Abstract

The deflection of light reported by Müller et al. in lithium niobate [Appl. Phys. B 78, 367–370] and lithium tantalate [Appl. Optics 43 (34), 6344–6347] under electric field originates from refraction at domain-walls, like in ferroelastics. In ferroelectrics the optical discontinuity takes place at domain-walls as a consequence of the electro-optic effect. The theoretical deflection angle calculated from Snell’s law is proportional to the square root of the electric field and matches the experimental results reported by Müller et al. for lithium niobate. The finite domain-wall thickness mentioned by the authors is not involved in the deflection phenomenon.

© 2009 Optical Society of America

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  1. T.  Horie, K.  Kawabe, M.  Tachiki, and S.  Sawada, "Thermal Transition of Transparency in Ferroelectric Single Crystal of Barium Titanate," J. Phys. Soc. Jpn. 10, 541-549 (1955).
    [CrossRef]
  2. T.  Tsukamoto, J.  Hatano, and H.  Futuma, Proc. 2nd Japanese-Soviet Symp. Ferroelectricity, Kyoto 1980, J. Phys. Soc. Jpn. 49 Suppl. B, 155 (1980).
  3. T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Refraction and reflection of light at ferroelastic domain walls in Rochelle Salt Crystal," J. Phys. Soc. Jpn. 51, 3948-3952 (1982).
    [CrossRef]
  4. T.  Tsukamoto, M.  Komuake, S.  Suzuki, H.  Futuma, and Y.  Makita, "Domain structure and deflection of light at domain walls in RbHSeO4," J. Phys. Soc. Jpn. 52, 3966-3973 (1983).
    [CrossRef]
  5. T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals," J. Phys. Soc. Jpn. 53, 838-843 (1984).
    [CrossRef]
  6. J.  Bornarel, P.  Staniorowski, and Z.  Czapla, "Light-deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal," J. Phys.: Condens. Matter 12, 653-667 (2000).
    [CrossRef]
  7. P.  Kolata, L.  Guilbert, M. D.  Fontana, J. P. Salvestrini, and Z.  Czapla, "Birefringence measurements by means of light deflection at domain walls in FEL crystals," J. Opt. Soc. Am. B 17, 1973-1979 (2000)
    [CrossRef]
  8. M.  Müller, E.  Soergel, M. C.  Wengler, and K.  Buse, "Light deflection from ferroelectric domain boundaries," Appl. Phys. B 78, 367-370 (2004).
    [CrossRef]
  9. M.  Müller, E.  Soergel, and K.  Buse, "Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals," Appl. Opt. 43, 6344-6347 (2004).
    [CrossRef] [PubMed]
  10. V. Y. Shur, I. S. Baturin, M. S. Nebogatikov, S. A. Negashev, A. I. Lobov, and E. A. Rodina, "Study of field-induced evolution of the domain geometry in lithium niobate and lithium tantalite single crystals by in situ optical method," Ferroelectrics 374, 78-87 (2008).
    [CrossRef]
  11. G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion equation for congruently-grown lithium niobate," Opt. Quantum Electron. 16, 373-375 (1984).
    [CrossRef]
  12. S.  Fries and S.  Bauschulte, "Wavelength dependence of the electrooptic coefficients in LiNbO3:Fe," Phys. Status Solidi A 125, 369-374 (1991).
    [CrossRef]
  13. L.  Guilbert, "Field-induced light-deflection in lithium niobate and lithium tantalate: the possible configurations," submitted to Appl. Phys. B (April 2009).

2008 (1)

V. Y. Shur, I. S. Baturin, M. S. Nebogatikov, S. A. Negashev, A. I. Lobov, and E. A. Rodina, "Study of field-induced evolution of the domain geometry in lithium niobate and lithium tantalite single crystals by in situ optical method," Ferroelectrics 374, 78-87 (2008).
[CrossRef]

2004 (2)

M.  Müller, E.  Soergel, M. C.  Wengler, and K.  Buse, "Light deflection from ferroelectric domain boundaries," Appl. Phys. B 78, 367-370 (2004).
[CrossRef]

M.  Müller, E.  Soergel, and K.  Buse, "Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals," Appl. Opt. 43, 6344-6347 (2004).
[CrossRef] [PubMed]

2000 (2)

J.  Bornarel, P.  Staniorowski, and Z.  Czapla, "Light-deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal," J. Phys.: Condens. Matter 12, 653-667 (2000).
[CrossRef]

P.  Kolata, L.  Guilbert, M. D.  Fontana, J. P. Salvestrini, and Z.  Czapla, "Birefringence measurements by means of light deflection at domain walls in FEL crystals," J. Opt. Soc. Am. B 17, 1973-1979 (2000)
[CrossRef]

1991 (1)

S.  Fries and S.  Bauschulte, "Wavelength dependence of the electrooptic coefficients in LiNbO3:Fe," Phys. Status Solidi A 125, 369-374 (1991).
[CrossRef]

1984 (2)

G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion equation for congruently-grown lithium niobate," Opt. Quantum Electron. 16, 373-375 (1984).
[CrossRef]

T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals," J. Phys. Soc. Jpn. 53, 838-843 (1984).
[CrossRef]

1983 (1)

T.  Tsukamoto, M.  Komuake, S.  Suzuki, H.  Futuma, and Y.  Makita, "Domain structure and deflection of light at domain walls in RbHSeO4," J. Phys. Soc. Jpn. 52, 3966-3973 (1983).
[CrossRef]

1982 (1)

T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Refraction and reflection of light at ferroelastic domain walls in Rochelle Salt Crystal," J. Phys. Soc. Jpn. 51, 3948-3952 (1982).
[CrossRef]

1955 (1)

T.  Horie, K.  Kawabe, M.  Tachiki, and S.  Sawada, "Thermal Transition of Transparency in Ferroelectric Single Crystal of Barium Titanate," J. Phys. Soc. Jpn. 10, 541-549 (1955).
[CrossRef]

Baturin, I. S.

V. Y. Shur, I. S. Baturin, M. S. Nebogatikov, S. A. Negashev, A. I. Lobov, and E. A. Rodina, "Study of field-induced evolution of the domain geometry in lithium niobate and lithium tantalite single crystals by in situ optical method," Ferroelectrics 374, 78-87 (2008).
[CrossRef]

Bauschulte, S.

S.  Fries and S.  Bauschulte, "Wavelength dependence of the electrooptic coefficients in LiNbO3:Fe," Phys. Status Solidi A 125, 369-374 (1991).
[CrossRef]

Bornarel, J.

J.  Bornarel, P.  Staniorowski, and Z.  Czapla, "Light-deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal," J. Phys.: Condens. Matter 12, 653-667 (2000).
[CrossRef]

Buse, K.

M.  Müller, E.  Soergel, M. C.  Wengler, and K.  Buse, "Light deflection from ferroelectric domain boundaries," Appl. Phys. B 78, 367-370 (2004).
[CrossRef]

M.  Müller, E.  Soergel, and K.  Buse, "Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals," Appl. Opt. 43, 6344-6347 (2004).
[CrossRef] [PubMed]

Czapla, Z.

P.  Kolata, L.  Guilbert, M. D.  Fontana, J. P. Salvestrini, and Z.  Czapla, "Birefringence measurements by means of light deflection at domain walls in FEL crystals," J. Opt. Soc. Am. B 17, 1973-1979 (2000)
[CrossRef]

J.  Bornarel, P.  Staniorowski, and Z.  Czapla, "Light-deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal," J. Phys.: Condens. Matter 12, 653-667 (2000).
[CrossRef]

Edwards, G. J.

G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion equation for congruently-grown lithium niobate," Opt. Quantum Electron. 16, 373-375 (1984).
[CrossRef]

Fontana, M. D.

Fries, S.

S.  Fries and S.  Bauschulte, "Wavelength dependence of the electrooptic coefficients in LiNbO3:Fe," Phys. Status Solidi A 125, 369-374 (1991).
[CrossRef]

Futuma, H.

T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals," J. Phys. Soc. Jpn. 53, 838-843 (1984).
[CrossRef]

T.  Tsukamoto, M.  Komuake, S.  Suzuki, H.  Futuma, and Y.  Makita, "Domain structure and deflection of light at domain walls in RbHSeO4," J. Phys. Soc. Jpn. 52, 3966-3973 (1983).
[CrossRef]

T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Refraction and reflection of light at ferroelastic domain walls in Rochelle Salt Crystal," J. Phys. Soc. Jpn. 51, 3948-3952 (1982).
[CrossRef]

Guilbert, L.

P.  Kolata, L.  Guilbert, M. D.  Fontana, J. P. Salvestrini, and Z.  Czapla, "Birefringence measurements by means of light deflection at domain walls in FEL crystals," J. Opt. Soc. Am. B 17, 1973-1979 (2000)
[CrossRef]

L.  Guilbert, "Field-induced light-deflection in lithium niobate and lithium tantalate: the possible configurations," submitted to Appl. Phys. B (April 2009).

Hatano, J.

T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals," J. Phys. Soc. Jpn. 53, 838-843 (1984).
[CrossRef]

T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Refraction and reflection of light at ferroelastic domain walls in Rochelle Salt Crystal," J. Phys. Soc. Jpn. 51, 3948-3952 (1982).
[CrossRef]

Horie, T.

T.  Horie, K.  Kawabe, M.  Tachiki, and S.  Sawada, "Thermal Transition of Transparency in Ferroelectric Single Crystal of Barium Titanate," J. Phys. Soc. Jpn. 10, 541-549 (1955).
[CrossRef]

Kawabe, K.

T.  Horie, K.  Kawabe, M.  Tachiki, and S.  Sawada, "Thermal Transition of Transparency in Ferroelectric Single Crystal of Barium Titanate," J. Phys. Soc. Jpn. 10, 541-549 (1955).
[CrossRef]

Kolata, P.

Komuake, M.

T.  Tsukamoto, M.  Komuake, S.  Suzuki, H.  Futuma, and Y.  Makita, "Domain structure and deflection of light at domain walls in RbHSeO4," J. Phys. Soc. Jpn. 52, 3966-3973 (1983).
[CrossRef]

Lawrence, M.

G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion equation for congruently-grown lithium niobate," Opt. Quantum Electron. 16, 373-375 (1984).
[CrossRef]

Lobov, A. I.

V. Y. Shur, I. S. Baturin, M. S. Nebogatikov, S. A. Negashev, A. I. Lobov, and E. A. Rodina, "Study of field-induced evolution of the domain geometry in lithium niobate and lithium tantalite single crystals by in situ optical method," Ferroelectrics 374, 78-87 (2008).
[CrossRef]

Makita, Y.

T.  Tsukamoto, M.  Komuake, S.  Suzuki, H.  Futuma, and Y.  Makita, "Domain structure and deflection of light at domain walls in RbHSeO4," J. Phys. Soc. Jpn. 52, 3966-3973 (1983).
[CrossRef]

Müller, M.

M.  Müller, E.  Soergel, and K.  Buse, "Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals," Appl. Opt. 43, 6344-6347 (2004).
[CrossRef] [PubMed]

M.  Müller, E.  Soergel, M. C.  Wengler, and K.  Buse, "Light deflection from ferroelectric domain boundaries," Appl. Phys. B 78, 367-370 (2004).
[CrossRef]

Nebogatikov, M. S.

V. Y. Shur, I. S. Baturin, M. S. Nebogatikov, S. A. Negashev, A. I. Lobov, and E. A. Rodina, "Study of field-induced evolution of the domain geometry in lithium niobate and lithium tantalite single crystals by in situ optical method," Ferroelectrics 374, 78-87 (2008).
[CrossRef]

Negashev, S. A.

V. Y. Shur, I. S. Baturin, M. S. Nebogatikov, S. A. Negashev, A. I. Lobov, and E. A. Rodina, "Study of field-induced evolution of the domain geometry in lithium niobate and lithium tantalite single crystals by in situ optical method," Ferroelectrics 374, 78-87 (2008).
[CrossRef]

Rodina, E. A.

V. Y. Shur, I. S. Baturin, M. S. Nebogatikov, S. A. Negashev, A. I. Lobov, and E. A. Rodina, "Study of field-induced evolution of the domain geometry in lithium niobate and lithium tantalite single crystals by in situ optical method," Ferroelectrics 374, 78-87 (2008).
[CrossRef]

Salvestrini, J. P.

Sawada, S.

T.  Horie, K.  Kawabe, M.  Tachiki, and S.  Sawada, "Thermal Transition of Transparency in Ferroelectric Single Crystal of Barium Titanate," J. Phys. Soc. Jpn. 10, 541-549 (1955).
[CrossRef]

Shur, V. Y.

V. Y. Shur, I. S. Baturin, M. S. Nebogatikov, S. A. Negashev, A. I. Lobov, and E. A. Rodina, "Study of field-induced evolution of the domain geometry in lithium niobate and lithium tantalite single crystals by in situ optical method," Ferroelectrics 374, 78-87 (2008).
[CrossRef]

Soergel, E.

M.  Müller, E.  Soergel, and K.  Buse, "Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals," Appl. Opt. 43, 6344-6347 (2004).
[CrossRef] [PubMed]

M.  Müller, E.  Soergel, M. C.  Wengler, and K.  Buse, "Light deflection from ferroelectric domain boundaries," Appl. Phys. B 78, 367-370 (2004).
[CrossRef]

Staniorowski, P.

J.  Bornarel, P.  Staniorowski, and Z.  Czapla, "Light-deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal," J. Phys.: Condens. Matter 12, 653-667 (2000).
[CrossRef]

Suzuki, S.

T.  Tsukamoto, M.  Komuake, S.  Suzuki, H.  Futuma, and Y.  Makita, "Domain structure and deflection of light at domain walls in RbHSeO4," J. Phys. Soc. Jpn. 52, 3966-3973 (1983).
[CrossRef]

Tachiki, M.

T.  Horie, K.  Kawabe, M.  Tachiki, and S.  Sawada, "Thermal Transition of Transparency in Ferroelectric Single Crystal of Barium Titanate," J. Phys. Soc. Jpn. 10, 541-549 (1955).
[CrossRef]

Tsukamoto, T.

T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals," J. Phys. Soc. Jpn. 53, 838-843 (1984).
[CrossRef]

T.  Tsukamoto, M.  Komuake, S.  Suzuki, H.  Futuma, and Y.  Makita, "Domain structure and deflection of light at domain walls in RbHSeO4," J. Phys. Soc. Jpn. 52, 3966-3973 (1983).
[CrossRef]

T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Refraction and reflection of light at ferroelastic domain walls in Rochelle Salt Crystal," J. Phys. Soc. Jpn. 51, 3948-3952 (1982).
[CrossRef]

Wengler, M. C.

M.  Müller, E.  Soergel, M. C.  Wengler, and K.  Buse, "Light deflection from ferroelectric domain boundaries," Appl. Phys. B 78, 367-370 (2004).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

M.  Müller, E.  Soergel, M. C.  Wengler, and K.  Buse, "Light deflection from ferroelectric domain boundaries," Appl. Phys. B 78, 367-370 (2004).
[CrossRef]

Ferroelectrics (1)

V. Y. Shur, I. S. Baturin, M. S. Nebogatikov, S. A. Negashev, A. I. Lobov, and E. A. Rodina, "Study of field-induced evolution of the domain geometry in lithium niobate and lithium tantalite single crystals by in situ optical method," Ferroelectrics 374, 78-87 (2008).
[CrossRef]

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

J. Phys. Soc. Jpn. (4)

T.  Horie, K.  Kawabe, M.  Tachiki, and S.  Sawada, "Thermal Transition of Transparency in Ferroelectric Single Crystal of Barium Titanate," J. Phys. Soc. Jpn. 10, 541-549 (1955).
[CrossRef]

T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Refraction and reflection of light at ferroelastic domain walls in Rochelle Salt Crystal," J. Phys. Soc. Jpn. 51, 3948-3952 (1982).
[CrossRef]

T.  Tsukamoto, M.  Komuake, S.  Suzuki, H.  Futuma, and Y.  Makita, "Domain structure and deflection of light at domain walls in RbHSeO4," J. Phys. Soc. Jpn. 52, 3966-3973 (1983).
[CrossRef]

T.  Tsukamoto, J.  Hatano, and H.  Futuma, "Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals," J. Phys. Soc. Jpn. 53, 838-843 (1984).
[CrossRef]

J. Phys.: Condens. Matter (1)

J.  Bornarel, P.  Staniorowski, and Z.  Czapla, "Light-deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal," J. Phys.: Condens. Matter 12, 653-667 (2000).
[CrossRef]

Opt. Quantum Electron. (1)

G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion equation for congruently-grown lithium niobate," Opt. Quantum Electron. 16, 373-375 (1984).
[CrossRef]

Phys. Status Solidi A (1)

S.  Fries and S.  Bauschulte, "Wavelength dependence of the electrooptic coefficients in LiNbO3:Fe," Phys. Status Solidi A 125, 369-374 (1991).
[CrossRef]

Other (2)

L.  Guilbert, "Field-induced light-deflection in lithium niobate and lithium tantalate: the possible configurations," submitted to Appl. Phys. B (April 2009).

T.  Tsukamoto, J.  Hatano, and H.  Futuma, Proc. 2nd Japanese-Soviet Symp. Ferroelectricity, Kyoto 1980, J. Phys. Soc. Jpn. 49 Suppl. B, 155 (1980).

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Figures (2)

Fig.1. .
Fig.1. .

Construction of the deflected beams on the slowness curves. Electric field and incident beam parallel to z-axis. For clarity, the angles and the birefringence have been widely exaggerated.

Fig. 2.
Fig. 2.

Variations of the deflection angle in lithium niobate: (a) versus electric field at wavelength 351 nm, (b) versus wavelength at field -14 kV/mm. Theoretical curves are calculated from Eqs (8) & (9), for the ordinary beam (solid line) and the extraordinary beam (dash line), assuming an internal field of 1.4 kV/mm in the crystal.

Equations (9)

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

1no(±)2=1no2±r13E
1ne(±)2=1ne2±r33E
cosθo=no(+)no()
sin2θo=2no2r13E1+no2r13E
sin αo=nosinθo(1no2r13E)12=no2(2r13E1no4r132E2)12
sin2θe=2ne2r13E1+ne2(2r13r33)E
sinαe=none(2r13E(1+no2r13E)(1ne2r33E))12
sin αo no2 ± (2r13E)12
sin αe no ne ± (2r13E)12

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