Abstract

We present a numerical and experimental study of vectorial two-wave mixing in cubic photorefractive crystals with nonlocal gratings in the case of strong wave coupling when the grating is not uniform along the propagation direction. We demonstrate that, in important experimental configurations, vectorial two-wave mixing leads to equal intensities and orthogonal polarizations of the interacting waves at the output of the photorefractive crystal. We analyze a bidirectional vectorial light amplification and discuss the effects of the crystal orientation and optical activity. Experimental results of two-wave and multiwave mixing in a Bi12TiO20 crystal with an ac applied electric field are presented.

© 2004 Optical Society of America

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References

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  1. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  2. D. D. Nolte, ed., Photorefractive Effect and Materials (Kluwer Academic, Boston, 1995).
  3. L. Solymar, D. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).
  4. M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Systems (Springer-Verlag, Berlin, 1991).
  5. 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]
  6. S. Mallick, D. Rouede, 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]
  7. A. Brignon and K. H. Wagner, “Polarization state evolution and eigenmode switching in photorefractive BSO,” Opt. Commun. 101, 239–246 (1993).
    [CrossRef]
  8. B. I. Sturman, D. J. Webb, R. Kowarschik, E. Shamonina, and K. H. Ringhofer, “Exact solution of the Bragg-diffraction problem in sillenites,” J. Opt. Soc. Am. B 11, 1813–1819 (1994).
    [CrossRef]
  9. 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]
  10. V. Yu. Krasnoperov, R. V. Litvinov, and S. M. Shandarov, “Nonunidirectional two-beam interaction in photorefractive bismuth silicate in alternating electric field,” Phys. Solid State 41, 568–572 (1999).
    [CrossRef]
  11. E. Shamonina, K. H. Ringhofer, B. I. Sturman, V. P. Kamenov, G. Cedilnik, M. Esselbach, A. Kiessling, R. Kowarschik, A. A. Kamshilin, V. V. Prokofiev, and T. Jaaskelainen, “Giant momentary readout produced by switching electric fields during two-wave mixing in sillenites,” Opt. Lett. 23, 1435–1437 (1998).
    [CrossRef]
  12. R. V. Litvinov, “Steady-state vectorial self-diffraction on a non-local photorefractive grating in a crystal of symmetry 43m at symmetrical transmitting geometry,” Appl. Phys. B 75, 853–860 (2002).
    [CrossRef]
  13. R. V. Litvinov, “Self-diffraction of light waves by a nonlocal photorefractive grating in a crystal with the 4¯3m symmetry,” J. Exp. Theor. Phys. 95, 820–832 (2002).
    [CrossRef]
  14. O. Filippov, K. H. Ringhofer, M. Shamonin, E. Shamonina, A. A. Kamshilin, E. Nippolainen, and B. I. Sturman, “Polarization properties of light-induced scattering in Bi12TiO20 crystals: theory and experiment for diagonal geometry,” J. Opt. Soc. Am. B 20, 677–684 (2003).
    [CrossRef]
  15. B. I. Sturman and O. Filippov, “Solutions for vectorial beam coupling under ac field in cubic photorefractive crystals,” Phys. Rev. E 68, 036613 (2003).
    [CrossRef]
  16. I. Rocha-Mendoza and A. V. Khomenko, “Bidirectional vec-torial light amplification in cubic crystals with unshifted photorefractive gratings,” Opt. Lett. 27, 1448–1450 (2002).
    [CrossRef]
  17. G. A. Brost, “Photorefractive grating formations at large modulation with alternating electric fields,” J. Opt. Soc. Am. B 9, 1454–1460 (1992).
    [CrossRef]
  18. A. V. Khomenko, I. Rocha-Mendoza, C. A. Fuentes-Hernández, V. V. Prokofiev, and E. Nippolainen, “Photorefractive effect in cubic crystal under a revolving electric field,” in Photorefractive Effects, Materials, and Devices, D. Nolte, G. J. Salamo, A. Siahmakoun, and S. Stepanov, eds., Vol. 62 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001) pp. 476–781.
  19. Yi Hu, K. H. Ringhofer, B. I. Sturman, “Two regimes of two-beam coupling in cubic 4¯3m crystals,” Appl. Phys. B 68, 931–936 (1999).
    [CrossRef]

2003 (2)

2002 (3)

I. Rocha-Mendoza and A. V. Khomenko, “Bidirectional vec-torial light amplification in cubic crystals with unshifted photorefractive gratings,” Opt. Lett. 27, 1448–1450 (2002).
[CrossRef]

R. V. Litvinov, “Steady-state vectorial self-diffraction on a non-local photorefractive grating in a crystal of symmetry 43m at symmetrical transmitting geometry,” Appl. Phys. B 75, 853–860 (2002).
[CrossRef]

R. V. Litvinov, “Self-diffraction of light waves by a nonlocal photorefractive grating in a crystal with the 4¯3m symmetry,” J. Exp. Theor. Phys. 95, 820–832 (2002).
[CrossRef]

1999 (3)

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]

V. Yu. Krasnoperov, R. V. Litvinov, and S. M. Shandarov, “Nonunidirectional two-beam interaction in photorefractive bismuth silicate in alternating electric field,” Phys. Solid State 41, 568–572 (1999).
[CrossRef]

Yi Hu, K. H. Ringhofer, B. I. Sturman, “Two regimes of two-beam coupling in cubic 4¯3m crystals,” Appl. Phys. B 68, 931–936 (1999).
[CrossRef]

1998 (1)

1994 (1)

1993 (1)

A. Brignon and K. H. Wagner, “Polarization state evolution and eigenmode switching in photorefractive BSO,” Opt. Commun. 101, 239–246 (1993).
[CrossRef]

1992 (1)

1987 (1)

1986 (1)

Apostolidis, A. G.

Brignon, A.

A. Brignon and K. H. Wagner, “Polarization state evolution and eigenmode switching in photorefractive BSO,” Opt. Commun. 101, 239–246 (1993).
[CrossRef]

Brost, G. A.

Cedilnik, G.

Esselbach, M.

Filippov, O.

Hu, Yi

Yi Hu, K. H. Ringhofer, B. I. Sturman, “Two regimes of two-beam coupling in cubic 4¯3m crystals,” Appl. Phys. B 68, 931–936 (1999).
[CrossRef]

Jaaskelainen, T.

Johnson, R. 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 60, 3332–3352 (1999).
[CrossRef]

E. Shamonina, K. H. Ringhofer, B. I. Sturman, V. P. Kamenov, G. Cedilnik, M. Esselbach, A. Kiessling, R. Kowarschik, A. A. Kamshilin, V. V. Prokofiev, and T. Jaaskelainen, “Giant momentary readout produced by switching electric fields during two-wave mixing in sillenites,” Opt. Lett. 23, 1435–1437 (1998).
[CrossRef]

Kamshilin, A. A.

Khomenko, A. V.

Kiessling, A.

Kowarschik, R.

Krasnoperov, V. Yu.

V. Yu. Krasnoperov, R. V. Litvinov, and S. M. Shandarov, “Nonunidirectional two-beam interaction in photorefractive bismuth silicate in alternating electric field,” Phys. Solid State 41, 568–572 (1999).
[CrossRef]

Litvinov, R. V.

R. V. Litvinov, “Steady-state vectorial self-diffraction on a non-local photorefractive grating in a crystal of symmetry 43m at symmetrical transmitting geometry,” Appl. Phys. B 75, 853–860 (2002).
[CrossRef]

R. V. Litvinov, “Self-diffraction of light waves by a nonlocal photorefractive grating in a crystal with the 4¯3m symmetry,” J. Exp. Theor. Phys. 95, 820–832 (2002).
[CrossRef]

V. Yu. Krasnoperov, R. V. Litvinov, and S. M. Shandarov, “Nonunidirectional two-beam interaction in photorefractive bismuth silicate in alternating electric field,” Phys. Solid State 41, 568–572 (1999).
[CrossRef]

Mallick, S.

Marrakchi, A.

Nippolainen, E.

O. Filippov, K. H. Ringhofer, M. Shamonin, E. Shamonina, A. A. Kamshilin, E. Nippolainen, and B. I. Sturman, “Polarization properties of light-induced scattering in Bi12TiO20 crystals: theory and experiment for diagonal geometry,” J. Opt. Soc. Am. B 20, 677–684 (2003).
[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]

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]

E. Shamonina, K. H. Ringhofer, B. I. Sturman, V. P. Kamenov, G. Cedilnik, M. Esselbach, A. Kiessling, R. Kowarschik, A. A. Kamshilin, V. V. Prokofiev, and T. Jaaskelainen, “Giant momentary readout produced by switching electric fields during two-wave mixing in sillenites,” Opt. Lett. 23, 1435–1437 (1998).
[CrossRef]

Ringhofer, K. H.

Rocha-Mendoza, I.

Rouede, D.

Shamonin, M.

Shamonina, E.

Shandarov, S. M.

V. Yu. Krasnoperov, R. V. Litvinov, and S. M. Shandarov, “Nonunidirectional two-beam interaction in photorefractive bismuth silicate in alternating electric field,” Phys. Solid State 41, 568–572 (1999).
[CrossRef]

Sturman, B. I.

Tanguay Jr., A. R.

Wagner, K. H.

A. Brignon and K. H. Wagner, “Polarization state evolution and eigenmode switching in photorefractive BSO,” Opt. Commun. 101, 239–246 (1993).
[CrossRef]

Webb, D. J.

Appl. Phys. B (2)

R. V. Litvinov, “Steady-state vectorial self-diffraction on a non-local photorefractive grating in a crystal of symmetry 43m at symmetrical transmitting geometry,” Appl. Phys. B 75, 853–860 (2002).
[CrossRef]

Yi Hu, K. H. Ringhofer, B. I. Sturman, “Two regimes of two-beam coupling in cubic 4¯3m crystals,” Appl. Phys. B 68, 931–936 (1999).
[CrossRef]

J. Exp. Theor. Phys. (1)

R. V. Litvinov, “Self-diffraction of light waves by a nonlocal photorefractive grating in a crystal with the 4¯3m symmetry,” J. Exp. Theor. Phys. 95, 820–832 (2002).
[CrossRef]

J. Opt. Soc. Am. B (5)

Opt. Commun. (1)

A. Brignon and K. H. Wagner, “Polarization state evolution and eigenmode switching in photorefractive BSO,” Opt. Commun. 101, 239–246 (1993).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. E (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 60, 3332–3352 (1999).
[CrossRef]

B. I. Sturman and O. Filippov, “Solutions for vectorial beam coupling under ac field in cubic photorefractive crystals,” Phys. Rev. E 68, 036613 (2003).
[CrossRef]

Phys. Solid State (1)

V. Yu. Krasnoperov, R. V. Litvinov, and S. M. Shandarov, “Nonunidirectional two-beam interaction in photorefractive bismuth silicate in alternating electric field,” Phys. Solid State 41, 568–572 (1999).
[CrossRef]

Other (5)

A. V. Khomenko, I. Rocha-Mendoza, C. A. Fuentes-Hernández, V. V. Prokofiev, and E. Nippolainen, “Photorefractive effect in cubic crystal under a revolving electric field,” in Photorefractive Effects, Materials, and Devices, D. Nolte, G. J. Salamo, A. Siahmakoun, and S. Stepanov, eds., Vol. 62 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001) pp. 476–781.

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

D. D. Nolte, ed., Photorefractive Effect and Materials (Kluwer Academic, Boston, 1995).

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

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

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Figures (6)

Fig. 1
Fig. 1

Mutual orientations of crystal axes, the principal axes of the index ellipsoid x and y, and external electric field E0 for three configurations of cubic crystal. Light propagates along the z axis.

Fig. 2
Fig. 2

Results of calculation for TWM in a cubic crystal without optical activity and Δnx=-Δny: (a) Intensities of the polarization modes as functions of the propagation distance. (b) The contrast of the interference pattern m and the respective contributions of the polarization modes mx and my. (c) Photorefractive gain.

Fig. 3
Fig. 3

Same as Fig. 2 but for the crystal configuration with Δnx=0 and Δny0.

Fig. 4
Fig. 4

Numerical simulation of TWM in cubic crystal with optical activity. Panels (a), (b), and (c) show the interference patterns I(x, z), Ix(x, z), and Iy(x, z), respectively.

Fig. 5
Fig. 5

Patterns of two waves’ interference recorded experimentally in the output plane of Bi12TiO20 crystal. Panel (a) was recorded with E0=0; panels (b)–(d) were recorded with E0=10 kV/cm. (b) Overall intensity. (c), (d) Intensities of x- and y-polarization components, respectively.

Fig. 6
Fig. 6

Intensities of the light recorded in the far field for multiwave mixing in BTO crystal. (a) E0=0; (b)–(d) E0=12.5 kV/cm. Panels (b), (c), and (d) show the overall, x- and y-polarization component intensities, respectively.

Equations (7)

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

dSdz=ηˆR+MˆS,dRdz=-ηˆS+MˆS.
ηˆ=k0Δnx(ESC)00Δny(ESC),
Mˆ=ik0Δnx(E0(t))-iαiαΔny(E0(t)),
ESC(z)=Emax[Sx(z)Rx*(z)+Sy(z)Ry*(z)],
dSidz=mΓi4I0Ri,dRidz=-m*Γi4I0Si,
g(L)=β+12,
tan2 ϕ2β1+β,

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