Abstract

We describe an electrically controllable diffuser made from a randomly depoled lithium niobate wafer. The level of scattering produced by this diffuser can be varied continuously from a negligible amount (equal to or less than ordinary glass) to a level where the coherent component is practically extinguished. A statistical model for describing the diffuser is developed, from which analytical expressions for the coherent and diffuse components of the mean scattered intensity are obtained. Measurements of the mean intensity versus scattering angle and applied voltage that agree well with the theory are also reported.

© 2004 Optical Society of America

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  1. D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
    [CrossRef]
  2. J. Webjörn, V. Pruneri, P. St. J. Russell, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation in bulk lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
    [CrossRef]
  3. G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22, 1834–1836 (1997).
    [CrossRef]
  4. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillator in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
    [CrossRef]
  5. W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, “Continuous wave singly resonant optical parametric oscillator based on periodically poled LiNbO3,” Opt. Lett. 21, 713–715 (1996).
    [CrossRef] [PubMed]
  6. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
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    [CrossRef]
  11. E. Jakeman and B. J. Hoenders, “Scattering by surface of rectangular grooves,” Opt. Acta 29, 1587–1598 (1982).
    [CrossRef]
  12. R. C. Hollins and D. L. Jordan, “Measurements of 10.6 μm radiation scattered by a pseudorandom surface of rectangular grooves,” Opt. Acta 30, 1275–1734 (1983).
    [CrossRef]
  13. M. J. Kim, E. R. Méndez, and K. A. O’Donnell, “Scattering from gamma-distributed surfaces,” J. Mod. Opt. 34, 1107–1119 (1987).
    [CrossRef]
  14. E. Jakeman, “Scattering by gamma-distributed phase screens,” Waves Random Media 2, 153–167 (1991).
    [CrossRef]
  15. H. M. Escamilla and E. R. Méndez, “Speckle statistics from gamma-distributed random-phase screens,” J. Opt. Soc. Am. A 8, 1929–1935 (1991).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  25. Y. Cho, S. Kazuta, and H. Ito, “Scanning-nonlinear-dielectric-microscopy study on periodically poled LiNbO3 for a high-performance quasi-phase-matching device,” Appl. Phys. Lett. 79, 2955–2957 (2001).
    [CrossRef]
  26. G. J. Edwards and M. Lawrence, “A temperature dependent dispersion for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–374 (1984).
    [CrossRef]
  27. J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
    [CrossRef]
  28. T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
    [CrossRef]
  29. M. Jazbinsek and M. Zgonik, “Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics,” Appl. Phys. B: Photophys. Laser Chem. 74, 407–414 (2002).

2002 (1)

M. Jazbinsek and M. Zgonik, “Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics,” Appl. Phys. B: Photophys. Laser Chem. 74, 407–414 (2002).

2001 (1)

Y. Cho, S. Kazuta, and H. Ito, “Scanning-nonlinear-dielectric-microscopy study on periodically poled LiNbO3 for a high-performance quasi-phase-matching device,” Appl. Phys. Lett. 79, 2955–2957 (2001).
[CrossRef]

2000 (1)

1999 (3)

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

V. Ya. Shur, E. L. Rumyantsev, R. G. Batchko, G. D. Miller, M. M. Fejer, and R. L. Byer, “Domain kinetics in the formation of a periodic domain structure in lithium niobate,” Phys. Solid State 41, 1681–1687 (1999).
[CrossRef]

I. E. Barry, G. W. Ross, P. G. R. Smith, and R. W. Eason, “Ridge waveguides in lithium niobate fabricated by differential etching following spatially selective domain inversion,” Appl. Phys. Lett. 74, 1487–1488 (1999).
[CrossRef]

1998 (1)

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

1997 (1)

1996 (1)

1995 (2)

1994 (1)

J. Webjörn, V. Pruneri, P. St. J. Russell, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation in bulk lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

1991 (3)

E. Jakeman, “Scattering by gamma-distributed phase screens,” Waves Random Media 2, 153–167 (1991).
[CrossRef]

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

H. M. Escamilla and E. R. Méndez, “Speckle statistics from gamma-distributed random-phase screens,” J. Opt. Soc. Am. A 8, 1929–1935 (1991).
[CrossRef]

1987 (1)

M. J. Kim, E. R. Méndez, and K. A. O’Donnell, “Scattering from gamma-distributed surfaces,” J. Mod. Opt. 34, 1107–1119 (1987).
[CrossRef]

1985 (1)

1984 (2)

G. J. Edwards and M. Lawrence, “A temperature dependent dispersion for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–374 (1984).
[CrossRef]

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. (Bellingham) 23, 453–461 (1984).
[CrossRef]

1983 (1)

R. C. Hollins and D. L. Jordan, “Measurements of 10.6 μm radiation scattered by a pseudorandom surface of rectangular grooves,” Opt. Acta 30, 1275–1734 (1983).
[CrossRef]

1982 (1)

E. Jakeman and B. J. Hoenders, “Scattering by surface of rectangular grooves,” Opt. Acta 29, 1587–1598 (1982).
[CrossRef]

1973 (1)

P. Beckmann, “Scattering by non-Gaussian surfaces,” IEEE Trans. Antennas Propag. AP-21, 169–175 (1973).
[CrossRef]

1969 (1)

M. DiDomenico, Jr., and S. H. Wemple, “Oxygen-octahedra ferroelectrics. I. Theory of electro-optical and nonlinear optical effects,” J. Appl. Phys. 40, 720–734 (1969).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Alexander, J. I.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Barr, J. R. M.

J. Webjörn, V. Pruneri, P. St. J. Russell, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation in bulk lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

Barry, I. E.

I. E. Barry, G. W. Ross, P. G. R. Smith, and R. W. Eason, “Ridge waveguides in lithium niobate fabricated by differential etching following spatially selective domain inversion,” Appl. Phys. Lett. 74, 1487–1488 (1999).
[CrossRef]

Batchko, R. G.

Beckmann, P.

P. Beckmann, “Scattering by non-Gaussian surfaces,” IEEE Trans. Antennas Propag. AP-21, 169–175 (1973).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Bosenberg, W. R.

Byer, R. L.

Cabrera, J. M.

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

Cho, Y.

Y. Cho, S. Kazuta, and H. Ito, “Scanning-nonlinear-dielectric-microscopy study on periodically poled LiNbO3 for a high-performance quasi-phase-matching device,” Appl. Phys. Lett. 79, 2955–2957 (2001).
[CrossRef]

de Toro, J. A.

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

DiDomenico Jr., M.

M. DiDomenico, Jr., and S. H. Wemple, “Oxygen-octahedra ferroelectrics. I. Theory of electro-optical and nonlinear optical effects,” J. Appl. Phys. 40, 720–734 (1969).
[CrossRef]

Dominic, V.

Drobshoff, A.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Eason, R. W.

I. E. Barry, G. W. Ross, P. G. R. Smith, and R. W. Eason, “Ridge waveguides in lithium niobate fabricated by differential etching following spatially selective domain inversion,” Appl. Phys. Lett. 74, 1487–1488 (1999).
[CrossRef]

Eckardt, R. C.

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature dependent dispersion for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–374 (1984).
[CrossRef]

Escamilla, H. M.

Fejer, M. M.

V. Ya. Shur, E. L. Rumyantsev, R. G. Batchko, G. D. Miller, M. M. Fejer, and R. L. Byer, “Domain kinetics in the formation of a periodic domain structure in lithium niobate,” Phys. Solid State 41, 1681–1687 (1999).
[CrossRef]

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22, 1834–1836 (1997).
[CrossRef]

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillator in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
[CrossRef]

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

Fujiwara, T.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

Furukawa, Y.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

García Cabañes, A.

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

Hanna, D. C.

J. Webjörn, V. Pruneri, P. St. J. Russell, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation in bulk lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

Hoenders, B. J.

E. Jakeman and B. J. Hoenders, “Scattering by surface of rectangular grooves,” Opt. Acta 29, 1587–1598 (1982).
[CrossRef]

Hollins, R. C.

R. C. Hollins and D. L. Jordan, “Measurements of 10.6 μm radiation scattered by a pseudorandom surface of rectangular grooves,” Opt. Acta 30, 1275–1734 (1983).
[CrossRef]

Houé, M.

M. Houé and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

Ikushima, A. J.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

Ito, H.

Y. Cho, S. Kazuta, and H. Ito, “Scanning-nonlinear-dielectric-microscopy study on periodically poled LiNbO3 for a high-performance quasi-phase-matching device,” Appl. Phys. Lett. 79, 2955–2957 (2001).
[CrossRef]

Jakeman, E.

E. Jakeman, “Scattering by gamma-distributed phase screens,” Waves Random Media 2, 153–167 (1991).
[CrossRef]

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. (Bellingham) 23, 453–461 (1984).
[CrossRef]

E. Jakeman and B. J. Hoenders, “Scattering by surface of rectangular grooves,” Opt. Acta 29, 1587–1598 (1982).
[CrossRef]

Jazbinsek, M.

M. Jazbinsek and M. Zgonik, “Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics,” Appl. Phys. B: Photophys. Laser Chem. 74, 407–414 (2002).

Jordan, D. L.

R. C. Hollins and D. L. Jordan, “Measurements of 10.6 μm radiation scattered by a pseudorandom surface of rectangular grooves,” Opt. Acta 30, 1275–1734 (1983).
[CrossRef]

Jundt, D. H.

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

Kazuta, S.

Y. Cho, S. Kazuta, and H. Ito, “Scanning-nonlinear-dielectric-microscopy study on periodically poled LiNbO3 for a high-performance quasi-phase-matching device,” Appl. Phys. Lett. 79, 2955–2957 (2001).
[CrossRef]

Kim, M. J.

M. J. Kim, E. R. Méndez, and K. A. O’Donnell, “Scattering from gamma-distributed surfaces,” J. Mod. Opt. 34, 1107–1119 (1987).
[CrossRef]

Kitamura, K.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature dependent dispersion for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–374 (1984).
[CrossRef]

Magel, G. A.

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

Marron, J.

Méndez, E. R.

H. M. Escamilla and E. R. Méndez, “Speckle statistics from gamma-distributed random-phase screens,” J. Opt. Soc. Am. A 8, 1929–1935 (1991).
[CrossRef]

M. J. Kim, E. R. Méndez, and K. A. O’Donnell, “Scattering from gamma-distributed surfaces,” J. Mod. Opt. 34, 1107–1119 (1987).
[CrossRef]

Miller, G. D.

V. Ya. Shur, E. L. Rumyantsev, R. G. Batchko, G. D. Miller, M. M. Fejer, and R. L. Byer, “Domain kinetics in the formation of a periodic domain structure in lithium niobate,” Phys. Solid State 41, 1681–1687 (1999).
[CrossRef]

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22, 1834–1836 (1997).
[CrossRef]

Missey, M. J.

Morris, G. M.

Myers, L. E.

O’Donnell, K. A.

M. J. Kim, E. R. Méndez, and K. A. O’Donnell, “Scattering from gamma-distributed surfaces,” J. Mod. Opt. 34, 1107–1119 (1987).
[CrossRef]

Ohama, M.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Pierce, J. W.

Pruneri, V.

J. Webjörn, V. Pruneri, P. St. J. Russell, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation in bulk lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

Ross, G. W.

I. E. Barry, G. W. Ross, P. G. R. Smith, and R. W. Eason, “Ridge waveguides in lithium niobate fabricated by differential etching following spatially selective domain inversion,” Appl. Phys. Lett. 74, 1487–1488 (1999).
[CrossRef]

Rumyantsev, E. L.

V. Ya. Shur, E. L. Rumyantsev, R. G. Batchko, G. D. Miller, M. M. Fejer, and R. L. Byer, “Domain kinetics in the formation of a periodic domain structure in lithium niobate,” Phys. Solid State 41, 1681–1687 (1999).
[CrossRef]

Russell, P. St. J.

J. Webjörn, V. Pruneri, P. St. J. Russell, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation in bulk lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

Russell, S.

Schepler, K. L.

Serrano, M. D.

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

Shur, V. Ya.

V. Ya. Shur, E. L. Rumyantsev, R. G. Batchko, G. D. Miller, M. M. Fejer, and R. L. Byer, “Domain kinetics in the formation of a periodic domain structure in lithium niobate,” Phys. Solid State 41, 1681–1687 (1999).
[CrossRef]

Smith, P. G. R.

I. E. Barry, G. W. Ross, P. G. R. Smith, and R. W. Eason, “Ridge waveguides in lithium niobate fabricated by differential etching following spatially selective domain inversion,” Appl. Phys. Lett. 74, 1487–1488 (1999).
[CrossRef]

Takahashi, M.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

Townsend, P. D.

M. Houé and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

Tulloch, W. M.

Webjörn, J.

J. Webjörn, V. Pruneri, P. St. J. Russell, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation in bulk lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

Weise, D. R.

Wemple, S. H.

M. DiDomenico, Jr., and S. H. Wemple, “Oxygen-octahedra ferroelectrics. I. Theory of electro-optical and nonlinear optical effects,” J. Appl. Phys. 40, 720–734 (1969).
[CrossRef]

Zgonik, M.

M. Jazbinsek and M. Zgonik, “Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics,” Appl. Phys. B: Photophys. Laser Chem. 74, 407–414 (2002).

Appl. Phys. B: Photophys. Laser Chem. (1)

M. Jazbinsek and M. Zgonik, “Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics,” Appl. Phys. B: Photophys. Laser Chem. 74, 407–414 (2002).

Appl. Phys. Lett. (3)

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

I. E. Barry, G. W. Ross, P. G. R. Smith, and R. W. Eason, “Ridge waveguides in lithium niobate fabricated by differential etching following spatially selective domain inversion,” Appl. Phys. Lett. 74, 1487–1488 (1999).
[CrossRef]

Y. Cho, S. Kazuta, and H. Ito, “Scanning-nonlinear-dielectric-microscopy study on periodically poled LiNbO3 for a high-performance quasi-phase-matching device,” Appl. Phys. Lett. 79, 2955–2957 (2001).
[CrossRef]

Electron. Lett. (2)

J. Webjörn, V. Pruneri, P. St. J. Russell, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation in bulk lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35, 499–501 (1999).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

P. Beckmann, “Scattering by non-Gaussian surfaces,” IEEE Trans. Antennas Propag. AP-21, 169–175 (1973).
[CrossRef]

J. Appl. Phys. (1)

M. DiDomenico, Jr., and S. H. Wemple, “Oxygen-octahedra ferroelectrics. I. Theory of electro-optical and nonlinear optical effects,” J. Appl. Phys. 40, 720–734 (1969).
[CrossRef]

J. Mod. Opt. (1)

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Figures (10)

Fig. 1
Fig. 1

Experimental setup used to create the mask.

Fig. 2
Fig. 2

Modeling of the voltage-controlled diffuser: (a) Light intensity of the speckle pattern used to create the mask. (b) Transparency of the mask; the mask becomes opaque wherever I(r)>Ic. (c) Domains produced by the photoresist replica of the mask. (d) Local phase distortions of the wave front of a normally incident beam on the diffuser. The magnitude of the phase shift depends on the applied voltage.

Fig. 3
Fig. 3

Experimental setup for the measurement of the scattered light.

Fig. 4
Fig. 4

Clipped speckle pattern: (a) Pattern recorded in the photoresist. (b) Domain structure in LiNbO3 revealed by etching with acid (hydrofluoric).

Fig. 5
Fig. 5

Scattered light intensity versus applied voltage. The sample has not been annealed. Thick lines curves: intensity measured at 0° (gray) and 1° (black). Thin curves: theoretical fits.

Fig. 6
Fig. 6

Coherent component of the scattered light intensity versus applied voltage. The sample has been annealed. Solid line curve: theoretical fit. θ0=0°; λ=476 nm.

Fig. 7
Fig. 7

I(θ0) versus applied voltage for four different angles. The solid curve is a theoretical fit to Eq. (22). λ=476 nm.

Fig. 8
Fig. 8

Mean scattered light intensity versus angle at three different voltages. λ=476 nm, w=3.9 mm, and f=500 mm.

Fig. 9
Fig. 9

Mean scattered light intensity versus angle at 500 and 1500 V. The data obtained at 0 V have been subtracted from the data shown. The gray curves are theoretical predictions. λ=476 nm, w=3.9 mm, f=500 mm.

Fig. 10
Fig. 10

Far-field image of the scattered light.

Equations (23)

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rijkl=1l=3gijklPs,l,
Ps(r)=-cˆ|Ps|ifI(r)>Ic+cˆ|Ps|ifI(r)Ic,
E(r0)=exp(ikf)iλf -E(r)t(r)exp-ikf r·r0dr,
E(r0)=A exp(ikf)iλf - exp-r2w2 × t(r)exp-ikf r·r0dr,
I(r0)=|E(r0)|2=|A|2(λf)2 -- exp-r2+r2w2 × t(r)t*(r)exp-ikf(r-r)·r0drdr,
ϕ(V)=πn03r13dλ Vd=πn03r13Vλ,
f(r)=1ifI(r)>Ic0ifI(r)Ic.
t(r)=exp[iϕ(V)]f(r)+exp[-iϕ(V)][1-f(r)].
t(r)=2i exp(-x)sin ϕ(V)+exp[-iϕ(V)],
x=IcI,
t(r)t*(r)=4 sin2 ϕ(V)f(r)f*(r)+{exp[2iϕ(V)]-1}f(r)+{exp[-2iϕ(V)]-1}f(r)+1.
f(r)f*(r)=n=0|μ(r, r)|2n[exp(-x)Ln-1(x)]2,
|μ(r, r)|2=exp-|r-r|2a2,
a=λmfmπwm,
Icoh(θ0)=|E(θ0)|2=|A|2πw2λf2 exp-2πwλ2 sin2 θ0 × {1+4[exp(-2x)-exp(-x)]sin2 ϕ(V)},
r0=f sin θ0,
I(θ0)=Icoh(θ0)+Id(θ0),
Id(θ0)=2|A|2aπwλf2 exp(-2x)sin2 ϕ(V)n=1 [Ln-1(x)]2n × exp-1n πaλ2 sin2 θ0
Icoh(θ0, x=ln 2)=|A|2πw2λf2 exp-2πwλ2 sin2 θ0cos2 ϕ(V).
area=0Ic exp-III dI=1-exp-IcI=1-exp(-x).
I(θ0=0, V)Icoh(V)=B{1+4[exp(-2x)-exp(-x)]sin2 ϕ(V)},
I(θ0, V)C sin2 ϕ(V)+D,
Id(θ0)=E exp(-2x)sin2 ϕ(V)n=1 [Ln-1(x)]2n × exp-1n πaλ2 sin2 θ0.

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