Phys. 43, 1042-1049 (1972).
[CrossRef]

1969 (1)

F. S. Chen, "Optically induced change of refractive indices in LiNbO3 and LiTaO3," J. Appl. Phys. 40, 3389-3396 (1969).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72-74 (1966).
[CrossRef]

Amodei, J. J.

D. L. Staebler and J. J. Amodei, "Coupled-wave analysis of holographic storage in LiNbO3," J. Appl. Phys. 43, 1042-1049 (1972).
[CrossRef]

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72-74 (1966).
[CrossRef]

Ballman, A. A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72-74 (1966).
[CrossRef]

Bond, W. L.

W. L. Bond, Crystal Technology (Wiley, 1976).

Boyd, G. D.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72-74 (1966).
[CrossRef]

Cedilnik, G.

G. Cedilnik, M. Esselbach, A. Kiessling, and R. Kowarschik, "Real-time holographic interferometry with double two-wave mixing in photorefractive crystals," Appl. Opt. 39, 2091-2100 (2000).
[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]

Chauvet, M.

Chen, F. S.

F. S. Chen, "Optically induced change of refractive indices in LiNbO3 and LiTaO3," J. Appl. Phys. 40, 3389-3396 (1969).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72-74 (1966).
[CrossRef]

Esselbach, M.

Feinberg, J.

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

Fu, Yuanfen

Simin Liu, Guangyin Zhang, Jinlong Wang, Xiaoyan Ma, and Yuanfen Fu, "Quasi-periodic oscillations in photoinduced conical light scattering from LiNbO3:Fe crystals," Opt. Commun. 70, 185-189 (1989).
[CrossRef]

Gunter, P.

P. Gunter and J.-P. Huignard, Photorefractive Materials and Their Applications (Springer-Verlag, 1989).

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

Hellwarth, R. W.

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

Huignard, J.-P.

P. Gunter and J.-P. Huignard, Photorefractive Materials and Their Applications (Springer-Verlag, 1989).

Joseph, J.

Kamra, K.

Khomenko, A. V.

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

Kiessling, A.

G. Cedilnik, M. Esselbach, A. Kiessling, and R. Kowarschik, "Real-time holographic interferometry with double two-wave mixing in photorefractive crystals," Appl. Opt. 39, 2091-2100 (2000).
[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]

Kowarschik, R.

G. Cedilnik, M. Esselbach, A. Kiessling, and R. Kowarschik, "Real-time holographic interferometry with double two-wave mixing in photorefractive crystals," Appl. Opt. 39, 2091-2100 (2000).
[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]

Levinstein, J. J.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72-74 (1966).
[CrossRef]

Liu, Simin

Simin Liu, Guangyin Zhang, Jinlong Wang, Xiaoyan Ma, and Yuanfen Fu, "Quasi-periodic oscillations in photoinduced conical light scattering from LiNbO3:Fe crystals," Opt. Commun. 70, 185-189 (1989).
[CrossRef]

Lu, Yueguang

Ma, Xiaoyan

Simin Liu, Guangyin Zhang, Jinlong Wang, Xiaoyan Ma, and Yuanfen Fu, "Quasi-periodic oscillations in photoinduced conical light scattering from LiNbO3:Fe crystals," Opt. Commun. 70, 185-189 (1989).
[CrossRef]

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]

Nassau, K.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72-74 (1966).
[CrossRef]

Petrov, M. P.

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

Pillai, P. K. C.

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]

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]

Singh, K.

Smith, R. G.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72-74 (1966).
[CrossRef]

Staebler, D. L.

D. L. Staebler and J. J. Amodei, "Coupled-wave analysis of holographic storage in LiNbO3," J. Appl. Phys. 43, 1042-1049 (1972).
[CrossRef]

Stepanov, S. I.

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

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

Wang, Jinlong

Simin Liu, Guangyin Zhang, Jinlong Wang, Xiaoyan Ma, and Yuanfen Fu, "Quasi-periodic oscillations in photoinduced conical light scattering from LiNbO3:Fe crystals," Opt. Commun. 70, 185-189 (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]

Xu, Haiying

Xu, Kebin

Yeh, P.

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

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).

Yuan, Yang

Zhang, Guangyin

Simin Liu, Guangyin Zhang, Jinlong Wang, Xiaoyan Ma, and Yuanfen Fu, "Quasi-periodic oscillations in photoinduced conical light scattering from LiNbO3:Fe crystals," Opt. Commun. 70, 185-189 (1989).
[CrossRef]

Appl. Opt. (3)

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. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, "Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3," Appl. Phys. Lett. 9, 72-74 (1966).
[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. (3)

F. S. Chen, "Optically induced change of refractive indices in LiNbO3 and LiTaO3," J. Appl. Phys. 40, 3389-3396 (1969).
[CrossRef]

D. L. Staebler and J. J. Amodei, "Coupled-wave analysis of holographic storage in LiNbO3," J. Appl. Phys. 43, 1042-1049 (1972).
[CrossRef]

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

Simin Liu, Guangyin Zhang, Jinlong Wang, Xiaoyan Ma, and Yuanfen Fu, "Quasi-periodic oscillations in photoinduced conical light scattering from LiNbO3:Fe crystals," Opt. Commun. 70, 185-189 (1989).
[CrossRef]

Other (4)

W. L. Bond, Crystal Technology (Wiley, 1976).

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).

P. Gunter and J.-P. Huignard, Photorefractive Materials and Their Applications (Springer-Verlag, 1989).

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

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Figures (4)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Experimental results along the z axis (i.e., the c axis):(a) incidence along +z; (b) incidence along −z.

Fig. 3
Fig. 3

Experimental results along the y axis:(a) incidence along −y; (b) incidence along +y.

Fig. 4
Fig. 4

Schematic plans of constructive interference and destructive interference:(a) constructive interference (dashed lines stand for the phase grating; solid lines stand for the interference stripe); (b) destructive interference (dashed lines stand for the phase grating; solid lines stand for the interference stripe); (c) phase relationship at O′.

Equations (3)

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

Δ n = 1 2 n 3 r eff E ,
r eff = e ^ 1 * [ ε ( r k ^ ) ε ] e ^ 2 / n 4 ,
r = [ 0 r 22 r 13 0 r 22 r 13 0 0 r 33 0 r 51 0 r 51 0 0 r 22 0 0 ] .

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