Abstract

Single-beam polarization interferometry was introduced to measure the Pockels coefficients in a Bi12SiO20 single crystal. The linear superposition principle of the induced birefringence and the optical activity was employed in an analysis of the Pockels effect measurement. The presence of the optical activity (the linear optical property) in a Bi12SiO20 crystal facilitated the measurement of the Pockels coefficients (the second-order nonlinear optical property) with a low modulation voltage. The longitudinal electro-optic configuration was adopted to determine one of the three Pockels tensor components. The magnitudes of r41 at the visible wavelengths were measured and found to be in the range of 3.5 to 5.0 pm/V.

© 2000 Optical Society of America

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References

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  1. M. Kauranen and A. Persoons, “Electro-optic effect in chiral isotropic media,” Nonlinear Opt. 19, 309–318 (1999).
  2. P. Pellet-Finet, “Measurement of the electro-optic coefficient of BSO crystals,” Opt. Commun. 50, 275–280 (1984).
    [CrossRef]
  3. P. Bayvel, “Electro-optic coefficient in BSO-type crystals with optical activity measurement and application to sensors,” Sens. Actuators 65, 247–254 (1989).
    [CrossRef]
  4. V. V. Kutsaenko, V. T. Potapov, and R. V. Shpilevskii, “Bi12SiO20 fiber-optic electric field sensor,” Sov. Phys. Tech. Phys. 30, 790–793 (1985).
  5. F. Vachss and L. Hesslink, “Measurement of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
    [CrossRef]
  6. P. Bayvel, M. McCall, and R. V. Wright, “Continuous method for measuring the electro-optic coefficient in Bi12SiO20 and Bi12GeO20,” Opt. Lett. 13, 27–29 (1988).
    [CrossRef] [PubMed]
  7. A. J. Fox and T. M. Bruton, “Electro-optic effects in the optically active compounds Bi12TiO20 and Bi40Ga2O63,” Appl. Phys. Lett. 27, 360–362 (1975).
    [CrossRef]
  8. 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]
  9. M. J. Shin, H. R. Cho, J. H. Kim, S. H. Han, and J. W. Wu, “Optical interferometric measurement of the electro-optic coefficient in nonlinear optical polymer films,” J. Korean Phys. Soc. 31, 99–103 (1997).
  10. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 4, pp. 69–120.
  11. J. F. Nye, Physical Properties of Crystals (Oxford University, Oxford, 1972), Chap. XIV, pp. 260–274.

1999 (1)

M. Kauranen and A. Persoons, “Electro-optic effect in chiral isotropic media,” Nonlinear Opt. 19, 309–318 (1999).

1997 (2)

M. J. Shin, H. R. Cho, J. H. Kim, S. H. Han, and J. W. Wu, “Optical interferometric measurement of the electro-optic coefficient in nonlinear optical polymer films,” J. Korean Phys. Soc. 31, 99–103 (1997).

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]

1989 (1)

P. Bayvel, “Electro-optic coefficient in BSO-type crystals with optical activity measurement and application to sensors,” Sens. Actuators 65, 247–254 (1989).
[CrossRef]

1988 (1)

1987 (1)

F. Vachss and L. Hesslink, “Measurement of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
[CrossRef]

1985 (1)

V. V. Kutsaenko, V. T. Potapov, and R. V. Shpilevskii, “Bi12SiO20 fiber-optic electric field sensor,” Sov. Phys. Tech. Phys. 30, 790–793 (1985).

1984 (1)

P. Pellet-Finet, “Measurement of the electro-optic coefficient of BSO crystals,” Opt. Commun. 50, 275–280 (1984).
[CrossRef]

1975 (1)

A. J. Fox and T. M. Bruton, “Electro-optic effects in the optically active compounds Bi12TiO20 and Bi40Ga2O63,” Appl. Phys. Lett. 27, 360–362 (1975).
[CrossRef]

Bayvel, P.

P. Bayvel, “Electro-optic coefficient in BSO-type crystals with optical activity measurement and application to sensors,” Sens. Actuators 65, 247–254 (1989).
[CrossRef]

P. Bayvel, M. McCall, and R. V. Wright, “Continuous method for measuring the electro-optic coefficient in Bi12SiO20 and Bi12GeO20,” Opt. Lett. 13, 27–29 (1988).
[CrossRef] [PubMed]

Bruton, T. M.

A. J. Fox and T. M. Bruton, “Electro-optic effects in the optically active compounds Bi12TiO20 and Bi40Ga2O63,” Appl. Phys. Lett. 27, 360–362 (1975).
[CrossRef]

Cho, H. R.

M. J. Shin, H. R. Cho, J. H. Kim, S. H. Han, and J. W. Wu, “Optical interferometric measurement of the electro-optic coefficient in nonlinear optical polymer films,” J. Korean Phys. Soc. 31, 99–103 (1997).

Fox, A. J.

A. J. Fox and T. M. Bruton, “Electro-optic effects in the optically active compounds Bi12TiO20 and Bi40Ga2O63,” Appl. Phys. Lett. 27, 360–362 (1975).
[CrossRef]

Han, S. H.

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]

M. J. Shin, H. R. Cho, J. H. Kim, S. H. Han, and J. W. Wu, “Optical interferometric measurement of the electro-optic coefficient in nonlinear optical polymer films,” J. Korean Phys. Soc. 31, 99–103 (1997).

Hesslink, L.

F. Vachss and L. Hesslink, “Measurement of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
[CrossRef]

Kauranen, M.

M. Kauranen and A. Persoons, “Electro-optic effect in chiral isotropic media,” Nonlinear Opt. 19, 309–318 (1999).

Kim, J. H.

M. J. Shin, H. R. Cho, J. H. Kim, S. H. Han, and J. W. Wu, “Optical interferometric measurement of the electro-optic coefficient in nonlinear optical polymer films,” J. Korean Phys. Soc. 31, 99–103 (1997).

Kutsaenko, V. V.

V. V. Kutsaenko, V. T. Potapov, and R. V. Shpilevskii, “Bi12SiO20 fiber-optic electric field sensor,” Sov. Phys. Tech. Phys. 30, 790–793 (1985).

McCall, M.

Pellet-Finet, P.

P. Pellet-Finet, “Measurement of the electro-optic coefficient of BSO crystals,” Opt. Commun. 50, 275–280 (1984).
[CrossRef]

Persoons, A.

M. Kauranen and A. Persoons, “Electro-optic effect in chiral isotropic media,” Nonlinear Opt. 19, 309–318 (1999).

Potapov, V. T.

V. V. Kutsaenko, V. T. Potapov, and R. V. Shpilevskii, “Bi12SiO20 fiber-optic electric field sensor,” Sov. Phys. Tech. Phys. 30, 790–793 (1985).

Shin, M. J.

M. J. Shin, H. R. Cho, J. H. Kim, S. H. Han, and J. W. Wu, “Optical interferometric measurement of the electro-optic coefficient in nonlinear optical polymer films,” J. Korean Phys. Soc. 31, 99–103 (1997).

Shpilevskii, R. V.

V. V. Kutsaenko, V. T. Potapov, and R. V. Shpilevskii, “Bi12SiO20 fiber-optic electric field sensor,” Sov. Phys. Tech. Phys. 30, 790–793 (1985).

Vachss, F.

F. Vachss and L. Hesslink, “Measurement of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
[CrossRef]

Wright, R. V.

Wu, J. W.

M. J. Shin, H. R. Cho, J. H. Kim, S. H. Han, and J. W. Wu, “Optical interferometric measurement of the electro-optic coefficient in nonlinear optical polymer films,” J. Korean Phys. Soc. 31, 99–103 (1997).

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]

Appl. Phys. Lett. (1)

A. J. Fox and T. M. Bruton, “Electro-optic effects in the optically active compounds Bi12TiO20 and Bi40Ga2O63,” Appl. Phys. Lett. 27, 360–362 (1975).
[CrossRef]

J. Korean Phys. Soc. (1)

M. J. Shin, H. R. Cho, J. H. Kim, S. H. Han, and J. W. Wu, “Optical interferometric measurement of the electro-optic coefficient in nonlinear optical polymer films,” J. Korean Phys. Soc. 31, 99–103 (1997).

J. Opt. Soc. Am. B (1)

Nonlinear Opt. (1)

M. Kauranen and A. Persoons, “Electro-optic effect in chiral isotropic media,” Nonlinear Opt. 19, 309–318 (1999).

Opt. Commun. (2)

P. Pellet-Finet, “Measurement of the electro-optic coefficient of BSO crystals,” Opt. Commun. 50, 275–280 (1984).
[CrossRef]

F. Vachss and L. Hesslink, “Measurement of the electrogyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
[CrossRef]

Opt. Lett. (1)

Sens. Actuators (1)

P. Bayvel, “Electro-optic coefficient in BSO-type crystals with optical activity measurement and application to sensors,” Sens. Actuators 65, 247–254 (1989).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

V. V. Kutsaenko, V. T. Potapov, and R. V. Shpilevskii, “Bi12SiO20 fiber-optic electric field sensor,” Sov. Phys. Tech. Phys. 30, 790–793 (1985).

Other (2)

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 4, pp. 69–120.

J. F. Nye, Physical Properties of Crystals (Oxford University, Oxford, 1972), Chap. XIV, pp. 260–274.

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Figures (7)

Fig. 1
Fig. 1

Layout of the optical path and the optical components arrangement for the single-beam polarization interferometry.

Fig. 2
Fig. 2

Experimental setup for the measurement of the Pockels coefficient r41 in BSO.

Fig. 3
Fig. 3

Modulated intensity is plotted as a function of the modulation voltage with β=45°, γ=0°, and Γ=90°. The solid line is a least-squares fit to the data points.

Fig. 4
Fig. 4

Modulated intensity (solid circles) and the dc intensity (solid squares) are plotted as a function of the azimuthal angle of the Soleil–Babinet compensator (γ) with Vpp=20 V, Γ=90°, and β=45°. The solid (dotted) curve is a least-square fit to the data points of the solid circles (squares).

Fig. 5
Fig. 5

Modulated intensity (open circles) and the dc intensity (open squares) are plotted as a function of the optical bias determined by the Soleil–Babinet compensator (Γ) with Vpp=20 V, γ=0°, and β=45°. The solid (dotted) curve is a least-square fit to the data points of the open circles (squares).

Fig. 6
Fig. 6

Modulated intensity (solid circles) and the dc intensity (solid squares) are plotted as a function of the polarization angle of the incident beam (β) with Vpp=20 V, γ=0°, and Γ=90°. The solid (dotted) curve is a least-squares fit to the data points of the solid circles (squares).

Fig. 7
Fig. 7

Modulated intensity (solid circles) and the dc intensity (solid squares) are plotted as a function of the crystal orientation. The ratio of the modulated intensity to the dc intensity (solid triangles) is directly related to the Pockels coefficient. The solid curve is the theoretical fit following Eq. (19).

Equations (25)

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D=E+ioG×E,=E,
k×(k×E)+μω2E+ioμω2(G×E)=0,
sx2n2-nx2+sy2n2-ny2+sz2n2-nz2-1n2
=G2sx2nx2+sy2ny2+sz2nz2n2(n2-nx2)(n2-ny2)(n2-nz2),
(n2-ny2)(n2-nz2)=G2.
ny=nz=no;
n2-no2=±G.
n=no±G2no,
x2no2+y2no2+z2no2+2r41yzEx=1,
nx=no,
ny=no-12no3r41Ex,
nz=no+12no3r41Ex.
δ=2πλ0(nz-ny),=2πλ0no3r41Ex,=2πλ0no3r41VmLsinωmt,
Δ=2πλ0(n+-n-).
Δ2=4π2λ02(nz-ny)2+4π2G2λ02n¯2δ2+(2ρ)2,
MBSO=cos(ΔL/2)I+isin(ΔL/2)sinθi cos θ-icos θ-sin θ,=cosΔL2+iδΔsinΔL2-2ρΔsinΔL22ρΔsinΔL2cosΔL2-iδΔsinΔL2,
Pin=cos βsin β,Pout=-sin βcos β.
Mcomp=R(-γ)WR(γ),=cos γsin γ-sin γcos γexp(-iΓ/2)00exp(iΓ/2)×cos γ-sin γsin γcos γ.
I=|PoutMcompMBSOPin|2,
=I0cos2Γ2sin2(ρL)+sin2Γ2sin2[ρL+2(β-γ)]+I0δ2ρsin Γ sin(ρL)sin(ρL+2β)sin [2(β-γ)],
=Idc+Imod. sinωmt,
r41=Imod.I0
×2λ0ρL2πno3Vm sinΓsin(ρL)sin(ρL+2β)sin[2(β-γ)].
IdcI0=12[1-cos Γ cos(2ρL)].
Imod. sinωmtI0=2πno3r41Vm sinωmtsin Γsin ρLsin(ρL+2β)sin[2(β-γ)]λ0L(2ρL),

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