Abstract

As previously predicted [Appl. Opt. 40, 5583 (2001)], we have now observed electric field-induced diffraction peaks in transmission and reflection experiments by use of a LiNbO3 sample with interdigital planar electrodes that serve as a diffraction grating. The magnitudes of the new peaks in the reflection experiments are ten times larger than those in the transmission experiments. We interpret these effects in terms of a field-induced refractive-index change produced by the linear electro-optic effect. The positive and negative changes in the refractive index produce two diffraction gratings that are period doubled with respect to the original grating and that have a phase difference between them. The superposition of the diffracted light from these gratings is shown to account for the new peaks. From the relative magnitude of the new peak to that of the central peak, we estimate the refractive-index change to be 0.004.

© 2002 Optical Society of America

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References

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  1. C. E. Land, “Longitudinal electrooptic effects and photosensitivities of lead zirconate titanate thin films,” J. Am. Ceram. Soc. 72, 2059–2064 (1989).
    [CrossRef]
  2. G. H. Haertling, “PLZT electrooptic materials and applications—a review,” Ferroelectrics 75, 25–55 (1987).
    [CrossRef]
  3. K. Carl, K. Geisen, “Dielectric and optical properties of a quasi-ferroelectric PLZT ceramic,” Proc. IEEE 61, 967–974 (1973).
    [CrossRef]
  4. G. W. Farnell, I. A. Cermak, P. Silverster, S. K. Wong, “Capacitance and field distributions for interdigital surface-wave transducers,” IEEE Trans. Sonics Ultrasonics SU-17, 188–195 (1970).
    [CrossRef]
  5. B. G. Potter, M. B. Sinclair, D. Dimos, “Electro-optical characterization of Pb(Zr, Ti)O3 thin films by waveguide refractometry,” Appl. Phys. Lett. 63, 2180–2182 (1993).
    [CrossRef]
  6. D. Trivedi, P. Tayebati, M. Tabat, “Measurement of large electro-optic coefficients in thin films of strontium barium niobate (Sr0.6Ba0.4Nb2O6),” Appl. Phys. Lett. 68, 3227–3229 (1996).
    [CrossRef]
  7. P. Tayebati, D. Trivedi, M. Tabat, “Pulsed laser deposition of SBN:75 thin films with electro-optic coefficient of 844pm/V,” Appl. Phys. Lett. 69, 1023–1025 (1996).
    [CrossRef]
  8. X. Yang, L. T. Wood, J. H. Miller, “Diffraction from tunable periodic structures: application for the determination of electro-optic coefficients,” Appl. Opt. 40, 5583–5587 (2001).
    [CrossRef]

2001

1996

D. Trivedi, P. Tayebati, M. Tabat, “Measurement of large electro-optic coefficients in thin films of strontium barium niobate (Sr0.6Ba0.4Nb2O6),” Appl. Phys. Lett. 68, 3227–3229 (1996).
[CrossRef]

P. Tayebati, D. Trivedi, M. Tabat, “Pulsed laser deposition of SBN:75 thin films with electro-optic coefficient of 844pm/V,” Appl. Phys. Lett. 69, 1023–1025 (1996).
[CrossRef]

1993

B. G. Potter, M. B. Sinclair, D. Dimos, “Electro-optical characterization of Pb(Zr, Ti)O3 thin films by waveguide refractometry,” Appl. Phys. Lett. 63, 2180–2182 (1993).
[CrossRef]

1989

C. E. Land, “Longitudinal electrooptic effects and photosensitivities of lead zirconate titanate thin films,” J. Am. Ceram. Soc. 72, 2059–2064 (1989).
[CrossRef]

1987

G. H. Haertling, “PLZT electrooptic materials and applications—a review,” Ferroelectrics 75, 25–55 (1987).
[CrossRef]

1973

K. Carl, K. Geisen, “Dielectric and optical properties of a quasi-ferroelectric PLZT ceramic,” Proc. IEEE 61, 967–974 (1973).
[CrossRef]

1970

G. W. Farnell, I. A. Cermak, P. Silverster, S. K. Wong, “Capacitance and field distributions for interdigital surface-wave transducers,” IEEE Trans. Sonics Ultrasonics SU-17, 188–195 (1970).
[CrossRef]

Carl, K.

K. Carl, K. Geisen, “Dielectric and optical properties of a quasi-ferroelectric PLZT ceramic,” Proc. IEEE 61, 967–974 (1973).
[CrossRef]

Cermak, I. A.

G. W. Farnell, I. A. Cermak, P. Silverster, S. K. Wong, “Capacitance and field distributions for interdigital surface-wave transducers,” IEEE Trans. Sonics Ultrasonics SU-17, 188–195 (1970).
[CrossRef]

Dimos, D.

B. G. Potter, M. B. Sinclair, D. Dimos, “Electro-optical characterization of Pb(Zr, Ti)O3 thin films by waveguide refractometry,” Appl. Phys. Lett. 63, 2180–2182 (1993).
[CrossRef]

Farnell, G. W.

G. W. Farnell, I. A. Cermak, P. Silverster, S. K. Wong, “Capacitance and field distributions for interdigital surface-wave transducers,” IEEE Trans. Sonics Ultrasonics SU-17, 188–195 (1970).
[CrossRef]

Geisen, K.

K. Carl, K. Geisen, “Dielectric and optical properties of a quasi-ferroelectric PLZT ceramic,” Proc. IEEE 61, 967–974 (1973).
[CrossRef]

Haertling, G. H.

G. H. Haertling, “PLZT electrooptic materials and applications—a review,” Ferroelectrics 75, 25–55 (1987).
[CrossRef]

Land, C. E.

C. E. Land, “Longitudinal electrooptic effects and photosensitivities of lead zirconate titanate thin films,” J. Am. Ceram. Soc. 72, 2059–2064 (1989).
[CrossRef]

Miller, J. H.

Potter, B. G.

B. G. Potter, M. B. Sinclair, D. Dimos, “Electro-optical characterization of Pb(Zr, Ti)O3 thin films by waveguide refractometry,” Appl. Phys. Lett. 63, 2180–2182 (1993).
[CrossRef]

Silverster, P.

G. W. Farnell, I. A. Cermak, P. Silverster, S. K. Wong, “Capacitance and field distributions for interdigital surface-wave transducers,” IEEE Trans. Sonics Ultrasonics SU-17, 188–195 (1970).
[CrossRef]

Sinclair, M. B.

B. G. Potter, M. B. Sinclair, D. Dimos, “Electro-optical characterization of Pb(Zr, Ti)O3 thin films by waveguide refractometry,” Appl. Phys. Lett. 63, 2180–2182 (1993).
[CrossRef]

Tabat, M.

D. Trivedi, P. Tayebati, M. Tabat, “Measurement of large electro-optic coefficients in thin films of strontium barium niobate (Sr0.6Ba0.4Nb2O6),” Appl. Phys. Lett. 68, 3227–3229 (1996).
[CrossRef]

P. Tayebati, D. Trivedi, M. Tabat, “Pulsed laser deposition of SBN:75 thin films with electro-optic coefficient of 844pm/V,” Appl. Phys. Lett. 69, 1023–1025 (1996).
[CrossRef]

Tayebati, P.

P. Tayebati, D. Trivedi, M. Tabat, “Pulsed laser deposition of SBN:75 thin films with electro-optic coefficient of 844pm/V,” Appl. Phys. Lett. 69, 1023–1025 (1996).
[CrossRef]

D. Trivedi, P. Tayebati, M. Tabat, “Measurement of large electro-optic coefficients in thin films of strontium barium niobate (Sr0.6Ba0.4Nb2O6),” Appl. Phys. Lett. 68, 3227–3229 (1996).
[CrossRef]

Trivedi, D.

D. Trivedi, P. Tayebati, M. Tabat, “Measurement of large electro-optic coefficients in thin films of strontium barium niobate (Sr0.6Ba0.4Nb2O6),” Appl. Phys. Lett. 68, 3227–3229 (1996).
[CrossRef]

P. Tayebati, D. Trivedi, M. Tabat, “Pulsed laser deposition of SBN:75 thin films with electro-optic coefficient of 844pm/V,” Appl. Phys. Lett. 69, 1023–1025 (1996).
[CrossRef]

Wong, S. K.

G. W. Farnell, I. A. Cermak, P. Silverster, S. K. Wong, “Capacitance and field distributions for interdigital surface-wave transducers,” IEEE Trans. Sonics Ultrasonics SU-17, 188–195 (1970).
[CrossRef]

Wood, L. T.

Yang, X.

Appl. Opt.

Appl. Phys. Lett.

B. G. Potter, M. B. Sinclair, D. Dimos, “Electro-optical characterization of Pb(Zr, Ti)O3 thin films by waveguide refractometry,” Appl. Phys. Lett. 63, 2180–2182 (1993).
[CrossRef]

D. Trivedi, P. Tayebati, M. Tabat, “Measurement of large electro-optic coefficients in thin films of strontium barium niobate (Sr0.6Ba0.4Nb2O6),” Appl. Phys. Lett. 68, 3227–3229 (1996).
[CrossRef]

P. Tayebati, D. Trivedi, M. Tabat, “Pulsed laser deposition of SBN:75 thin films with electro-optic coefficient of 844pm/V,” Appl. Phys. Lett. 69, 1023–1025 (1996).
[CrossRef]

Ferroelectrics

G. H. Haertling, “PLZT electrooptic materials and applications—a review,” Ferroelectrics 75, 25–55 (1987).
[CrossRef]

IEEE Trans. Sonics Ultrasonics

G. W. Farnell, I. A. Cermak, P. Silverster, S. K. Wong, “Capacitance and field distributions for interdigital surface-wave transducers,” IEEE Trans. Sonics Ultrasonics SU-17, 188–195 (1970).
[CrossRef]

J. Am. Ceram. Soc.

C. E. Land, “Longitudinal electrooptic effects and photosensitivities of lead zirconate titanate thin films,” J. Am. Ceram. Soc. 72, 2059–2064 (1989).
[CrossRef]

Proc. IEEE

K. Carl, K. Geisen, “Dielectric and optical properties of a quasi-ferroelectric PLZT ceramic,” Proc. IEEE 61, 967–974 (1973).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) Electric field lines. The horizontal arrows show the in-plane electric field components; the vertical arrows show the normal field components, (b) Interdigital planar electrodes. Grating groups 1 and 2 are indicated.

Fig. 2
Fig. 2

(a) Interference term (I int) between two gratings. The solid curve represents the interference before the electric field is applied, and the dashed-dotted curve represents the interference after the electric field is applied. (b) Diffraction term (I diff) from one of the two gratings. (c) Far-field diffraction pattern (I int × I diff) before the electric field is applied; this pattern is proportional to the production of the interference term shown in the solid curve of (a) and the diffraction term shown in (b). (d) Far-field diffraction pattern after the electric field is applied; this pattern is proportional to the production of the dashed curve in (a) and the curve in (b).

Fig. 3
Fig. 3

Intensity of the first new peak versus the refractive-index change (solid curve) and of the center diffraction peak versus the refractive-index change (dashed curve).

Fig. 4
Fig. 4

Experimental setup of the LiNbO3 sample in the transmission mode.

Fig. 5
Fig. 5

(a) Signals with modulating electric field on. (b) Intensities of the corresponding positions in (a) with electric field off. (c) Normalized signals.

Fig. 6
Fig. 6

Experimental setup of the LiNbO3 sample in the reflection mode.

Fig. 7
Fig. 7

(a) Signals with modulating electric field on. (b) Intensities of the corresponding positions in (a) with electric field off. (c) Normalized signals.

Equations (3)

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Iθ=sinka sinθ/2ka sinθ/22sinmδ/2m sinδ/22×cosΦ/22,
Φ0=k2a+b2cosθ/2+α×sinθ/2+k2ΔnE2t.
Δn=1/2n03reffE,

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