Abstract

We have measured the refractive indices of potassium niobate in the orthorhombic phase at six different temperatures between 22 and 180°C in the wavelength range 400–3400 nm. Sellmeier coefficients are determined by using a two-term oscillator model with an IR correction term. The temperature-dependent spontaneous polarization and the quadratic polarization optical coefficients are obtained from the index data. For practical purposes the temperature dependence can be well approximated by a polynomial expansion of degree 2.

© 1992 Optical Society of America

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  1. P. Günter, Electro-Optics/Laser Proceedings International ’76 UK, H. G. Jerrard, ed. (IPC Science and Technology, Guildford, UK, 1976), pp. 121–130.
  2. Y. Uematsu, T. Fukuda, Jpn. J. Appl. Phys. 12, 841 (1973).
    [CrossRef]
  3. J. C. Baumert, J. Hoffnagle, P. Günter, in 1984 European Conference on Optics, Optical Systems, and Applications, B. Balger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374 (1984).
    [CrossRef]
  4. P. Günter, F. Micheron, Ferroelectrics 18, 27 (1978).
    [CrossRef]
  5. E. Voit, C. Zaldo, P. Günter, Opt. Lett. 11, 309 (1986).
    [CrossRef]
  6. E. Wiesendanger, Ferroelectrics 1, 141 (1970).
    [CrossRef]
  7. Y. Uematsu, Jpn. J. Appl. Phys. 13, 1362 (1974).
    [CrossRef]
  8. U. J. Flückiger, “Darstellung und Eigenschaften von reinen und dotierten, eindomänigen KNbO3Kristallen,” Ph.D. dissertation (University of Zurich, Zurich, 1976).
  9. L. Katz, H. D. Megaw, Acta Cryst. 22, 639 (1966).
    [CrossRef]
  10. X. Wu, H. Looser, H. Wilst, H. Arend, J. Cryst. Growth 78, 431 (1986).
    [CrossRef]
  11. F. M. Michel-Calendini, P. Pertosa, G. Metrat, Ferroelectrics 21, 637 (1978).
    [CrossRef]
  12. P. Pertosa, F. M. Michel-Calendini, Phys. Rev. B 17, 2011 (1978).
    [CrossRef]
  13. F. M. Michel-Calendini, H. Chermette, J. Weber, J. Phys. C 13, 1427 (1980).
    [CrossRef]
  14. M. DiDomenico, S. H. Wemple, J. Appl. Phys. 40, 720 (1969).
    [CrossRef]
  15. P. Günter, Opt. Commun. 11, 285 (1974).
    [CrossRef]
  16. P. Günter, J. Appl. Phys. 48, 3475 (1977).
    [CrossRef]
  17. A. F. Devonshire, Philos. Mag. 40, 1040 (1949); Philos. Mag. 42, 1065 (1951); Adv. Phys. 3, 85 (1954).
  18. S. Triebwasser, Phys. Rev. 101, 993 (1956).
    [CrossRef]
  19. E. Wiesendanger, Ferroelectrics 6, 263 (1974).
    [CrossRef]
  20. F. M. Michel-Calendini, M. Peltier, F. Micheron, Solid State Commun. 33, 145 (1980).
    [CrossRef]
  21. I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, B. Zysset, “Refractive indices of orthorhombic KNbO3. II. Phasematching configurations for nonlinear-optical interactions,” J. Opt. Soc. Am. B (to be published).

1986 (2)

X. Wu, H. Looser, H. Wilst, H. Arend, J. Cryst. Growth 78, 431 (1986).
[CrossRef]

E. Voit, C. Zaldo, P. Günter, Opt. Lett. 11, 309 (1986).
[CrossRef]

1980 (2)

F. M. Michel-Calendini, M. Peltier, F. Micheron, Solid State Commun. 33, 145 (1980).
[CrossRef]

F. M. Michel-Calendini, H. Chermette, J. Weber, J. Phys. C 13, 1427 (1980).
[CrossRef]

1978 (3)

F. M. Michel-Calendini, P. Pertosa, G. Metrat, Ferroelectrics 21, 637 (1978).
[CrossRef]

P. Pertosa, F. M. Michel-Calendini, Phys. Rev. B 17, 2011 (1978).
[CrossRef]

P. Günter, F. Micheron, Ferroelectrics 18, 27 (1978).
[CrossRef]

1977 (1)

P. Günter, J. Appl. Phys. 48, 3475 (1977).
[CrossRef]

1974 (3)

E. Wiesendanger, Ferroelectrics 6, 263 (1974).
[CrossRef]

Y. Uematsu, Jpn. J. Appl. Phys. 13, 1362 (1974).
[CrossRef]

P. Günter, Opt. Commun. 11, 285 (1974).
[CrossRef]

1973 (1)

Y. Uematsu, T. Fukuda, Jpn. J. Appl. Phys. 12, 841 (1973).
[CrossRef]

1970 (1)

E. Wiesendanger, Ferroelectrics 1, 141 (1970).
[CrossRef]

1969 (1)

M. DiDomenico, S. H. Wemple, J. Appl. Phys. 40, 720 (1969).
[CrossRef]

1966 (1)

L. Katz, H. D. Megaw, Acta Cryst. 22, 639 (1966).
[CrossRef]

1956 (1)

S. Triebwasser, Phys. Rev. 101, 993 (1956).
[CrossRef]

1949 (1)

A. F. Devonshire, Philos. Mag. 40, 1040 (1949); Philos. Mag. 42, 1065 (1951); Adv. Phys. 3, 85 (1954).

Arend, H.

X. Wu, H. Looser, H. Wilst, H. Arend, J. Cryst. Growth 78, 431 (1986).
[CrossRef]

Baumert, J. C.

J. C. Baumert, J. Hoffnagle, P. Günter, in 1984 European Conference on Optics, Optical Systems, and Applications, B. Balger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374 (1984).
[CrossRef]

Biaggio, I.

I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, B. Zysset, “Refractive indices of orthorhombic KNbO3. II. Phasematching configurations for nonlinear-optical interactions,” J. Opt. Soc. Am. B (to be published).

Chermette, H.

F. M. Michel-Calendini, H. Chermette, J. Weber, J. Phys. C 13, 1427 (1980).
[CrossRef]

Devonshire, A. F.

A. F. Devonshire, Philos. Mag. 40, 1040 (1949); Philos. Mag. 42, 1065 (1951); Adv. Phys. 3, 85 (1954).

DiDomenico, M.

M. DiDomenico, S. H. Wemple, J. Appl. Phys. 40, 720 (1969).
[CrossRef]

Flückiger, U. J.

U. J. Flückiger, “Darstellung und Eigenschaften von reinen und dotierten, eindomänigen KNbO3Kristallen,” Ph.D. dissertation (University of Zurich, Zurich, 1976).

Fukuda, T.

Y. Uematsu, T. Fukuda, Jpn. J. Appl. Phys. 12, 841 (1973).
[CrossRef]

Günter, P.

E. Voit, C. Zaldo, P. Günter, Opt. Lett. 11, 309 (1986).
[CrossRef]

P. Günter, F. Micheron, Ferroelectrics 18, 27 (1978).
[CrossRef]

P. Günter, J. Appl. Phys. 48, 3475 (1977).
[CrossRef]

P. Günter, Opt. Commun. 11, 285 (1974).
[CrossRef]

P. Günter, Electro-Optics/Laser Proceedings International ’76 UK, H. G. Jerrard, ed. (IPC Science and Technology, Guildford, UK, 1976), pp. 121–130.

I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, B. Zysset, “Refractive indices of orthorhombic KNbO3. II. Phasematching configurations for nonlinear-optical interactions,” J. Opt. Soc. Am. B (to be published).

J. C. Baumert, J. Hoffnagle, P. Günter, in 1984 European Conference on Optics, Optical Systems, and Applications, B. Balger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374 (1984).
[CrossRef]

Hoffnagle, J.

J. C. Baumert, J. Hoffnagle, P. Günter, in 1984 European Conference on Optics, Optical Systems, and Applications, B. Balger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374 (1984).
[CrossRef]

Katz, L.

L. Katz, H. D. Megaw, Acta Cryst. 22, 639 (1966).
[CrossRef]

Kerkoc, P.

I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, B. Zysset, “Refractive indices of orthorhombic KNbO3. II. Phasematching configurations for nonlinear-optical interactions,” J. Opt. Soc. Am. B (to be published).

Looser, H.

X. Wu, H. Looser, H. Wilst, H. Arend, J. Cryst. Growth 78, 431 (1986).
[CrossRef]

Megaw, H. D.

L. Katz, H. D. Megaw, Acta Cryst. 22, 639 (1966).
[CrossRef]

Metrat, G.

F. M. Michel-Calendini, P. Pertosa, G. Metrat, Ferroelectrics 21, 637 (1978).
[CrossRef]

Michel-Calendini, F. M.

F. M. Michel-Calendini, H. Chermette, J. Weber, J. Phys. C 13, 1427 (1980).
[CrossRef]

F. M. Michel-Calendini, M. Peltier, F. Micheron, Solid State Commun. 33, 145 (1980).
[CrossRef]

P. Pertosa, F. M. Michel-Calendini, Phys. Rev. B 17, 2011 (1978).
[CrossRef]

F. M. Michel-Calendini, P. Pertosa, G. Metrat, Ferroelectrics 21, 637 (1978).
[CrossRef]

Micheron, F.

F. M. Michel-Calendini, M. Peltier, F. Micheron, Solid State Commun. 33, 145 (1980).
[CrossRef]

P. Günter, F. Micheron, Ferroelectrics 18, 27 (1978).
[CrossRef]

Peltier, M.

F. M. Michel-Calendini, M. Peltier, F. Micheron, Solid State Commun. 33, 145 (1980).
[CrossRef]

Pertosa, P.

F. M. Michel-Calendini, P. Pertosa, G. Metrat, Ferroelectrics 21, 637 (1978).
[CrossRef]

P. Pertosa, F. M. Michel-Calendini, Phys. Rev. B 17, 2011 (1978).
[CrossRef]

Triebwasser, S.

S. Triebwasser, Phys. Rev. 101, 993 (1956).
[CrossRef]

Uematsu, Y.

Y. Uematsu, Jpn. J. Appl. Phys. 13, 1362 (1974).
[CrossRef]

Y. Uematsu, T. Fukuda, Jpn. J. Appl. Phys. 12, 841 (1973).
[CrossRef]

Voit, E.

Weber, J.

F. M. Michel-Calendini, H. Chermette, J. Weber, J. Phys. C 13, 1427 (1980).
[CrossRef]

Wemple, S. H.

M. DiDomenico, S. H. Wemple, J. Appl. Phys. 40, 720 (1969).
[CrossRef]

Wiesendanger, E.

E. Wiesendanger, Ferroelectrics 6, 263 (1974).
[CrossRef]

E. Wiesendanger, Ferroelectrics 1, 141 (1970).
[CrossRef]

Wilst, H.

X. Wu, H. Looser, H. Wilst, H. Arend, J. Cryst. Growth 78, 431 (1986).
[CrossRef]

Wu, L.-S.

I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, B. Zysset, “Refractive indices of orthorhombic KNbO3. II. Phasematching configurations for nonlinear-optical interactions,” J. Opt. Soc. Am. B (to be published).

Wu, X.

X. Wu, H. Looser, H. Wilst, H. Arend, J. Cryst. Growth 78, 431 (1986).
[CrossRef]

Zaldo, C.

Zysset, B.

I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, B. Zysset, “Refractive indices of orthorhombic KNbO3. II. Phasematching configurations for nonlinear-optical interactions,” J. Opt. Soc. Am. B (to be published).

Acta Cryst. (1)

L. Katz, H. D. Megaw, Acta Cryst. 22, 639 (1966).
[CrossRef]

Ferroelectrics (4)

E. Wiesendanger, Ferroelectrics 1, 141 (1970).
[CrossRef]

F. M. Michel-Calendini, P. Pertosa, G. Metrat, Ferroelectrics 21, 637 (1978).
[CrossRef]

E. Wiesendanger, Ferroelectrics 6, 263 (1974).
[CrossRef]

P. Günter, F. Micheron, Ferroelectrics 18, 27 (1978).
[CrossRef]

J. Appl. Phys. (2)

P. Günter, J. Appl. Phys. 48, 3475 (1977).
[CrossRef]

M. DiDomenico, S. H. Wemple, J. Appl. Phys. 40, 720 (1969).
[CrossRef]

J. Cryst. Growth (1)

X. Wu, H. Looser, H. Wilst, H. Arend, J. Cryst. Growth 78, 431 (1986).
[CrossRef]

J. Phys. C (1)

F. M. Michel-Calendini, H. Chermette, J. Weber, J. Phys. C 13, 1427 (1980).
[CrossRef]

Jpn. J. Appl. Phys. (2)

Y. Uematsu, Jpn. J. Appl. Phys. 13, 1362 (1974).
[CrossRef]

Y. Uematsu, T. Fukuda, Jpn. J. Appl. Phys. 12, 841 (1973).
[CrossRef]

Opt. Commun. (1)

P. Günter, Opt. Commun. 11, 285 (1974).
[CrossRef]

Opt. Lett. (1)

Philos. Mag. (1)

A. F. Devonshire, Philos. Mag. 40, 1040 (1949); Philos. Mag. 42, 1065 (1951); Adv. Phys. 3, 85 (1954).

Phys. Rev. (1)

S. Triebwasser, Phys. Rev. 101, 993 (1956).
[CrossRef]

Phys. Rev. B (1)

P. Pertosa, F. M. Michel-Calendini, Phys. Rev. B 17, 2011 (1978).
[CrossRef]

Solid State Commun. (1)

F. M. Michel-Calendini, M. Peltier, F. Micheron, Solid State Commun. 33, 145 (1980).
[CrossRef]

Other (4)

I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, B. Zysset, “Refractive indices of orthorhombic KNbO3. II. Phasematching configurations for nonlinear-optical interactions,” J. Opt. Soc. Am. B (to be published).

P. Günter, Electro-Optics/Laser Proceedings International ’76 UK, H. G. Jerrard, ed. (IPC Science and Technology, Guildford, UK, 1976), pp. 121–130.

J. C. Baumert, J. Hoffnagle, P. Günter, in 1984 European Conference on Optics, Optical Systems, and Applications, B. Balger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374 (1984).
[CrossRef]

U. J. Flückiger, “Darstellung und Eigenschaften von reinen und dotierten, eindomänigen KNbO3Kristallen,” Ph.D. dissertation (University of Zurich, Zurich, 1976).

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of the structure of orthorhombic KNbO3. The axes a, b, c span the nonprimitive orthorhombic unit cell. Also shown are the pseudocubic unit cell and an oxygen octahedron. The spontaneous polarization is along the c axis. Lightly shaded circles, oxygen; filled circles, niobium; darkly shaded circles, potassium.

Fig. 2
Fig. 2

Overview of the refractive indices of KNbO3 in the wavelength region 400–3400 nm. Solid curves, 22°C; dotted curves, 180°C.

Fig. 3
Fig. 3

Relative contributions of the various terms of the Sellmeier model for the refractive index of KNbO3 as function of wavelength. The values for the a axis at 22°C are given. Note the different scales. The left-hand Y axis corresponds to the UV terms and the right-hand Y axis to the IR correction.

Fig. 4
Fig. 4

Spontaneous polarization of orthorhombic KnbO3 temperature. Our data (thick and dashed curves), data from Ref. 16 (thin curve) and data from Ref. 20 (filled circles) are given. The dashed curve was obtained from the refractive-index data at 546 nm. The thick curve represents the fits at IR wavelengths.

Fig. 5
Fig. 5

Temperature dependence of 1/ni2 − 1/nj2 at some wavelengths. The solid curves were obtained by using Eqs. (5) with Ps from Fig. 4. The fits do not use the extrapolated cubic index n0.

Fig. 6
Fig. 6

Refractive indices as function of temperature at the wavelength of 546 nm. The solid curves are from Eqs. (3) fitted with Ps from Fig. 4. The dashed curve n0 shows the extrapolated cubic-phase refractive index used in the calculation.

Fig. 7
Fig. 7

Temperature dependence of the refractive indices of KNbO3. The curves were obtained by a polynomial least-squares fit to the data at 435.83, 1064, and 3000 nm. Plotted is the index relative to the value at 0°C. Solid curves, 435.83 nm; dashed curves, 1064 nm; dotted–dashed curves, 3000 nm.

Tables (5)

Tables Icon

Table 1 Refractive Indices of KNbO3 at Selected Wavelengths (22°C)

Tables Icon

Table 2 Sellmeier Coefficients for Orthorhombic KNbO3 at Six Temperaturesa

Tables Icon

Table 3 Comparison of Quadratic Polarization Optic Coefficients of KNbO3 from Optical (at 546 nm) and Electro-Optical Measurements (m4/C2)

Tables Icon

Table 4 Wavelength Dependence of Quadratic Polarization Optical Coefficients g44 and g11g12 (m4/C2)

Tables Icon

Table 5 Coefficients of the Polynomial Expansion [Eq. (6)] for the Temperature Dependence of the Refractive Indices of KnbO3 at Three Wavelengths

Equations (7)

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

n = sin [ ( δ + φ ) / 2 ] sin ( φ / 2 ) ,
n 2 - 1 = S 1 λ 2 λ 1 2 λ 2 - λ 1 2 + S 2 λ 2 λ 2 2 λ 2 - λ 2 2 - D λ 2 ,
Δ ( 1 / n ) a 2 = 1 / n a 2 - 1 / n 0 2 = ½ ( g 11 + g 12 - g 44 ) P s 2 , Δ ( 1 / n ) b 2 = 1 / n b 2 - 1 / n 0 2 = g 12 P s 2 , Δ ( 1 / n ) c 2 = 1 / n c 2 - 1 / n 0 2 = ½ ( g 11 + g 12 + g 44 ) P s 2 ,
P s 2 = P 0 2 ( 2 C { 1 + [ 1 - 1 3 C 2 ( T - T 1 T c - T 1 ) ] 1 / 2 } ) ,
( 1 / n a ) 2 - ( 1 / n b ) 2 = ½ ( g 11 - g 12 - g 44 ) P s 2 , ( 1 / n c ) 2 - ( 1 / n a ) 2 = g 44 P s 2 , ( 1 / n c ) 2 - ( 1 / n b ) 2 = ½ ( g 11 - g 12 + g 44 ) P s 2 .
n ( T , λ ) = C 0 ( λ ) + C 1 ( λ ) T + C 2 ( λ ) T 2 .
g a = ½ ( g 11 + g 12 - g 44 ) = 0.025 < g c = ½ ( g 11 + g 12 + g 44 ) = 0.15 ( m 4 / C 2 )

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