Abstract

Certain optical properties can be described in terms of two linear birefringences existing in separate Jones platelets of a medium. One of these, known as Jones birefringence, although occurring naturally in some crystals is too small to be measurable. However, the two birefringences can be induced by an electric field in 4¯ and 6¯ crystals for propagation along the optic axis. For an even slightly divergent light beam, natural birefringence may affect accuracy of measurement. Calculations show that in an experiment with a static field the error depends critically on beam divergence, whereas with a modulated field this is not so.

© 2001 Optical Society of America

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References

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  1. R. C. Jones, “A new calculus for the treatment of optical systems. VII. Properties of the N-matrices,” J. Opt. Soc. Am. 38, 671–685 (1948).
    [CrossRef]
  2. E. B. Graham, R. E. Raab, “On the Jones birefringence,” Proc. R. Soc. London, Ser. A 390, 73–90 (1983).
    [CrossRef]
  3. E. B. Graham, R. E. Raab, “Light propagation in cubic and other anisotropic crystals,” Proc. R. Soc. London, Ser. A 430, 593–614 (1990).
    [CrossRef]
  4. C. Graham, R. E. Raab, “Eigenvector approach to the evaluation of the Jones N matrices of nonabsorbing crystalline media,” J. Opt. Soc. Am. A 11, 2137–2144 (1994).
    [CrossRef]
  5. T. Roth, G. L. J. A. Rikken, “Observation of magnetoelectric Jones birefringence,” Phys. Rev. Lett. 85, 4478–4481 (2000).
    [CrossRef] [PubMed]
  6. E. M. Meintjes, R. E. Raab, “A new theory of Pockels birefringence in non-magnetic crystals,” J. Opt. A Pure Appl. Opt. 1, 146–151 (1999).
    [CrossRef]
  7. I. P. Kaminov, An Introduction to Electrooptic Devices (Academic, New York, 1974), Chap. 2.
  8. W. Kucharczyk, M. J. Gunning, R. E. Raab, C. Graham, “Interferometric investigation of the quadratic electro-optic effect in KDP,” Physica B 212, 5–9 (1995).
    [CrossRef]
  9. M. J. Gunning, R. E. Raab, P. Górski, W. Kucharczyk, “The quadratic electrooptic effect and estimation of antipolarization in ADP,” Ferroelectr. Lett. Sect. 24, 63–68 (1998).
    [CrossRef]
  10. R. R. Birss, Symmetry and Magnetism, 2nd ed. (North–Holland, Amsterdam, 1966).
  11. M. J. Gunning, R. E. Raab, “Systematic eigenvalue approach to crystal optics: an analytic alternative to the geometric ellipsoid model,” J. Opt. Soc. Am. A 15, 2199–2207 (1998).
    [CrossRef]
  12. J. D. H. Donnay, W. Nowacki, Crystal Data:  Classification of Substances by Space Groups and Their Identification from Cell Dimensions (Geological Society of America, New York, 1954).
  13. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  14. V. E. Perfilova, A. S. Sonin, “Quadratic electrooptic effect in KDP and ADP crystals,” Bull. Acad. Sci. USSR, Phys. Ser. 31, 1154–1157 (1967).
  15. M. J. Gunning, R. E. Raab, W. Kucharczyk, “Magnitude and nature of the quadratic electro-optic effect in KDP and ADP single crystals,” J. Opt. Soc. Am. B (to be published).

2000

T. Roth, G. L. J. A. Rikken, “Observation of magnetoelectric Jones birefringence,” Phys. Rev. Lett. 85, 4478–4481 (2000).
[CrossRef] [PubMed]

1999

E. M. Meintjes, R. E. Raab, “A new theory of Pockels birefringence in non-magnetic crystals,” J. Opt. A Pure Appl. Opt. 1, 146–151 (1999).
[CrossRef]

1998

M. J. Gunning, R. E. Raab, P. Górski, W. Kucharczyk, “The quadratic electrooptic effect and estimation of antipolarization in ADP,” Ferroelectr. Lett. Sect. 24, 63–68 (1998).
[CrossRef]

M. J. Gunning, R. E. Raab, “Systematic eigenvalue approach to crystal optics: an analytic alternative to the geometric ellipsoid model,” J. Opt. Soc. Am. A 15, 2199–2207 (1998).
[CrossRef]

1995

W. Kucharczyk, M. J. Gunning, R. E. Raab, C. Graham, “Interferometric investigation of the quadratic electro-optic effect in KDP,” Physica B 212, 5–9 (1995).
[CrossRef]

1994

1990

E. B. Graham, R. E. Raab, “Light propagation in cubic and other anisotropic crystals,” Proc. R. Soc. London, Ser. A 430, 593–614 (1990).
[CrossRef]

1983

E. B. Graham, R. E. Raab, “On the Jones birefringence,” Proc. R. Soc. London, Ser. A 390, 73–90 (1983).
[CrossRef]

1967

V. E. Perfilova, A. S. Sonin, “Quadratic electrooptic effect in KDP and ADP crystals,” Bull. Acad. Sci. USSR, Phys. Ser. 31, 1154–1157 (1967).

1948

Birss, R. R.

R. R. Birss, Symmetry and Magnetism, 2nd ed. (North–Holland, Amsterdam, 1966).

Donnay, J. D. H.

J. D. H. Donnay, W. Nowacki, Crystal Data:  Classification of Substances by Space Groups and Their Identification from Cell Dimensions (Geological Society of America, New York, 1954).

Górski, P.

M. J. Gunning, R. E. Raab, P. Górski, W. Kucharczyk, “The quadratic electrooptic effect and estimation of antipolarization in ADP,” Ferroelectr. Lett. Sect. 24, 63–68 (1998).
[CrossRef]

Graham, C.

W. Kucharczyk, M. J. Gunning, R. E. Raab, C. Graham, “Interferometric investigation of the quadratic electro-optic effect in KDP,” Physica B 212, 5–9 (1995).
[CrossRef]

C. Graham, R. E. Raab, “Eigenvector approach to the evaluation of the Jones N matrices of nonabsorbing crystalline media,” J. Opt. Soc. Am. A 11, 2137–2144 (1994).
[CrossRef]

Graham, E. B.

E. B. Graham, R. E. Raab, “Light propagation in cubic and other anisotropic crystals,” Proc. R. Soc. London, Ser. A 430, 593–614 (1990).
[CrossRef]

E. B. Graham, R. E. Raab, “On the Jones birefringence,” Proc. R. Soc. London, Ser. A 390, 73–90 (1983).
[CrossRef]

Gunning, M. J.

M. J. Gunning, R. E. Raab, “Systematic eigenvalue approach to crystal optics: an analytic alternative to the geometric ellipsoid model,” J. Opt. Soc. Am. A 15, 2199–2207 (1998).
[CrossRef]

M. J. Gunning, R. E. Raab, P. Górski, W. Kucharczyk, “The quadratic electrooptic effect and estimation of antipolarization in ADP,” Ferroelectr. Lett. Sect. 24, 63–68 (1998).
[CrossRef]

W. Kucharczyk, M. J. Gunning, R. E. Raab, C. Graham, “Interferometric investigation of the quadratic electro-optic effect in KDP,” Physica B 212, 5–9 (1995).
[CrossRef]

M. J. Gunning, R. E. Raab, W. Kucharczyk, “Magnitude and nature of the quadratic electro-optic effect in KDP and ADP single crystals,” J. Opt. Soc. Am. B (to be published).

Jones, R. C.

Kaminov, I. P.

I. P. Kaminov, An Introduction to Electrooptic Devices (Academic, New York, 1974), Chap. 2.

Kucharczyk, W.

M. J. Gunning, R. E. Raab, P. Górski, W. Kucharczyk, “The quadratic electrooptic effect and estimation of antipolarization in ADP,” Ferroelectr. Lett. Sect. 24, 63–68 (1998).
[CrossRef]

W. Kucharczyk, M. J. Gunning, R. E. Raab, C. Graham, “Interferometric investigation of the quadratic electro-optic effect in KDP,” Physica B 212, 5–9 (1995).
[CrossRef]

M. J. Gunning, R. E. Raab, W. Kucharczyk, “Magnitude and nature of the quadratic electro-optic effect in KDP and ADP single crystals,” J. Opt. Soc. Am. B (to be published).

Meintjes, E. M.

E. M. Meintjes, R. E. Raab, “A new theory of Pockels birefringence in non-magnetic crystals,” J. Opt. A Pure Appl. Opt. 1, 146–151 (1999).
[CrossRef]

Nowacki, W.

J. D. H. Donnay, W. Nowacki, Crystal Data:  Classification of Substances by Space Groups and Their Identification from Cell Dimensions (Geological Society of America, New York, 1954).

Perfilova, V. E.

V. E. Perfilova, A. S. Sonin, “Quadratic electrooptic effect in KDP and ADP crystals,” Bull. Acad. Sci. USSR, Phys. Ser. 31, 1154–1157 (1967).

Raab, R. E.

E. M. Meintjes, R. E. Raab, “A new theory of Pockels birefringence in non-magnetic crystals,” J. Opt. A Pure Appl. Opt. 1, 146–151 (1999).
[CrossRef]

M. J. Gunning, R. E. Raab, “Systematic eigenvalue approach to crystal optics: an analytic alternative to the geometric ellipsoid model,” J. Opt. Soc. Am. A 15, 2199–2207 (1998).
[CrossRef]

M. J. Gunning, R. E. Raab, P. Górski, W. Kucharczyk, “The quadratic electrooptic effect and estimation of antipolarization in ADP,” Ferroelectr. Lett. Sect. 24, 63–68 (1998).
[CrossRef]

W. Kucharczyk, M. J. Gunning, R. E. Raab, C. Graham, “Interferometric investigation of the quadratic electro-optic effect in KDP,” Physica B 212, 5–9 (1995).
[CrossRef]

C. Graham, R. E. Raab, “Eigenvector approach to the evaluation of the Jones N matrices of nonabsorbing crystalline media,” J. Opt. Soc. Am. A 11, 2137–2144 (1994).
[CrossRef]

E. B. Graham, R. E. Raab, “Light propagation in cubic and other anisotropic crystals,” Proc. R. Soc. London, Ser. A 430, 593–614 (1990).
[CrossRef]

E. B. Graham, R. E. Raab, “On the Jones birefringence,” Proc. R. Soc. London, Ser. A 390, 73–90 (1983).
[CrossRef]

M. J. Gunning, R. E. Raab, W. Kucharczyk, “Magnitude and nature of the quadratic electro-optic effect in KDP and ADP single crystals,” J. Opt. Soc. Am. B (to be published).

Rikken, G. L. J. A.

T. Roth, G. L. J. A. Rikken, “Observation of magnetoelectric Jones birefringence,” Phys. Rev. Lett. 85, 4478–4481 (2000).
[CrossRef] [PubMed]

Roth, T.

T. Roth, G. L. J. A. Rikken, “Observation of magnetoelectric Jones birefringence,” Phys. Rev. Lett. 85, 4478–4481 (2000).
[CrossRef] [PubMed]

Sonin, A. S.

V. E. Perfilova, A. S. Sonin, “Quadratic electrooptic effect in KDP and ADP crystals,” Bull. Acad. Sci. USSR, Phys. Ser. 31, 1154–1157 (1967).

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Bull. Acad. Sci. USSR, Phys. Ser.

V. E. Perfilova, A. S. Sonin, “Quadratic electrooptic effect in KDP and ADP crystals,” Bull. Acad. Sci. USSR, Phys. Ser. 31, 1154–1157 (1967).

Ferroelectr. Lett. Sect.

M. J. Gunning, R. E. Raab, P. Górski, W. Kucharczyk, “The quadratic electrooptic effect and estimation of antipolarization in ADP,” Ferroelectr. Lett. Sect. 24, 63–68 (1998).
[CrossRef]

J. Opt. A Pure Appl. Opt.

E. M. Meintjes, R. E. Raab, “A new theory of Pockels birefringence in non-magnetic crystals,” J. Opt. A Pure Appl. Opt. 1, 146–151 (1999).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Phys. Rev. Lett.

T. Roth, G. L. J. A. Rikken, “Observation of magnetoelectric Jones birefringence,” Phys. Rev. Lett. 85, 4478–4481 (2000).
[CrossRef] [PubMed]

Physica B

W. Kucharczyk, M. J. Gunning, R. E. Raab, C. Graham, “Interferometric investigation of the quadratic electro-optic effect in KDP,” Physica B 212, 5–9 (1995).
[CrossRef]

Proc. R. Soc. London, Ser. A

E. B. Graham, R. E. Raab, “On the Jones birefringence,” Proc. R. Soc. London, Ser. A 390, 73–90 (1983).
[CrossRef]

E. B. Graham, R. E. Raab, “Light propagation in cubic and other anisotropic crystals,” Proc. R. Soc. London, Ser. A 430, 593–614 (1990).
[CrossRef]

Other

M. J. Gunning, R. E. Raab, W. Kucharczyk, “Magnitude and nature of the quadratic electro-optic effect in KDP and ADP single crystals,” J. Opt. Soc. Am. B (to be published).

I. P. Kaminov, An Introduction to Electrooptic Devices (Academic, New York, 1974), Chap. 2.

R. R. Birss, Symmetry and Magnetism, 2nd ed. (North–Holland, Amsterdam, 1966).

J. D. H. Donnay, W. Nowacki, Crystal Data:  Classification of Substances by Space Groups and Their Identification from Cell Dimensions (Geological Society of America, New York, 1954).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

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Figures (6)

Fig. 1
Fig. 1

Angles β and γ describing the divergence of the propagation vector k from the optic z axis.

Fig. 2
Fig. 2

Azimuth α of the fast wave as a function of the angle γ and the electric field strength E for no=1.5, ne=1.55, rxxz=rxyz=3×10-12 m/V, and β=0.1°.

Fig. 3
Fig. 3

Dependence on the angles β and γ of the minimum field Emin for a 5% error in the azimuth α for no=1.5, ne=1.55, and rxxz=rxyz=3×10-12 m/V.

Fig. 4
Fig. 4

Dependence on the angles β and γ of the minimum field Emin for a 5% error in the azimuth α for no=1.5, ne=1.55, rxxz=5×10-12 m/V, and rxyz=1×10-12 m/V.

Fig. 5
Fig. 5

Dependence of the modulation index A(ω) on the angles θ and γ for no=1.5, ne=1.55, rxxz=rxyz=3×10-12 m/V.

Fig. 6
Fig. 6

Dependence of the modulation index A(ω) on the angles θ and γ for no=1.5, ne=1.55, rxxz=5×10-12 m/V, and rxyz=1×10-12 m/V.

Equations (45)

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Pα=ϵ0(χαβEβ+χαβγEβEγ+),
n2(σx2-1)+nx2+χxxγEγn2σxσy+χxyγEγn2σxσz+χxzγEγn2σyσx+χyxγEγn2(σy2-1)+ny2+χyyγEγn2σyσz+χyzγEγn2σzσx+χzxγEγn2σzσy+χzyγEγn2(σz2-1)+nz2+χzzγEγ=0,
ni2=1+χii,i=x, y, z.
χxx=χyy
no2=1+χxx,ne2=1+χzz,
-n2+no2+χxxzEχxyzE0χxyzE-n2+no2-χxxzE000ne2=0,
relativetox, yaxes:nx-ny=χxxzE/no,
relativeto+,-axes:n--n+=-χxyzE/no.
σ=(0, 0, 1),E=(E, 0, 0):
nx-ny=χxxxE/no,n--n+=χyyyE/no,
σ=(0, 0, 1),E=(0, E, 0):
nx-ny=-χyyyE/no,n--n+=χxxxE/no.
n12=no2-(χxxz2+χxyz2)1/2E,
n22=no2+(χxxz2+χxyz2)1/2E,
Eˆ1(0)=χxyz2(a2+aχxxz)1/21, -a+χxxzχxyz, 0,
a=+(χxxz2+χxyz2)1/2.
cos α=Eˆ1(0)·xˆ,sin α=-Eˆ1(0)·yˆ,
tan 2α=-χxyz/χxxz.
n2-n1=(χxxz2+χxyz2)1/2E/no
σ=(0, 0, 1),E=(E, 0, 0):
tan 2α=-χyyy/χxxx,n2-n1=(χxxx2+χyyy2)1/2E/no,
σ=(0, 0, 1),E=(0, E, 0):
tan 2α=χxxx/χyyy,n2-n1=(χyyy2+χxxx2)1/2E/no.
χxxz=-no4rxxz,χxyz=-no4rxyz,
tan 2α=-rxyz/rxxz,
n2-n1=no3(rxxz2+rxyz2)1/2E.
Γ=2πL(n2-n1)/λ=2πno3LE(rxxz2+rxyz2)1/2λ.
rxxz=λ/(2no3Vλ/2)cos 2α,
rxyz=-λ/(2no3Vλ/2)sin 2α.
B1X2+B2Y2+2B6XY=1,
B1=cos2 γ+sin2 γ sin2 βno2+sin2 γ cos2 βne2+rxxzE(cos2 γ-sin2 γ sin2 β)+2rxyzE cos γ sin γ sin β,
B2=cos2 βno2+sin2 βne2-rxxzE cos2 β,
B6=1ne2-1no2+rxxzE sin γ cos β sin β+rxyzE cos γ cos β.
tan 2α=-2B6B1-B2.
no=1.5,ne=1.55,rxxz=rxyz=3×10-12m/V.
N=100|(α-α)/α|.
Emin=W1-W3 tan(1±N)arctanrxyzrxxzW4 tan(1±N)arctanrxyzrxxz-W2,
W1=2(1/ne2-1/no2)sin γ cos β sin β,
W2=2rxxz sin γ cos β sin β+2rxyz cos γ cos β,
W3=cos2 γ+sin2 γ sin2 β-cos2 βno2+sin2 γ cos2 β-sin2 βne2,
W4=rxxz(cos2 γ+cos2 β-sin2 γ sin2 β)+2rxyz cos γ sin γ sin β.
Γ=Γ0 sin ωt,
I=12I0(1+Γ0 sin ωt),
rxxz=λAmax(ω)/(2πno3LE0)cos 2α,
rxyz=-λAmax(ω)/(2πno3LE0)sin 2α,

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