Abstract

A two-beam polarization (TBP) interferometer with a reflection configuration for measuring the linear electro-optic coefficient is described and investigated experimentally and theoretically. It is shown that a TBP interferometer can be used for measuring the Pockels coefficient of a thin film with a strong Fabry–Perot effect. Relative errors of the simple proposed method for Pockels coefficient measurement are estimated. The TBP interferometer technique is used to measure the effective differential linear electro-optic coefficient re=r33-(no/ne)3r13 of a lead zirconate titanate thin film. The results are in agreement with known data.

© 1998 Optical Society of America

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References

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  1. C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
    [CrossRef]
  2. J. S. Schildkraut, “Determination of the electrooptic coefficient of a poled film,” Appl. Opt. 29, 2839–2841 (1990).
    [CrossRef] [PubMed]
  3. S. H. Han and J. W. Wu, “Single-beam polarization interferometry measurement of the linear electro-optic effect in poled polymer films with a reflection configuration,” J. Opt. Soc. Am. B 14, 1131–1137 (1997).
    [CrossRef]
  4. Y. Shuto and M. Armano, “Reflection measurement technique of electro-optic coefficients in lithium niobate crystals and poled polymer films,” J. Appl. Phys. 77, 4632–4638 (1995).
    [CrossRef]
  5. P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third-order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
    [CrossRef]
  6. K. Clays and J. S. Schildkraut, “Dispersion of the complex electro-optic coefficient and electrochromic effects in poled polymer films,” J. Opt. Soc. Am. B 9, 2274–2282 (1992).
    [CrossRef]
  7. D. Morichere, P. A. Chollet, W. Fleming, M. Jurich, B. A. Smith, and J. D. Swalen, “Electro-optic effects in two tolane side-chain nonlinear-optical polymers: comparison between measured coefficients and second-harmonic generation,” J. Opt. Soc. Am. B 10, 1894–1900 (1993).
    [CrossRef]
  8. P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132–138 (1994).
    [CrossRef]
  9. M. V. Klein, Optics (Wiley, New York, 1970).
  10. D. Eimerl, “Crystal symmetry and the electrooptic effect,” IEEE J. Quantum Electron. QE-23, 2104–2115 (1987).
    [CrossRef]
  11. A. L. Kholkin, E. L. Colla, A. K. Tagantsev, D. V. Taylor, and N. Setter, “Fatigue of piezoelectric properties in Pb(Zr, Ti)O3 films,” Appl. Phys. Lett. 68, 2577–2579 (1996).
    [CrossRef]
  12. F. Agullo-Lopez, J. M. Cabrera, and F. Agullo-Rieda, Electrooptics (Academic, San Diego, Calif., 1994).
  13. A. Moulson and J. M. Herbert, Electroceramics (Chapman & Hall, London, 1993).
  14. J.-F. Li, D. D. Viehkand, T. Tani, C. D. E. Lakeman, and D. A. Payne, “Piezoelectric properties of sol-gel-derived ferroelectric and antiferroelectric thin layers,” J. Appl. Phys. 75, 442–448 (1994).
    [CrossRef]
  15. C. E. Land, “Longitudinal electrooptic effects and photosensitivities of lead zirconate titanate thin films,” J. Am. Ceram. Soc. 72, 2059–2064 (1989).
    [CrossRef]
  16. K. D. Preston and G. H. Haertling, “Comparison of electro-optic lead-lanthanum zirconate titanate films on crystalline and glass substrates,” Appl. Phys. Lett. 60, 2831–2833 (1992).
    [CrossRef]
  17. C.-H. Lee, V. Spirin, H.-W. Song, and K.-S. No, “Drying temperature effects on microstructure, electrical properties and electro-optic coefficients of sol-gel derived PZT thin films,” J. Mater. Res. (to be published).

1997 (1)

1996 (1)

A. L. Kholkin, E. L. Colla, A. K. Tagantsev, D. V. Taylor, and N. Setter, “Fatigue of piezoelectric properties in Pb(Zr, Ti)O3 films,” Appl. Phys. Lett. 68, 2577–2579 (1996).
[CrossRef]

1995 (1)

Y. Shuto and M. Armano, “Reflection measurement technique of electro-optic coefficients in lithium niobate crystals and poled polymer films,” J. Appl. Phys. 77, 4632–4638 (1995).
[CrossRef]

1994 (2)

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132–138 (1994).
[CrossRef]

J.-F. Li, D. D. Viehkand, T. Tani, C. D. E. Lakeman, and D. A. Payne, “Piezoelectric properties of sol-gel-derived ferroelectric and antiferroelectric thin layers,” J. Appl. Phys. 75, 442–448 (1994).
[CrossRef]

1993 (1)

1992 (2)

K. Clays and J. S. Schildkraut, “Dispersion of the complex electro-optic coefficient and electrochromic effects in poled polymer films,” J. Opt. Soc. Am. B 9, 2274–2282 (1992).
[CrossRef]

K. D. Preston and G. H. Haertling, “Comparison of electro-optic lead-lanthanum zirconate titanate films on crystalline and glass substrates,” Appl. Phys. Lett. 60, 2831–2833 (1992).
[CrossRef]

1991 (1)

P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third-order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
[CrossRef]

1990 (2)

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[CrossRef]

J. S. Schildkraut, “Determination of the electrooptic coefficient of a poled film,” Appl. Opt. 29, 2839–2841 (1990).
[CrossRef] [PubMed]

1989 (1)

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

1987 (1)

D. Eimerl, “Crystal symmetry and the electrooptic effect,” IEEE J. Quantum Electron. QE-23, 2104–2115 (1987).
[CrossRef]

Agullo-Lopez, F.

F. Agullo-Lopez, J. M. Cabrera, and F. Agullo-Rieda, Electrooptics (Academic, San Diego, Calif., 1994).

Agullo-Rieda, F.

F. Agullo-Lopez, J. M. Cabrera, and F. Agullo-Rieda, Electrooptics (Academic, San Diego, Calif., 1994).

Andress, B.

P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third-order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
[CrossRef]

Armano, M.

Y. Shuto and M. Armano, “Reflection measurement technique of electro-optic coefficients in lithium niobate crystals and poled polymer films,” J. Appl. Phys. 77, 4632–4638 (1995).
[CrossRef]

Cabrera, J. M.

F. Agullo-Lopez, J. M. Cabrera, and F. Agullo-Rieda, Electrooptics (Academic, San Diego, Calif., 1994).

Chollet, P. A.

Chollet, P.-A.

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132–138 (1994).
[CrossRef]

Clays, K.

Colla, E. L.

A. L. Kholkin, E. L. Colla, A. K. Tagantsev, D. V. Taylor, and N. Setter, “Fatigue of piezoelectric properties in Pb(Zr, Ti)O3 films,” Appl. Phys. Lett. 68, 2577–2579 (1996).
[CrossRef]

Eimerl, D.

D. Eimerl, “Crystal symmetry and the electrooptic effect,” IEEE J. Quantum Electron. QE-23, 2104–2115 (1987).
[CrossRef]

Fleming, W.

Gadret, G.

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132–138 (1994).
[CrossRef]

Haertling, G. H.

K. D. Preston and G. H. Haertling, “Comparison of electro-optic lead-lanthanum zirconate titanate films on crystalline and glass substrates,” Appl. Phys. Lett. 60, 2831–2833 (1992).
[CrossRef]

Han, S. H.

Herbert, J. M.

A. Moulson and J. M. Herbert, Electroceramics (Chapman & Hall, London, 1993).

Jurich, M.

Kajzar, F.

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132–138 (1994).
[CrossRef]

Kholkin, A. L.

A. L. Kholkin, E. L. Colla, A. K. Tagantsev, D. V. Taylor, and N. Setter, “Fatigue of piezoelectric properties in Pb(Zr, Ti)O3 films,” Appl. Phys. Lett. 68, 2577–2579 (1996).
[CrossRef]

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970).

Lakeman, C. D. E.

J.-F. Li, D. D. Viehkand, T. Tani, C. D. E. Lakeman, and D. A. Payne, “Piezoelectric properties of sol-gel-derived ferroelectric and antiferroelectric thin layers,” J. Appl. Phys. 75, 442–448 (1994).
[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]

Lee, C.-H.

C.-H. Lee, V. Spirin, H.-W. Song, and K.-S. No, “Drying temperature effects on microstructure, electrical properties and electro-optic coefficients of sol-gel derived PZT thin films,” J. Mater. Res. (to be published).

Li, J.-F.

J.-F. Li, D. D. Viehkand, T. Tani, C. D. E. Lakeman, and D. A. Payne, “Piezoelectric properties of sol-gel-derived ferroelectric and antiferroelectric thin layers,” J. Appl. Phys. 75, 442–448 (1994).
[CrossRef]

Man, H. T.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[CrossRef]

Morichere, D.

Moulson, A.

A. Moulson and J. M. Herbert, Electroceramics (Chapman & Hall, London, 1993).

No, K.-S.

C.-H. Lee, V. Spirin, H.-W. Song, and K.-S. No, “Drying temperature effects on microstructure, electrical properties and electro-optic coefficients of sol-gel derived PZT thin films,” J. Mater. Res. (to be published).

Nordmann, J.

P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third-order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
[CrossRef]

Payne, D. A.

J.-F. Li, D. D. Viehkand, T. Tani, C. D. E. Lakeman, and D. A. Payne, “Piezoelectric properties of sol-gel-derived ferroelectric and antiferroelectric thin layers,” J. Appl. Phys. 75, 442–448 (1994).
[CrossRef]

Preston, K. D.

K. D. Preston and G. H. Haertling, “Comparison of electro-optic lead-lanthanum zirconate titanate films on crystalline and glass substrates,” Appl. Phys. Lett. 60, 2831–2833 (1992).
[CrossRef]

Raimond, P.

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132–138 (1994).
[CrossRef]

Rohl, P.

P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third-order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
[CrossRef]

Schildkraut, J. S.

Setter, N.

A. L. Kholkin, E. L. Colla, A. K. Tagantsev, D. V. Taylor, and N. Setter, “Fatigue of piezoelectric properties in Pb(Zr, Ti)O3 films,” Appl. Phys. Lett. 68, 2577–2579 (1996).
[CrossRef]

Shuto, Y.

Y. Shuto and M. Armano, “Reflection measurement technique of electro-optic coefficients in lithium niobate crystals and poled polymer films,” J. Appl. Phys. 77, 4632–4638 (1995).
[CrossRef]

Smith, B. A.

Song, H.-W.

C.-H. Lee, V. Spirin, H.-W. Song, and K.-S. No, “Drying temperature effects on microstructure, electrical properties and electro-optic coefficients of sol-gel derived PZT thin films,” J. Mater. Res. (to be published).

Spirin, V.

C.-H. Lee, V. Spirin, H.-W. Song, and K.-S. No, “Drying temperature effects on microstructure, electrical properties and electro-optic coefficients of sol-gel derived PZT thin films,” J. Mater. Res. (to be published).

Swalen, J. D.

Tagantsev, A. K.

A. L. Kholkin, E. L. Colla, A. K. Tagantsev, D. V. Taylor, and N. Setter, “Fatigue of piezoelectric properties in Pb(Zr, Ti)O3 films,” Appl. Phys. Lett. 68, 2577–2579 (1996).
[CrossRef]

Tani, T.

J.-F. Li, D. D. Viehkand, T. Tani, C. D. E. Lakeman, and D. A. Payne, “Piezoelectric properties of sol-gel-derived ferroelectric and antiferroelectric thin layers,” J. Appl. Phys. 75, 442–448 (1994).
[CrossRef]

Taylor, D. V.

A. L. Kholkin, E. L. Colla, A. K. Tagantsev, D. V. Taylor, and N. Setter, “Fatigue of piezoelectric properties in Pb(Zr, Ti)O3 films,” Appl. Phys. Lett. 68, 2577–2579 (1996).
[CrossRef]

Teng, C. C.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[CrossRef]

Viehkand, D. D.

J.-F. Li, D. D. Viehkand, T. Tani, C. D. E. Lakeman, and D. A. Payne, “Piezoelectric properties of sol-gel-derived ferroelectric and antiferroelectric thin layers,” J. Appl. Phys. 75, 442–448 (1994).
[CrossRef]

Wu, J. W.

Appl. Opt. (1)

Appl. Phys. Lett. (4)

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[CrossRef]

P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third-order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
[CrossRef]

A. L. Kholkin, E. L. Colla, A. K. Tagantsev, D. V. Taylor, and N. Setter, “Fatigue of piezoelectric properties in Pb(Zr, Ti)O3 films,” Appl. Phys. Lett. 68, 2577–2579 (1996).
[CrossRef]

K. D. Preston and G. H. Haertling, “Comparison of electro-optic lead-lanthanum zirconate titanate films on crystalline and glass substrates,” Appl. Phys. Lett. 60, 2831–2833 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Eimerl, “Crystal symmetry and the electrooptic effect,” IEEE J. Quantum Electron. QE-23, 2104–2115 (1987).
[CrossRef]

J. Am. Ceram. Soc. (1)

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

J. Appl. Phys. (2)

J.-F. Li, D. D. Viehkand, T. Tani, C. D. E. Lakeman, and D. A. Payne, “Piezoelectric properties of sol-gel-derived ferroelectric and antiferroelectric thin layers,” J. Appl. Phys. 75, 442–448 (1994).
[CrossRef]

Y. Shuto and M. Armano, “Reflection measurement technique of electro-optic coefficients in lithium niobate crystals and poled polymer films,” J. Appl. Phys. 77, 4632–4638 (1995).
[CrossRef]

J. Opt. Soc. Am. B (3)

Thin Solid Films (1)

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132–138 (1994).
[CrossRef]

Other (4)

M. V. Klein, Optics (Wiley, New York, 1970).

F. Agullo-Lopez, J. M. Cabrera, and F. Agullo-Rieda, Electrooptics (Academic, San Diego, Calif., 1994).

A. Moulson and J. M. Herbert, Electroceramics (Chapman & Hall, London, 1993).

C.-H. Lee, V. Spirin, H.-W. Song, and K.-S. No, “Drying temperature effects on microstructure, electrical properties and electro-optic coefficients of sol-gel derived PZT thin films,” J. Mater. Res. (to be published).

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Figures (7)

Fig. 1
Fig. 1

Optical configuration of the reflection technique.

Fig. 2
Fig. 2

Experimental setup for PZT thin-film testing.

Fig. 3
Fig. 3

Output interferometer intensity with a half-wave retardation plate (ITBP) and without it (IFP) versus an additional phase shift ψ between s- and p-polarized beams. L, left; R, right.

Fig. 4
Fig. 4

Modulated output intensity of TBP, FP, and 2SP interferometers versus an additional phase shift ψ between s- and p-polarized beams for different values of the top surface of the PZT thin-film reflectivity: (a) R1=0.001, (b) R1=0.025, and (c) R1=0.1.

Fig. 5
Fig. 5

Modulated intensity of the 2SP interferometer at the first harmonic of excitation versus alternating field amplitude.

Fig. 6
Fig. 6

Experimental dependence of the modulated intensity of the TBP interferometer versus an additional phase shift ψ between s- and p-polarized beams.

Fig. 7
Fig. 7

Dependence of the effective differential Pockels coefficient re on the dc electric field (Em=20 kV/cm).

Equations (40)

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ϕ1s=(4πd/λ)tan(αs)ng sin θ,
ϕ1p=(4πd/λ)tan(αs)ng sin θ,
ϕ2s=(4πd/λ)ns/cos(αs),
ϕ2p=(4πd/λ)[np/cos(αp)+ng sin θ(tan αs-tan αp)],
sin θ=ng sin θ=np sin αp=ns sin αs,
ns=no,
1/np2=cos2 αp/no2+sin2 αp/ne2,
np2=[no2ne2+sin2 θ(ne2-no2)]/ne2,
ϕ2sp=(4πd/λ)[ns/cos αs-np/cos αp-sin θ(tan αs-tan αp)]=(4πd/λ)[(ns-sin θ sin αs)/cos αs-(np-sin θ sin αp)/cos αp]=(4πd/λ)[(ns2-sin2 θ)1/2-(np2-sin2 θ)1/2]=(4πd/λ)[(no2-sin2 θ)1/2-(no/ne)(ne2-sin2 θ)1/2].
δϕ2sp=(ϕ2sp/no)δno+(ϕ2sp/ne)δne+(ϕ2sp/d)δd,
δno=-(no3/2)r13δE,
δne=-(ne3/2)r33δE,
δd=dd33δE,
δϕ2sp(2πdreEm/λ)[n2 sin2 θ/(n2-sin2 θ)1/2],
nonen.
IFP=|E1s+E2s|2/2+|E1p+E2p|2/2,
E1s=R1E0 exp(-iϕ1s),
E1p=R1E0 exp[-i(ϕ1p+ψ)],
E2s=R2E0(1-R12)T exp(-iϕ2s),
E2p=R2E0(1-R12)T exp[-i(ϕ2p+ψ)],
ITBP=|E1s+E1p+E2s+E2p|2/2.
I2SP=|E2s+E2p|2/2.
STBP=ITBP/E,
SFP=IFP/E,
S2SP=I2SP/E.
S2SP(ψa)[STBP(ψa)-STBP(ψb)]/2STBP(ψa)-SFP(ψa)-[STBP(ψb)-SFP(ψb)],
F=STBP(ψb)/STBP(ψa).
Δn(E)=-n32 -E0*E0*re(E)dE,
ϕ2sp=ϕ2spno δno+ϕ2spne δne+ϕ2spd δd,
δno=-(no3/2)r13δE,
δne=-(ne3/2)r33δE,
δd=dd33δE,
ϕ2spno δno+ϕ2spne δne
=2πdδEλ r13no3×(ne2-sin2 θ)1/2(no2-sin2 θ)1/2-nenone(no2-sin2 θ)1/2+r33none sin2 θ(ne2-sin2 θ)1/2=2πdδEλ none sin2 θ(ne2-sin2 θ)1/2 (r33+r13A),
A=(ne2-sin2 θ)1/2(no2-sin2 θ)1/2 no2ne2× [(ne2-sin2 θ)1/2(no2-sin2 θ)1/2-neno]sin2 θ.
ϕ2spno δno+ϕ2spne δne
2πdδEλ ne2 sin2 θ(ne2-sin2 θ)1/2 (r33-r13)2πdδEλ no2 sin2 θ(no2-sin2 θ)1/2 (r33-r13).
ϕ2spd δd=4πdd33δEλ [(no2-sin2 θ)1/2-(no/ne)(ne2-sin2 θ)1/2]=4πdd33noδEλ 1-sin2 θno21/2-1-sin2 θne21/2=4πdd33δEλ sin2 θ(no+ne)none21-sin2 θno21/2+1-sin2 θne21/2 Δn.
ϕ2spd δd/ϕ2spno δno+ϕ2spne δne0.01,
δϕ2sp2πdδEλ ne2 sin2 θ(ne2-sin2 θ)1/2 (r33-r13)2πdδEλ no2 sin2 θ(no2-sin2 θ)1/2 (r33-r13).

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