Abstract

We describe a simple method for performing accurate computer simulation and modeling of arbitrary-geometry electro-optic (EO) devices. We use a material EO model that includes the effects of scattering and depolarization as well as the change in the index of refraction. Finite-element analysis is used to determine the electrostatic field distribution for EO device designs. Attenuation of the transmitted light intensity as a result of scattering is modeled as an exponential function, and the intensity of transmitted depolarized light is shown to be a function of the scattering intensity. The total optical transmittance is determined by integration of these values over all the elements in the path of the propagating light. Lanthanum-modified lead zirconate titanate-based surface-electrode and transverse-electrode EO devices are designed and fabricated. Their experimentally measured performance is found to be in excellent agreement with our computer-simulation results.

© 1998 Optical Society of America

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References

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  1. G. Haertling, “Electro-optic ceramics and devices,” in Electronic Ceramics: Properties, Devices and Applications, L. Levinson, ed. (Marcel Dekker, New York, 1988), pp. 371–492.
  2. J. T. Cutchen, J. O. Harris, and G. R. Laguna, “PLZT electro-optic shutters: applications,” Appl. Opt. 14, 1866–1873 (1975).
    [CrossRef] [PubMed]
  3. T. Utsunomiya, “Optical switch using PLZT ceramics,” Ferroelectrics 109, 235–240 (1990).
    [CrossRef]
  4. R. Viennet, “Driving voltage calculation for a ferroelectric display device,” J. Math. Phys. Appl. 29, 715–722 (1978).
    [CrossRef]
  5. E. E. Klotin’sh, Yu. Ya. Kotleris, and Ya. A. Seglin’sh, “Geometrical optics of an electrically controlled phase plate made of PLZT-10 ferroelectric ceramic,” Avtometriya 6, 68–72 (1984).
  6. K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, and K. Wakino, “Analyses of PLZT electro-optic shutter and shutter array,” Jpn. J. Appl. Phys. 24, 177–182 (1985).
    [CrossRef]
  7. A. R. Dias, R. F. Kalman, J. W. Goodman, and A. A. Sawchuck, “Fiber-optic crossbar switch with broadcast capability,” Opt. Eng. 27, 955–960 (1988).
    [CrossRef]
  8. M. Title and S. H. Lee, “Modeling and characterization of embedded electrode performance in transverse electrooptic modulators,” Appl. Opt. 29, 85–98 (1990).
    [CrossRef] [PubMed]
  9. A. Y. Wu, T. C. Chen, and H. Y. Chen, “Model of electro-optic effects by Green’s function and summary representation: applications to bulk and thin film PLZT displays and spatial light modulators,” in Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics, M. Liu, A. Safari, A. Kingon, and G. Haertling, eds. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 600–603.
    [CrossRef]
  10. F. S. Chen, “Evaluation of PLZT ceramics for application in optical communications,” Opt. Commun. 6, 297–300 (1972).
    [CrossRef]
  11. J. Thomas and Y. Fainman, “Programmable diffractive optical elements using a multichannel lanthanum-modified lead zirconate titanate phase modulator,” Opt. Lett. 20, 1510–1512 (1995).
    [CrossRef] [PubMed]
  12. Q. W. Song, X. M. Wang, and R. Bussjager, “Lanthanum-modified lead zirconate titanate ceramic wafer-based electro-optic dynamic diverging lens,” Opt. Lett. 21, 242–244 (1996).
    [CrossRef] [PubMed]
  13. Q. W. Song, P. J. Talbot, and J. H. Maurice, “PLZT based high-efficiency electro-optic grating for optical switching,” J. Mod. Opt. 41, 717–727 (1994).
    [CrossRef]
  14. F. Castro and B. Nabet, “Design of dual-effect lens on lanthanum-modified lead zirconate titanate for continuous variation of focal length,” Appl. Opt. 34, 2317–2323 (1995).
    [CrossRef] [PubMed]
  15. M. Ivey and V. W. Bolie, “Birefringent light scattering in PLZT ceramics,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 38, 579–584 (1991).
    [CrossRef]
  16. C. E. Land, “Variable birefringence, light scattering, and surface-deformation effects in PLZT ceramics,” Ferroelectrics 7, 45–51 (1974).
    [CrossRef]
  17. P. E. Shames, P. C. Sun, and Y. Fainman, “Modeling of scattering and depolarizing electro-optic devices. I. Characterization of lanthanum-modified lead zirconate titanate,” Appl. Opt. 37, 3717–3725 (1998).
    [CrossRef]
  18. R. A. Chipman, “The mechanics of polarization ray tracing,” in Polarization Analysis and Measurement, D. H. Goldstein and R. A. Chipman, eds., Proc. SPIE 1746, 62–75 (1992).
    [CrossRef]
  19. P. Shames, P. C. Sun, and Y. Fainman, “Modeling and optimization of electro-optic phase modulator,” in Physics and Simulation of Optoelectronic Devices IV, W. W. Chow and M. Osinski, eds., Proc. SPIE 2693, 787–796 (1996).
    [CrossRef]
  20. J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993), Chap. 2.
  21. Y. Yeh and Q. Zeng, “Exact solution to the electric field of the double-sided electrode structure in a lead lanthanum zirconate titanate transverse electro-optic modulator,” Opt. Lett. 21, 961–963 (1996).
    [CrossRef] [PubMed]
  22. H. Engan, “Excitation of elastic surface waves by spatial harmonics of interdigital transducers,” IEEE Trans. Electron. Devices 16, 1014–1017 (1969).
    [CrossRef]
  23. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.
  24. A. Yariv, Quantum Electronics (Wiley, New York, 1989), Chap. 5.
  25. J. F. Nye, Physical Properties of Crystals (Clarendon, London, 1985), Chap. 2.
  26. R. Boyd, Nonlinear Optics (Academic, Boston, 1992), Chap. 7.
  27. A. L. Dalisa and R. J. Seymour, “Convolution scattering model for ferroelectric ceramics and other display media,” Proc. IEEE 61, 981–991 (1973).
    [CrossRef]
  28. P. D. Thacher, “Refractive index and surface layers of ceramic (Pb, La)(Zr, Ti)O3,” Appl. Opt. 16, 3210–3213 (1977).
    [CrossRef] [PubMed]
  29. P. J. Chen, C. E. Land, and M. M. Madsen, “A theory of the influence of space-charge field on domain switching in PLZT 7/65/35 ceramic,” Acta Mechan. 43, 61–72 (1982).
    [CrossRef]
  30. C. E. Land, “Effects of photoferroelectric space charge fields on visible-light scattering in PLZT ceramics,” Ferroelectrics 27, 143–146 (1980).
    [CrossRef]
  31. F. Xu, R. C. Tyan, P. C. Sun, Y. Fainman, “Fabrication, modeling and characterization of form-birefringent nanostructures,” Opt. Lett. 20, 2457–2459 (1995).
    [CrossRef] [PubMed]

1998 (1)

1996 (2)

1995 (3)

1994 (1)

Q. W. Song, P. J. Talbot, and J. H. Maurice, “PLZT based high-efficiency electro-optic grating for optical switching,” J. Mod. Opt. 41, 717–727 (1994).
[CrossRef]

1991 (1)

M. Ivey and V. W. Bolie, “Birefringent light scattering in PLZT ceramics,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 38, 579–584 (1991).
[CrossRef]

1990 (2)

1988 (1)

A. R. Dias, R. F. Kalman, J. W. Goodman, and A. A. Sawchuck, “Fiber-optic crossbar switch with broadcast capability,” Opt. Eng. 27, 955–960 (1988).
[CrossRef]

1985 (1)

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, and K. Wakino, “Analyses of PLZT electro-optic shutter and shutter array,” Jpn. J. Appl. Phys. 24, 177–182 (1985).
[CrossRef]

1984 (1)

E. E. Klotin’sh, Yu. Ya. Kotleris, and Ya. A. Seglin’sh, “Geometrical optics of an electrically controlled phase plate made of PLZT-10 ferroelectric ceramic,” Avtometriya 6, 68–72 (1984).

1982 (1)

P. J. Chen, C. E. Land, and M. M. Madsen, “A theory of the influence of space-charge field on domain switching in PLZT 7/65/35 ceramic,” Acta Mechan. 43, 61–72 (1982).
[CrossRef]

1980 (1)

C. E. Land, “Effects of photoferroelectric space charge fields on visible-light scattering in PLZT ceramics,” Ferroelectrics 27, 143–146 (1980).
[CrossRef]

1978 (1)

R. Viennet, “Driving voltage calculation for a ferroelectric display device,” J. Math. Phys. Appl. 29, 715–722 (1978).
[CrossRef]

1977 (1)

1975 (1)

1974 (1)

C. E. Land, “Variable birefringence, light scattering, and surface-deformation effects in PLZT ceramics,” Ferroelectrics 7, 45–51 (1974).
[CrossRef]

1973 (1)

A. L. Dalisa and R. J. Seymour, “Convolution scattering model for ferroelectric ceramics and other display media,” Proc. IEEE 61, 981–991 (1973).
[CrossRef]

1972 (1)

F. S. Chen, “Evaluation of PLZT ceramics for application in optical communications,” Opt. Commun. 6, 297–300 (1972).
[CrossRef]

1969 (1)

H. Engan, “Excitation of elastic surface waves by spatial harmonics of interdigital transducers,” IEEE Trans. Electron. Devices 16, 1014–1017 (1969).
[CrossRef]

Bolie, V. W.

M. Ivey and V. W. Bolie, “Birefringent light scattering in PLZT ceramics,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 38, 579–584 (1991).
[CrossRef]

Boyd, R.

R. Boyd, Nonlinear Optics (Academic, Boston, 1992), Chap. 7.

Bussjager, R.

Castro, F.

Chen, F. S.

F. S. Chen, “Evaluation of PLZT ceramics for application in optical communications,” Opt. Commun. 6, 297–300 (1972).
[CrossRef]

Chen, H. Y.

A. Y. Wu, T. C. Chen, and H. Y. Chen, “Model of electro-optic effects by Green’s function and summary representation: applications to bulk and thin film PLZT displays and spatial light modulators,” in Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics, M. Liu, A. Safari, A. Kingon, and G. Haertling, eds. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 600–603.
[CrossRef]

Chen, P. J.

P. J. Chen, C. E. Land, and M. M. Madsen, “A theory of the influence of space-charge field on domain switching in PLZT 7/65/35 ceramic,” Acta Mechan. 43, 61–72 (1982).
[CrossRef]

Chen, T. C.

A. Y. Wu, T. C. Chen, and H. Y. Chen, “Model of electro-optic effects by Green’s function and summary representation: applications to bulk and thin film PLZT displays and spatial light modulators,” in Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics, M. Liu, A. Safari, A. Kingon, and G. Haertling, eds. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 600–603.
[CrossRef]

Chipman, R. A.

R. A. Chipman, “The mechanics of polarization ray tracing,” in Polarization Analysis and Measurement, D. H. Goldstein and R. A. Chipman, eds., Proc. SPIE 1746, 62–75 (1992).
[CrossRef]

Cutchen, J. T.

Dalisa, A. L.

A. L. Dalisa and R. J. Seymour, “Convolution scattering model for ferroelectric ceramics and other display media,” Proc. IEEE 61, 981–991 (1973).
[CrossRef]

Dias, A. R.

A. R. Dias, R. F. Kalman, J. W. Goodman, and A. A. Sawchuck, “Fiber-optic crossbar switch with broadcast capability,” Opt. Eng. 27, 955–960 (1988).
[CrossRef]

Engan, H.

H. Engan, “Excitation of elastic surface waves by spatial harmonics of interdigital transducers,” IEEE Trans. Electron. Devices 16, 1014–1017 (1969).
[CrossRef]

Fainman, Y.

Goodman, J. W.

A. R. Dias, R. F. Kalman, J. W. Goodman, and A. A. Sawchuck, “Fiber-optic crossbar switch with broadcast capability,” Opt. Eng. 27, 955–960 (1988).
[CrossRef]

Haertling, G.

G. Haertling, “Electro-optic ceramics and devices,” in Electronic Ceramics: Properties, Devices and Applications, L. Levinson, ed. (Marcel Dekker, New York, 1988), pp. 371–492.

Harris, J. O.

Ivey, M.

M. Ivey and V. W. Bolie, “Birefringent light scattering in PLZT ceramics,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 38, 579–584 (1991).
[CrossRef]

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993), Chap. 2.

Kalman, R. F.

A. R. Dias, R. F. Kalman, J. W. Goodman, and A. A. Sawchuck, “Fiber-optic crossbar switch with broadcast capability,” Opt. Eng. 27, 955–960 (1988).
[CrossRef]

Klotin’sh, E. E.

E. E. Klotin’sh, Yu. Ya. Kotleris, and Ya. A. Seglin’sh, “Geometrical optics of an electrically controlled phase plate made of PLZT-10 ferroelectric ceramic,” Avtometriya 6, 68–72 (1984).

Kotleris, Yu. Ya.

E. E. Klotin’sh, Yu. Ya. Kotleris, and Ya. A. Seglin’sh, “Geometrical optics of an electrically controlled phase plate made of PLZT-10 ferroelectric ceramic,” Avtometriya 6, 68–72 (1984).

Laguna, G. R.

Land, C. E.

P. J. Chen, C. E. Land, and M. M. Madsen, “A theory of the influence of space-charge field on domain switching in PLZT 7/65/35 ceramic,” Acta Mechan. 43, 61–72 (1982).
[CrossRef]

C. E. Land, “Effects of photoferroelectric space charge fields on visible-light scattering in PLZT ceramics,” Ferroelectrics 27, 143–146 (1980).
[CrossRef]

C. E. Land, “Variable birefringence, light scattering, and surface-deformation effects in PLZT ceramics,” Ferroelectrics 7, 45–51 (1974).
[CrossRef]

Lee, S. H.

Madsen, M. M.

P. J. Chen, C. E. Land, and M. M. Madsen, “A theory of the influence of space-charge field on domain switching in PLZT 7/65/35 ceramic,” Acta Mechan. 43, 61–72 (1982).
[CrossRef]

Maurice, J. H.

Q. W. Song, P. J. Talbot, and J. H. Maurice, “PLZT based high-efficiency electro-optic grating for optical switching,” J. Mod. Opt. 41, 717–727 (1994).
[CrossRef]

Murata, M.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, and K. Wakino, “Analyses of PLZT electro-optic shutter and shutter array,” Jpn. J. Appl. Phys. 24, 177–182 (1985).
[CrossRef]

Nabet, B.

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, London, 1985), Chap. 2.

Sawchuck, A. A.

A. R. Dias, R. F. Kalman, J. W. Goodman, and A. A. Sawchuck, “Fiber-optic crossbar switch with broadcast capability,” Opt. Eng. 27, 955–960 (1988).
[CrossRef]

Seglin’sh, Ya. A.

E. E. Klotin’sh, Yu. Ya. Kotleris, and Ya. A. Seglin’sh, “Geometrical optics of an electrically controlled phase plate made of PLZT-10 ferroelectric ceramic,” Avtometriya 6, 68–72 (1984).

Seto, H.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, and K. Wakino, “Analyses of PLZT electro-optic shutter and shutter array,” Jpn. J. Appl. Phys. 24, 177–182 (1985).
[CrossRef]

Seymour, R. J.

A. L. Dalisa and R. J. Seymour, “Convolution scattering model for ferroelectric ceramics and other display media,” Proc. IEEE 61, 981–991 (1973).
[CrossRef]

Shames, P.

P. Shames, P. C. Sun, and Y. Fainman, “Modeling and optimization of electro-optic phase modulator,” in Physics and Simulation of Optoelectronic Devices IV, W. W. Chow and M. Osinski, eds., Proc. SPIE 2693, 787–796 (1996).
[CrossRef]

Shames, P. E.

Song, Q. W.

Q. W. Song, X. M. Wang, and R. Bussjager, “Lanthanum-modified lead zirconate titanate ceramic wafer-based electro-optic dynamic diverging lens,” Opt. Lett. 21, 242–244 (1996).
[CrossRef] [PubMed]

Q. W. Song, P. J. Talbot, and J. H. Maurice, “PLZT based high-efficiency electro-optic grating for optical switching,” J. Mod. Opt. 41, 717–727 (1994).
[CrossRef]

Sun, P. C.

Talbot, P. J.

Q. W. Song, P. J. Talbot, and J. H. Maurice, “PLZT based high-efficiency electro-optic grating for optical switching,” J. Mod. Opt. 41, 717–727 (1994).
[CrossRef]

Tanaka, K.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, and K. Wakino, “Analyses of PLZT electro-optic shutter and shutter array,” Jpn. J. Appl. Phys. 24, 177–182 (1985).
[CrossRef]

Thacher, P. D.

Thomas, J.

Title, M.

Tyan, R. C.

Utsunomiya, T.

T. Utsunomiya, “Optical switch using PLZT ceramics,” Ferroelectrics 109, 235–240 (1990).
[CrossRef]

Viennet, R.

R. Viennet, “Driving voltage calculation for a ferroelectric display device,” J. Math. Phys. Appl. 29, 715–722 (1978).
[CrossRef]

Wakino, K.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, and K. Wakino, “Analyses of PLZT electro-optic shutter and shutter array,” Jpn. J. Appl. Phys. 24, 177–182 (1985).
[CrossRef]

Wang, X. M.

Wu, A. Y.

A. Y. Wu, T. C. Chen, and H. Y. Chen, “Model of electro-optic effects by Green’s function and summary representation: applications to bulk and thin film PLZT displays and spatial light modulators,” in Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics, M. Liu, A. Safari, A. Kingon, and G. Haertling, eds. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 600–603.
[CrossRef]

Xu, F.

Yamaguchi, M.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, and K. Wakino, “Analyses of PLZT electro-optic shutter and shutter array,” Jpn. J. Appl. Phys. 24, 177–182 (1985).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

A. Yariv, Quantum Electronics (Wiley, New York, 1989), Chap. 5.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

Yeh, Y.

Zeng, Q.

Acta Mechan. (1)

P. J. Chen, C. E. Land, and M. M. Madsen, “A theory of the influence of space-charge field on domain switching in PLZT 7/65/35 ceramic,” Acta Mechan. 43, 61–72 (1982).
[CrossRef]

Appl. Opt. (5)

Avtometriya (1)

E. E. Klotin’sh, Yu. Ya. Kotleris, and Ya. A. Seglin’sh, “Geometrical optics of an electrically controlled phase plate made of PLZT-10 ferroelectric ceramic,” Avtometriya 6, 68–72 (1984).

Ferroelectrics (3)

T. Utsunomiya, “Optical switch using PLZT ceramics,” Ferroelectrics 109, 235–240 (1990).
[CrossRef]

C. E. Land, “Variable birefringence, light scattering, and surface-deformation effects in PLZT ceramics,” Ferroelectrics 7, 45–51 (1974).
[CrossRef]

C. E. Land, “Effects of photoferroelectric space charge fields on visible-light scattering in PLZT ceramics,” Ferroelectrics 27, 143–146 (1980).
[CrossRef]

IEEE Trans. Electron. Devices (1)

H. Engan, “Excitation of elastic surface waves by spatial harmonics of interdigital transducers,” IEEE Trans. Electron. Devices 16, 1014–1017 (1969).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. (1)

M. Ivey and V. W. Bolie, “Birefringent light scattering in PLZT ceramics,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 38, 579–584 (1991).
[CrossRef]

J. Math. Phys. Appl. (1)

R. Viennet, “Driving voltage calculation for a ferroelectric display device,” J. Math. Phys. Appl. 29, 715–722 (1978).
[CrossRef]

J. Mod. Opt. (1)

Q. W. Song, P. J. Talbot, and J. H. Maurice, “PLZT based high-efficiency electro-optic grating for optical switching,” J. Mod. Opt. 41, 717–727 (1994).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, and K. Wakino, “Analyses of PLZT electro-optic shutter and shutter array,” Jpn. J. Appl. Phys. 24, 177–182 (1985).
[CrossRef]

Opt. Commun. (1)

F. S. Chen, “Evaluation of PLZT ceramics for application in optical communications,” Opt. Commun. 6, 297–300 (1972).
[CrossRef]

Opt. Eng. (1)

A. R. Dias, R. F. Kalman, J. W. Goodman, and A. A. Sawchuck, “Fiber-optic crossbar switch with broadcast capability,” Opt. Eng. 27, 955–960 (1988).
[CrossRef]

Opt. Lett. (4)

Proc. IEEE (1)

A. L. Dalisa and R. J. Seymour, “Convolution scattering model for ferroelectric ceramics and other display media,” Proc. IEEE 61, 981–991 (1973).
[CrossRef]

Other (9)

A. Y. Wu, T. C. Chen, and H. Y. Chen, “Model of electro-optic effects by Green’s function and summary representation: applications to bulk and thin film PLZT displays and spatial light modulators,” in Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics, M. Liu, A. Safari, A. Kingon, and G. Haertling, eds. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 600–603.
[CrossRef]

G. Haertling, “Electro-optic ceramics and devices,” in Electronic Ceramics: Properties, Devices and Applications, L. Levinson, ed. (Marcel Dekker, New York, 1988), pp. 371–492.

R. A. Chipman, “The mechanics of polarization ray tracing,” in Polarization Analysis and Measurement, D. H. Goldstein and R. A. Chipman, eds., Proc. SPIE 1746, 62–75 (1992).
[CrossRef]

P. Shames, P. C. Sun, and Y. Fainman, “Modeling and optimization of electro-optic phase modulator,” in Physics and Simulation of Optoelectronic Devices IV, W. W. Chow and M. Osinski, eds., Proc. SPIE 2693, 787–796 (1996).
[CrossRef]

J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993), Chap. 2.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

A. Yariv, Quantum Electronics (Wiley, New York, 1989), Chap. 5.

J. F. Nye, Physical Properties of Crystals (Clarendon, London, 1985), Chap. 2.

R. Boyd, Nonlinear Optics (Academic, Boston, 1992), Chap. 7.

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Figures (8)

Fig. 1
Fig. 1

FEA-calculated electric-field strength distribution for trapezoid-shaped embedded electrodes separated by 40 and 60 μm, with a potential difference of 124 V.

Fig. 2
Fig. 2

Depolarized light (normalized) intensity as a function of the polarized-light intensity for identical PLZT samples with propagation lengths of 1 and 2 mm.

Fig. 3
Fig. 3

(a) Surface-electrode device in which CrAu electrodes are evaporated onto the surface of the PLZT wafer and light is normally incident on the surface (along the y axis). (b) Transverse-electrode device in which electrodes are on opposite sides of the wafer and light is normally incident on the polished edges (along the z axis).

Fig. 4
Fig. 4

Two-dimensional cross section of the electric-field strength distribution within PLZT for a surface-electrode device with electrodes separated by 40 μm and a potential difference of 124 V. Charge buildup at the corners of the electrodes results in a large gradient of the electric field within the electrode gap near the surface of the device.

Fig. 5
Fig. 5

Single element of the 2-D cross section where we calculate an average electric-field magnitude and direction. We show the variation of the index ellipse following the direction of the electric field.

Fig. 6
Fig. 6

Simulation (solid curve) of the surface-electrode device performance, with an electrode gap of 500 μm for PLZT 9.0/65/35 that is 388 μm thick, and experimental data for a fabricated device (circles) in comparison with the simulation results (dotted curve) with the commonly employed Jones calculus and quadratic EO model.

Fig. 7
Fig. 7

(a) Experimentally measured CCD image for a transverse-electrode device with 280-μm electrodes separated by 200 μm of PLZT 9.0/65/35 with an applied voltage of 98 V. The interaction length, i.e., thickness of PLZT, is 1 mm. The diagonal fringe pattern is due to the glass cover plate on the CCD camera. (b) Computer-simulated intensity by use of identical electrode geometry. The black dots are remnants of the PostScript rendering. Below each image is an intensity profile taken across the center of the image.

Fig. 8
Fig. 8

Experimental data (circles) and simulated results (curve) of transmission through the central 20 μm × 20 μm area of the transverse-electrode device with 280-μm electrodes separated by 200 μm of PLZT 9.0/65/35 [see Figs. 7(a) and 7(b)].

Equations (24)

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

E = E x 2 + E y 2 + E z 2 1 / 2 ,
x 2 n x 2 + y 2 n y 2 + z 2 n z 2 = 1
ϕ r = 2 π λ     n r d s ,
ϕ k = 2 π λ   n k L ,
ϕ k = 2 π λ i = 1 N   n k i L i ,
Δ ϕ = 2 π λ i = 1 N   Δ n i L i ,
A = A 0 exp - α E L ,
B = B 0 exp - β E L ,
A = A 0 i = 1 N exp - α E i L i = A 0 exp - i = 1 N   α E i L i ,
B = B 0 i = 1 N exp - β E i L i = B 0 exp - i = 1 N   β E i L i .
U = f A 0 - A ,
I 45 ° , 45 ° = 1 4 A + B + U AA + U AB + U BB + U BA - 2 AB cos Δ ϕ .
I 45 ° , 45 ° = 1 2 A + 2 U - A   cos Δ ϕ .
x 2 n e 2 + y 2 n o 2 + z 2 n o 2 = 1 ,
n A = n z = n o ,
n B = n x = cos 2 θ x ,   y n e 2 + sin 2 θ x ,   y n o 2 - 1 / 2 ,
n e = n o - Δ n meas E ,
Δ n = | n x E - n z | ,
- α = 1 L ln A 0 A meas E .
A = A 0 i = 1 N A meas E i A 0 L i / L .
n A = n y = sin 2 θ x ,   y n e 2 + cos 2 θ x ,   y n o 2 - 1 / 2 .
Δ n = | n x E - n y E | ,
Δ ϕ x ,   y = 2 π λ   Δ n x ,   y L w ,
A x ,   y = A meas E A 0 L w / L

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