Abstract

Taking KDP as an example of a uniaxial crystal, we analyze contributions to its quadratic electro-optic response with a view to explaining differences in published values of certain quadratic coefficients. In an eigenvalue theory of light propagation we show that the linear electro-optic coefficient contributes to the quadratic response, even under ideal laboratory conditions. In addition, the effect of imperfect crystal cutting and alignment is investigated by means of computer calculations based on the Jones calculus. It is found that, for relatively small inaccuracies, the calculated values of the quadratic coefficient gxyxy are approximately two orders of magnitude greater when measured with a static field than with a dynamic one. This finding could explain the observed spread in some results for KDP-type crystals.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. E. Pervilova, A. S. Sonin, “Quadratic electro-optic effect in KDP group crystals,” Izv. Akad. Nauk SSSR Ser. Fiz. 31, 1136–1138; Bull. Acad. Sci. USSR Phys. Ser. (English Transl.) 31, 1154–1157 (1967).
  2. W. Jamroz, J. Karniewicz, J. Stachowiak, “Nonlinear electrooptic effects in KDP and DKDP crystals,” Kvant. Elektron. (Moscow) 6, 1365–1369 (1979); Sov. J. Quantum Electron. (English Transl.) 6, 803–805 (1979).
  3. P. Górski, D. Mik, W. Kucharczyk, R. E. Raab, “On the quadratic electro-optic effect in KDP,” Physica B 193, 17–24 (1994).
    [CrossRef]
  4. 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]
  5. M. J. Gunning, R. E. Raab, W. Kucharczyk, “Magnitude and nature of the quadratic electro-optic effect in KDP and ADP crystals,” J. Opt. Soc. Am. B 18, 1092–1098 (2001).
    [CrossRef]
  6. W. Kucharczyk, “Quadratic electro-optic effect and second order strain derivatives of electronic susceptibility,” Physica B 176, 189–208 (1992).
    [CrossRef]
  7. M. Izdebski, W. Kucharczyk, R. E. Raab, “Effect of beam divergence from the optic axis in an electro-optic experiment to measure an induced Jones birefringence,” J. Opt. Soc. Am. A 18, 1393–1398 (2001).
    [CrossRef]
  8. R. R. Birss, Symmetry and Magnetism, 2nd ed. (North-Holland, Amsterdam, 1966).
  9. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  10. 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]
  11. 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]
  12. M. J. Gunning, R. E. Raab, “Systematic eigenvalue approach to crystal optics: an analytic alternative to the geo-metric ellipsoid model,” J. Opt. Soc. Am. A 15, 2199–2207 (1998).
    [CrossRef]
  13. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, UK, 1985).
  14. I. P. Kaminov, An Introduction to Electrooptic Devices (Academic, New York, 1974).
  15. R. C. Jones, “A new calculus for the treatment of optical systems. I. Description and discussion of the calculus,” J. Opt. Soc. Am. 31, 488–493 (1941).
    [CrossRef]
  16. R. C. Jones, “A new calculus for the treatment of optical systems. VIII. Electromagnetic theory,” J. Opt. Soc. Am. 46, 126–131 (1956).
    [CrossRef]
  17. I. Ścierski, F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik (Stuttgart) 68, 121–125 (1984).
  18. M. Izdebski, W. Kucharczyk, “Effect of divergence of light wave and alignment of crystal on the response of electrooptic modulators,” in International Conference on Solid State Crystals 2000: Growth, Characterization, and Applications of Single Crystals, A. Rogalski, P. Madejczyk, eds., Proc SPIE4412, 400–405 (2001).
    [CrossRef]
  19. K.-H. Hellwege, A. M. Hellwege, eds., Numerical Data and Functional Relationships in Science and Technology, Vols. 11 and 18 of Landolt-Börnstein, New Series, Group III (Springer, Berlin, 1979 and 1984).

2001 (2)

1999 (1)

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 (2)

M. J. Gunning, R. E. Raab, “Systematic eigenvalue approach to crystal optics: an analytic alternative to the geo-metric 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]

1994 (2)

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]

P. Górski, D. Mik, W. Kucharczyk, R. E. Raab, “On the quadratic electro-optic effect in KDP,” Physica B 193, 17–24 (1994).
[CrossRef]

1992 (1)

W. Kucharczyk, “Quadratic electro-optic effect and second order strain derivatives of electronic susceptibility,” Physica B 176, 189–208 (1992).
[CrossRef]

1984 (1)

I. Ścierski, F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik (Stuttgart) 68, 121–125 (1984).

1979 (1)

W. Jamroz, J. Karniewicz, J. Stachowiak, “Nonlinear electrooptic effects in KDP and DKDP crystals,” Kvant. Elektron. (Moscow) 6, 1365–1369 (1979); Sov. J. Quantum Electron. (English Transl.) 6, 803–805 (1979).

1956 (1)

1941 (1)

Birss, R. R.

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

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]

P. Górski, D. Mik, W. Kucharczyk, R. E. Raab, “On the quadratic electro-optic effect in KDP,” Physica B 193, 17–24 (1994).
[CrossRef]

Graham, C.

Gunning, M. J.

Izdebski, M.

M. Izdebski, W. Kucharczyk, R. E. Raab, “Effect of beam divergence from the optic axis in an electro-optic experiment to measure an induced Jones birefringence,” J. Opt. Soc. Am. A 18, 1393–1398 (2001).
[CrossRef]

M. Izdebski, W. Kucharczyk, “Effect of divergence of light wave and alignment of crystal on the response of electrooptic modulators,” in International Conference on Solid State Crystals 2000: Growth, Characterization, and Applications of Single Crystals, A. Rogalski, P. Madejczyk, eds., Proc SPIE4412, 400–405 (2001).
[CrossRef]

Jamroz, W.

W. Jamroz, J. Karniewicz, J. Stachowiak, “Nonlinear electrooptic effects in KDP and DKDP crystals,” Kvant. Elektron. (Moscow) 6, 1365–1369 (1979); Sov. J. Quantum Electron. (English Transl.) 6, 803–805 (1979).

Jones, R. C.

Kaminov, I. P.

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

Karniewicz, J.

W. Jamroz, J. Karniewicz, J. Stachowiak, “Nonlinear electrooptic effects in KDP and DKDP crystals,” Kvant. Elektron. (Moscow) 6, 1365–1369 (1979); Sov. J. Quantum Electron. (English Transl.) 6, 803–805 (1979).

Kucharczyk, W.

M. Izdebski, W. Kucharczyk, R. E. Raab, “Effect of beam divergence from the optic axis in an electro-optic experiment to measure an induced Jones birefringence,” J. Opt. Soc. Am. A 18, 1393–1398 (2001).
[CrossRef]

M. J. Gunning, R. E. Raab, W. Kucharczyk, “Magnitude and nature of the quadratic electro-optic effect in KDP and ADP crystals,” J. Opt. Soc. Am. B 18, 1092–1098 (2001).
[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]

P. Górski, D. Mik, W. Kucharczyk, R. E. Raab, “On the quadratic electro-optic effect in KDP,” Physica B 193, 17–24 (1994).
[CrossRef]

W. Kucharczyk, “Quadratic electro-optic effect and second order strain derivatives of electronic susceptibility,” Physica B 176, 189–208 (1992).
[CrossRef]

M. Izdebski, W. Kucharczyk, “Effect of divergence of light wave and alignment of crystal on the response of electrooptic modulators,” in International Conference on Solid State Crystals 2000: Growth, Characterization, and Applications of Single Crystals, A. Rogalski, P. Madejczyk, eds., Proc SPIE4412, 400–405 (2001).
[CrossRef]

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]

Mik, D.

P. Górski, D. Mik, W. Kucharczyk, R. E. Raab, “On the quadratic electro-optic effect in KDP,” Physica B 193, 17–24 (1994).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, UK, 1985).

Pervilova, V. E.

V. E. Pervilova, A. S. Sonin, “Quadratic electro-optic effect in KDP group crystals,” Izv. Akad. Nauk SSSR Ser. Fiz. 31, 1136–1138; Bull. Acad. Sci. USSR Phys. Ser. (English Transl.) 31, 1154–1157 (1967).

Raab, R. E.

Ratajczyk, F.

I. Ścierski, F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik (Stuttgart) 68, 121–125 (1984).

Scierski, I.

I. Ścierski, F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik (Stuttgart) 68, 121–125 (1984).

Sonin, A. S.

V. E. Pervilova, A. S. Sonin, “Quadratic electro-optic effect in KDP group crystals,” Izv. Akad. Nauk SSSR Ser. Fiz. 31, 1136–1138; Bull. Acad. Sci. USSR Phys. Ser. (English Transl.) 31, 1154–1157 (1967).

Stachowiak, J.

W. Jamroz, J. Karniewicz, J. Stachowiak, “Nonlinear electrooptic effects in KDP and DKDP crystals,” Kvant. Elektron. (Moscow) 6, 1365–1369 (1979); Sov. J. Quantum Electron. (English Transl.) 6, 803–805 (1979).

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).

Ferroelectr. Lett. Sect. (1)

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]

Izv. Akad. Nauk SSSR Ser. Fiz. (1)

V. E. Pervilova, A. S. Sonin, “Quadratic electro-optic effect in KDP group crystals,” Izv. Akad. Nauk SSSR Ser. Fiz. 31, 1136–1138; Bull. Acad. Sci. USSR Phys. Ser. (English Transl.) 31, 1154–1157 (1967).

J. Opt. A Pure Appl. Opt. (1)

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. (2)

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

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

Kvant. Elektron. (Moscow) (1)

W. Jamroz, J. Karniewicz, J. Stachowiak, “Nonlinear electrooptic effects in KDP and DKDP crystals,” Kvant. Elektron. (Moscow) 6, 1365–1369 (1979); Sov. J. Quantum Electron. (English Transl.) 6, 803–805 (1979).

Optik (Stuttgart) (1)

I. Ścierski, F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik (Stuttgart) 68, 121–125 (1984).

Physica B (2)

P. Górski, D. Mik, W. Kucharczyk, R. E. Raab, “On the quadratic electro-optic effect in KDP,” Physica B 193, 17–24 (1994).
[CrossRef]

W. Kucharczyk, “Quadratic electro-optic effect and second order strain derivatives of electronic susceptibility,” Physica B 176, 189–208 (1992).
[CrossRef]

Other (6)

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, UK, 1985).

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

M. Izdebski, W. Kucharczyk, “Effect of divergence of light wave and alignment of crystal on the response of electrooptic modulators,” in International Conference on Solid State Crystals 2000: Growth, Characterization, and Applications of Single Crystals, A. Rogalski, P. Madejczyk, eds., Proc SPIE4412, 400–405 (2001).
[CrossRef]

K.-H. Hellwege, A. M. Hellwege, eds., Numerical Data and Functional Relationships in Science and Technology, Vols. 11 and 18 of Landolt-Börnstein, New Series, Group III (Springer, Berlin, 1979 and 1984).

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Angles β and γ describing the inaccuracy in crystal cutting in terms of the deviation of the axis z of the crystal parallelepiped from its optic axis z.

Fig. 2
Fig. 2

Effect of inaccurate cutting of the KDP crystal on the apparent quadratic electro-optic coefficient gxyxy determined by the static polarimetric method. The electric field strength is 105 Vm-1, and the light beam propagates parallel to the z direction.

Fig. 3
Fig. 3

Effect of inaccurate cutting of the KDP crystal on gxyxy/gxyxy for a sinusoidal field of amplitude 105 Vm-1 and the light beam propagating parallel to the z direction. Here gxyxy and gxyxy are the apparent and the true values of the quadratic electro-optic coefficients, respectively.

Equations (29)

Equations on this page are rendered with MathJax. Learn more.

n2(σx2-1)+nx2+Txxn2σxσy+Txyn2σxσz+Txzn2σyσx+Tyxn2(σy2-1)+ny2+Tyyn2σyσz+Tyzn2σzσx+Tzxn2σzσy+Tzyn2(σz2-1)+nz2+Tzz=0,
ni2=1+χii,i=x, y, z,
Tαβ=χαβγ Eγ+χαβγδ Eγ Eδ.
Pα=0(χαβEβ+χαβγEβ Eγ+χαβγδEβ Eγ Eδ+),
χxx=χyyχzz,
nx2=ny2=no2=1+χxx,nz2=ne2=1+χzz,
χαβγ=χβαγ,χαβγδ=χβαγδ=χαβδγ=χβαδγ.
χxyz,χyzx,
χxxxx,χzzzz,χxxyy,χxyxy,χxxzz,χxzxz,χzzxx.
Txx=χxxxxEx2+χxxyyEy2+χxxzzEz2,
Txy=χxyzEz+2χxyxyExEy=Tyx,
Txz=χyzxEy+2χxzxzExEz=Tzx,
Tyy=χxxxxEy2+χxxyyEx2+χxxzzEz2,
Tyz=χyzxEx+2χxzxzEyEz=Tzy,
Tzz=χzzzzEz2+χzzxx(Ex2+Ey2).
σ=(0, 0, 1),E=(E, E, 0)/2.
n12=no2+(χxxxx-2χxyxy+χxxyy)E2/2,
n22=no2+[(χxxxx+2χxyxy+χxxyy)/2-χyzx2/ne2]E2.
E1=E(0)(1, -1, 0)/2,
E2=E(0)(1, 1, -2ryzxE/ne2)/[2(1+r2E2/ne4)],
n1=no+(χxxxx-2χxyxy+χxxyy)E2/(4no),
n2=no+[(χxxxx+2χxyxy+χxxyy)/2-χyzx2/ne2]E2/(2no).
n1-n2=(-2χxyxy+χyzx2/ne2)E2/(2no).
χyzx=-no2ne2ryzx,χxxxx=-no4gxxxx,
χxxyy=-no4gxxyy,χxyxy=-no4gxyxy.
n1-n2=no3(gxyxy+12ne2ryzx2)E2.
rxyz=-10.5×10-12 mV-1,
ryzx=-8.6×10-12 mV-1,
no=1.5075,ne=1.4670.

Metrics