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.

[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. APPLAB 56 , 1734 1736 ( 1990
    [CrossRef]
  2. J. S. Schildkraut , Determination of the electrooptic coefficient of a poled film , Appl. Opt. APOPAI 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 JOBPDE 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. JAPIAU 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. APPLAB 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 JOBPDE 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 JOBPDE 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 THSFAP 242 , 132 138 ( 1994
    [CrossRef]
  9. D. Eimerl , Crystal symmetry and the electrooptic effect , IEEE J. Quantum Electron. IEJQA7 QE-23 , 2104 2115 ( 1987
    [CrossRef]
  10. A. L. Kholkin , E. L. Colla , A. K. Tagantsev , D. V. Taylor , and N. Setter , Fatigue of piezoelectric properties in Pb(Zr, Ti)O 3 films , Appl. Phys. Lett. APPLAB 68 , 2577 2579 ( 1996
    [CrossRef]
  11. 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. JAPIAU 75 , 442 448 ( 1994
    [CrossRef]
  12. C. E. Land , Longitudinal electrooptic effects and photosensitivities of lead zirconate titanate thin films , J. Am. Ceram. Soc. JACTAW 72 , 2059 2064 ( 1989
    [CrossRef]
  13. K. D. Preston and G. H. Haertling , Comparison of electro-optic lead-lanthanum zirconate titanate films on crystalline and glass substrates , Appl. Phys. Lett. APPLAB 60 , 2831 2833 ( 1992
    [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. JAPIAU 77 , 4632 4638 ( 1995
[CrossRef]

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)O 3 films , Appl. Phys. Lett. APPLAB 68 , 2577 2579 ( 1996
[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)O 3 films , Appl. Phys. Lett. APPLAB 68 , 2577 2579 ( 1996
[CrossRef]

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. JAPIAU 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. JACTAW 72 , 2059 2064 ( 1989
[CrossRef]

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. JAPIAU 75 , 442 448 ( 1994
[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. JAPIAU 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. APPLAB 60 , 2831 2833 ( 1992
[CrossRef]

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)O 3 films , Appl. Phys. Lett. APPLAB 68 , 2577 2579 ( 1996
[CrossRef]

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)O 3 films , Appl. Phys. Lett. APPLAB 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. JAPIAU 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)O 3 films , Appl. Phys. Lett. APPLAB 68 , 2577 2579 ( 1996
[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. JAPIAU 75 , 442 448 ( 1994
[CrossRef]

Other (13)

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

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

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 THSFAP 242 , 132 138 ( 1994
[CrossRef]

D. Eimerl , Crystal symmetry and the electrooptic effect , IEEE J. Quantum Electron. IEJQA7 QE-23 , 2104 2115 ( 1987
[CrossRef]

A. L. Kholkin , E. L. Colla , A. K. Tagantsev , D. V. Taylor , and N. Setter , Fatigue of piezoelectric properties in Pb(Zr, Ti)O 3 films , Appl. Phys. Lett. APPLAB 68 , 2577 2579 ( 1996
[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. JAPIAU 75 , 442 448 ( 1994
[CrossRef]

C. E. Land , Longitudinal electrooptic effects and photosensitivities of lead zirconate titanate thin films , J. Am. Ceram. Soc. JACTAW 72 , 2059 2064 ( 1989
[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. APPLAB 60 , 2831 2833 ( 1992
[CrossRef]

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

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

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 JOBPDE 9 , 2274 2282 ( 1992
[CrossRef]

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 JOBPDE 14 , 1131 1137 ( 1997
[CrossRef]

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 JOBPDE 10 , 1894 1900 ( 1993
[CrossRef]

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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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