Abstract

Analytical expressions for the electric field and the capacitance of a double-sided electrode structure are derived by the conformal-mapping method. A clear picture of the electric field is given for an analysis of the quadratic electro-optic effect in a lead lanthanum zirconated titanate transverse modulator. The excess birefringence in the region near the edge of the electrodes causes a reduction of the nonuniformity in the intensity modulation of a double-sided electrode structure compared with that of single-sided electrodes; this reduction is calculated.

© 1996 Optical Society of America

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References

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  1. Q. Zeng, Y. Huang, Z. Zhong, Y. Yeh, Proc. SPIE 2321, 92 (1994).
    [CrossRef]
  2. S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik, Opt. Eng. 25, 250 (1986).
  3. G. H. Haertling, Ferroelectrics 75, 25 (1987).
    [CrossRef]
  4. M. A. Title, S. H. Lee, Appl. Opt. 29, 85 (1990).
    [CrossRef] [PubMed]
  5. K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, K. Wakino, Jpn. J. Appl. Phys. 24, 177 (1985).
    [CrossRef]
  6. A. Y. Wu, T. C. Chen, H. Y. Chen, in Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics (Institute of Electrical and Electronics Engineers, New York, 1992), p. 600.
    [CrossRef]

1994

Q. Zeng, Y. Huang, Z. Zhong, Y. Yeh, Proc. SPIE 2321, 92 (1994).
[CrossRef]

1990

1987

G. H. Haertling, Ferroelectrics 75, 25 (1987).
[CrossRef]

1986

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik, Opt. Eng. 25, 250 (1986).

1985

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, K. Wakino, Jpn. J. Appl. Phys. 24, 177 (1985).
[CrossRef]

Chen, H. Y.

A. Y. Wu, T. C. Chen, H. Y. Chen, in Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics (Institute of Electrical and Electronics Engineers, New York, 1992), p. 600.
[CrossRef]

Chen, T. C.

A. Y. Wu, T. C. Chen, H. Y. Chen, in Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics (Institute of Electrical and Electronics Engineers, New York, 1992), p. 600.
[CrossRef]

Drabik, T. J.

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik, Opt. Eng. 25, 250 (1986).

Esener, S. C.

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik, Opt. Eng. 25, 250 (1986).

Haertling, G. H.

G. H. Haertling, Ferroelectrics 75, 25 (1987).
[CrossRef]

Huang, Y.

Q. Zeng, Y. Huang, Z. Zhong, Y. Yeh, Proc. SPIE 2321, 92 (1994).
[CrossRef]

Lee, S. H.

M. A. Title, S. H. Lee, Appl. Opt. 29, 85 (1990).
[CrossRef] [PubMed]

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik, Opt. Eng. 25, 250 (1986).

Murata, M.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, K. Wakino, Jpn. J. Appl. Phys. 24, 177 (1985).
[CrossRef]

Seto, H.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, K. Wakino, Jpn. J. Appl. Phys. 24, 177 (1985).
[CrossRef]

Tanaka, K.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, K. Wakino, Jpn. J. Appl. Phys. 24, 177 (1985).
[CrossRef]

Title, M. A.

M. A. Title, S. H. Lee, Appl. Opt. 29, 85 (1990).
[CrossRef] [PubMed]

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik, Opt. Eng. 25, 250 (1986).

Wakino, K.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, K. Wakino, Jpn. J. Appl. Phys. 24, 177 (1985).
[CrossRef]

Wu, A. Y.

A. Y. Wu, T. C. Chen, H. Y. Chen, in Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics (Institute of Electrical and Electronics Engineers, New York, 1992), p. 600.
[CrossRef]

Yamaguchi, M.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, K. Wakino, Jpn. J. Appl. Phys. 24, 177 (1985).
[CrossRef]

Yeh, Y.

Q. Zeng, Y. Huang, Z. Zhong, Y. Yeh, Proc. SPIE 2321, 92 (1994).
[CrossRef]

Zeng, Q.

Q. Zeng, Y. Huang, Z. Zhong, Y. Yeh, Proc. SPIE 2321, 92 (1994).
[CrossRef]

Zhong, Z.

Q. Zeng, Y. Huang, Z. Zhong, Y. Yeh, Proc. SPIE 2321, 92 (1994).
[CrossRef]

Appl. Opt.

Ferroelectrics

G. H. Haertling, Ferroelectrics 75, 25 (1987).
[CrossRef]

Jpn. J. Appl. Phys.

K. Tanaka, M. Yamaguchi, H. Seto, M. Murata, K. Wakino, Jpn. J. Appl. Phys. 24, 177 (1985).
[CrossRef]

Opt. Eng.

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik, Opt. Eng. 25, 250 (1986).

Proc. SPIE

Q. Zeng, Y. Huang, Z. Zhong, Y. Yeh, Proc. SPIE 2321, 92 (1994).
[CrossRef]

Other

A. Y. Wu, T. C. Chen, H. Y. Chen, in Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics (Institute of Electrical and Electronics Engineers, New York, 1992), p. 600.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the double-sided surface electrode structure.

Fig. 2
Fig. 2

Conformal-mapping procedure.

Fig. 3
Fig. 3

Electric-field penetration of double-sided electrodes (calculated down the electrode gap center line) as a function of the electrode geometry. The thickness of the dielectric material is 100 μm when unit voltage is applied.

Fig. 4
Fig. 4

Distribution of the electric-field components of the double-sided electrode structure with g = 25 μm, w = 25 μm, and t = 100 μm when unit voltage is applied. (a) Ex, (b) Ey.

Fig. 5
Fig. 5

Optical transmission profiles when the half-wave voltage is applied: (a) g = 25 μm, w = 25 μm, (b) g = 40 μm, w = 10 μm.

Equations (9)

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Z 1 = exp ( π Z / c ) ,
Z 2 = 1 + Z 1 1 Z 1 ,
Z 3 = Z 2 / a 1 ,
Z 4 = 0 Z 3 d Z [ ( 1 Z 2 ) ( 1 k 1 2 Z 2 ) ] 1 / 2 ,
E Z = E Z 4 ( d Z 4 d Z ) * = V b 1 π c K ( k 1 ) ( exp ( π Z / c ) 1 { a 1 2 [ 1 exp ( π Z / c ) ] 2 [ 1 + exp ( π Z / c ) ] 2 } 1 / 2 × 1 { b 1 2 [ 1 exp ( π Z / c ) ] 2 [ 1 + exp ( π Z / c ) ] 2 } 1 / 2 ) * ,
C S = 0 K ( k ) K ( k ) + 0 r K ( k 1 ) K ( k 1 ) ,
Γ ( x ) = 2 π λ t / 2 t / 2 Δ n ( x , y ) d y π n 3 R λ t / 2 t / 2 E x 2 ( x , y ) d y ,
V π = V Γ ( 0 ) / π = V [ n 3 R λ t / 2 t / 2 E x 2 ( 0 , y ) d y ] 1 / 2 .
T ( x ) = sin 2 [ Γ ( x ) 2 ] sin 2 [ π 2 0 t / 2 E x 2 ( x , y ) d y 0 t / 2 E x 2 ( 0 , y ) d y ]

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