Abstract

Based on temperature-dependent refractive-index data of orthorhombic KNbO3 [ J. Opt. Soc. Am. B 9, 380 ( 1992)], we analyze various nonlinear-optical second-order interactions. Phase-matching curves as a function of wavelength, propagation direction, and temperature are given. Both type I and type II phase matching are found to be possible in KNbO3 for second-harmonic generation and for sum-frequency generation and optical parametric oscillation. To demonstrate the precision of the calculations based on the new refractive-index data, we compare experimentally measured values with calculated values of acceptance angles, phase-matching angles, and phase-matching temperatures for some specific cases. A temperature-tuned optical parametric oscillator employing KNbO3 is demonstrated. Good agreement is found between calculated and experimental results.

© 1992 Optical Society of America

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  1. W. Xing, H. Looser, H. Wüest, H. Arend, “Progress in KNbO3crystal growth,” J. Cryst. Growth 78, 431–437 (1986).
    [CrossRef]
  2. G. C. Mizell, W. R. Fay, Y. Shimoji, “Advances in the production of KNbO3crystals,” in Ceramics and Inorganic Crystals for Optics, Electro-Optics, and Nonlinear Conversion, R. W. Schwartz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.968, 88–92 (1988).
    [CrossRef]
  3. B. Zysset, I. Biaggio, P. Günter, “Refractive indices of orthorhombic KNbO3. I: Dispersion and temperature dependence,” J. Opt. Soc. Am. B 9, 380–386 (1992).
    [CrossRef]
  4. F. Bréhat, B. Wyncke, “Calculation of double-refraction walk-off angle along the phase-matching directions in non-linear biaxial crystals,” J. Phys. B 22, 1891–1898 (1989).
    [CrossRef]
  5. B. Wyncke, F. Bréhat, “Calculation of the effective second-order non-linear coefficients along the phase matching directions in acentric orthorhombic biaxial crystals,” J. Phys. B 22, 363–376 (1989).
    [CrossRef]
  6. J. Q. Yao, T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
    [CrossRef]
  7. Y. Uematsu, “Nonlinear optical properties of KNbO3single crystal in the orthorhombic phase,” Jpn. J. Appl. Phys. 13, 1362–1368 (1974).
    [CrossRef]
  8. J.-C. Baumert, J. Hoffnagle, P. Günter, “Nonlinear optical effects in KNbO3crystals at Alx Ga1−x As, dye, ruby and Nd:YAG laser wavelengths,” in 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374–385 (1984).
    [CrossRef]
  9. J.-C. Baumert, “Nichtlineare optische Eigenschaften und Anwendungen von KNbO3Kristallen,” Ph.D. dissertation ETH 7802 (Swiss Federal Institute of Technology, Zurich, 1985).
  10. R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
    [CrossRef]
  11. M. V. Hobden, “Phase matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38, 4365–4372 (1967).
    [CrossRef]
  12. J. Hajfler, Institute of Quantum Electronics, Swiss Federal Institute of Technology, Zurich, Switzerland (personal communication, 1991).
  13. J.-C. Baumert, P. Günter, H. Melchior, “High-efficiency second-harmonic generation in KNbO3crystals,” Opt. Commun. 48, 215–220 (1983).
    [CrossRef]
  14. A. Hemmerich, D. H. McIntyre, C. Zimmermann, T. W. Hänsch, “Second-harmonic generation and optical stabilization of a diode laser in an external ring resonator,” Opt. Lett. 15, 372–374 (1990).
    [CrossRef] [PubMed]
  15. M. K. Chun, L. Goldberg, J. F. Weller, “Second-harmonic generation at 421 nm using injection-locked GaAlAs laser array and KNbO3,” Appl. Phys. Lett. 53, 1170–1171 (1988).
    [CrossRef]
  16. W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
    [CrossRef]
  17. P. Günter, “Near-infrared noncritically phase matched second-harmonic generation in KNbO3,” Appl. Phys. Lett. 34, 650–652 (1979).
    [CrossRef]
  18. J.-C. Baumert, J. Hoffnagle, P. Günter, “High-efficiency intracavity frequency doubling of a Styril-9 dye laser with KNbO3crystals,” Appl. Opt. 24, 1299–1301 (1985).
    [CrossRef]
  19. L. S. Wu, H. Looser, P. Günter, “High-efficiency intracavity frequency doubling of Ti:Al2O3lasers with KNbO3crystals,” Appl. Phys. Lett. 56, 2163–2165 (1990).
    [CrossRef]
  20. G. J. Dixon, Z. M. Zhang, R. S. F. Chang, N. Djeu, “Efficient blue emission from an intracavity-doubled 946-nm Nd:YAG laser,” Opt. Lett. 13, 137–139 (1988).
    [CrossRef]
  21. I. Biaggio, H. Looser, P. Günter, “Intracavity frequency doubling of a diode pumped Nd:YAG laser using a KNbO3crystal,” Ferroelectrics 94, 157–161 (1989).
    [CrossRef]
  22. K. Kato, “High-efficiency second-harmonic generation at 4250–4680 Å in KNbO3,” IEEE J. Quantum Electron. QE-15, 410–411 (1979).
    [CrossRef]
  23. R. C. Miller, “Second harmonic generation with a broadband optical maser,” Phys. Lett. 26A, 177–178 (1968).
  24. S. Singh, D. A. Draegert, J. E. Geusic, “Optical and ferroelectric properties of barium sodium niobate,” Phys. Rev. B 2, 2709–2724 (1970).
    [CrossRef]
  25. K. Kato, “High-efficiency high-power parametric oscillation in KNbO3,” IEEE J. Quantum Electron. 18, 451–452 (1982).
    [CrossRef]
  26. J.-C. Baumert, P. Günter, “Noncritically phase-matched sum frequency generation and image up-conversion in KNbO3crystals,” Appl. Phys. Lett. 50, 554–556 (1987).
    [CrossRef]
  27. L. Goldberg, M. K. Chun, I. N. Duling, T. F. Carruthers, “Blue light generation by nonlinear mixing of Nd:YAG and GaAlAs laser emission in a KNbO3resonant cavity,” Appl. Phys. Lett. 56, 2071–2073 (1990).
    [CrossRef]

1992 (1)

1990 (4)

A. Hemmerich, D. H. McIntyre, C. Zimmermann, T. W. Hänsch, “Second-harmonic generation and optical stabilization of a diode laser in an external ring resonator,” Opt. Lett. 15, 372–374 (1990).
[CrossRef] [PubMed]

L. Goldberg, M. K. Chun, I. N. Duling, T. F. Carruthers, “Blue light generation by nonlinear mixing of Nd:YAG and GaAlAs laser emission in a KNbO3resonant cavity,” Appl. Phys. Lett. 56, 2071–2073 (1990).
[CrossRef]

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

L. S. Wu, H. Looser, P. Günter, “High-efficiency intracavity frequency doubling of Ti:Al2O3lasers with KNbO3crystals,” Appl. Phys. Lett. 56, 2163–2165 (1990).
[CrossRef]

1989 (3)

I. Biaggio, H. Looser, P. Günter, “Intracavity frequency doubling of a diode pumped Nd:YAG laser using a KNbO3crystal,” Ferroelectrics 94, 157–161 (1989).
[CrossRef]

F. Bréhat, B. Wyncke, “Calculation of double-refraction walk-off angle along the phase-matching directions in non-linear biaxial crystals,” J. Phys. B 22, 1891–1898 (1989).
[CrossRef]

B. Wyncke, F. Bréhat, “Calculation of the effective second-order non-linear coefficients along the phase matching directions in acentric orthorhombic biaxial crystals,” J. Phys. B 22, 363–376 (1989).
[CrossRef]

1988 (2)

M. K. Chun, L. Goldberg, J. F. Weller, “Second-harmonic generation at 421 nm using injection-locked GaAlAs laser array and KNbO3,” Appl. Phys. Lett. 53, 1170–1171 (1988).
[CrossRef]

G. J. Dixon, Z. M. Zhang, R. S. F. Chang, N. Djeu, “Efficient blue emission from an intracavity-doubled 946-nm Nd:YAG laser,” Opt. Lett. 13, 137–139 (1988).
[CrossRef]

1987 (1)

J.-C. Baumert, P. Günter, “Noncritically phase-matched sum frequency generation and image up-conversion in KNbO3crystals,” Appl. Phys. Lett. 50, 554–556 (1987).
[CrossRef]

1986 (1)

W. Xing, H. Looser, H. Wüest, H. Arend, “Progress in KNbO3crystal growth,” J. Cryst. Growth 78, 431–437 (1986).
[CrossRef]

1985 (1)

1984 (1)

J. Q. Yao, T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

1983 (1)

J.-C. Baumert, P. Günter, H. Melchior, “High-efficiency second-harmonic generation in KNbO3crystals,” Opt. Commun. 48, 215–220 (1983).
[CrossRef]

1982 (1)

K. Kato, “High-efficiency high-power parametric oscillation in KNbO3,” IEEE J. Quantum Electron. 18, 451–452 (1982).
[CrossRef]

1979 (2)

K. Kato, “High-efficiency second-harmonic generation at 4250–4680 Å in KNbO3,” IEEE J. Quantum Electron. QE-15, 410–411 (1979).
[CrossRef]

P. Günter, “Near-infrared noncritically phase matched second-harmonic generation in KNbO3,” Appl. Phys. Lett. 34, 650–652 (1979).
[CrossRef]

1974 (1)

Y. Uematsu, “Nonlinear optical properties of KNbO3single crystal in the orthorhombic phase,” Jpn. J. Appl. Phys. 13, 1362–1368 (1974).
[CrossRef]

1970 (1)

S. Singh, D. A. Draegert, J. E. Geusic, “Optical and ferroelectric properties of barium sodium niobate,” Phys. Rev. B 2, 2709–2724 (1970).
[CrossRef]

1968 (1)

R. C. Miller, “Second harmonic generation with a broadband optical maser,” Phys. Lett. 26A, 177–178 (1968).

1967 (1)

M. V. Hobden, “Phase matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38, 4365–4372 (1967).
[CrossRef]

1964 (1)

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

Arend, H.

W. Xing, H. Looser, H. Wüest, H. Arend, “Progress in KNbO3crystal growth,” J. Cryst. Growth 78, 431–437 (1986).
[CrossRef]

Baumert, J.-C.

J.-C. Baumert, P. Günter, “Noncritically phase-matched sum frequency generation and image up-conversion in KNbO3crystals,” Appl. Phys. Lett. 50, 554–556 (1987).
[CrossRef]

J.-C. Baumert, J. Hoffnagle, P. Günter, “High-efficiency intracavity frequency doubling of a Styril-9 dye laser with KNbO3crystals,” Appl. Opt. 24, 1299–1301 (1985).
[CrossRef]

J.-C. Baumert, P. Günter, H. Melchior, “High-efficiency second-harmonic generation in KNbO3crystals,” Opt. Commun. 48, 215–220 (1983).
[CrossRef]

J.-C. Baumert, J. Hoffnagle, P. Günter, “Nonlinear optical effects in KNbO3crystals at Alx Ga1−x As, dye, ruby and Nd:YAG laser wavelengths,” in 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374–385 (1984).
[CrossRef]

J.-C. Baumert, “Nichtlineare optische Eigenschaften und Anwendungen von KNbO3Kristallen,” Ph.D. dissertation ETH 7802 (Swiss Federal Institute of Technology, Zurich, 1985).

Biaggio, I.

B. Zysset, I. Biaggio, P. Günter, “Refractive indices of orthorhombic KNbO3. I: Dispersion and temperature dependence,” J. Opt. Soc. Am. B 9, 380–386 (1992).
[CrossRef]

I. Biaggio, H. Looser, P. Günter, “Intracavity frequency doubling of a diode pumped Nd:YAG laser using a KNbO3crystal,” Ferroelectrics 94, 157–161 (1989).
[CrossRef]

Bona, G. L.

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

Bréhat, F.

B. Wyncke, F. Bréhat, “Calculation of the effective second-order non-linear coefficients along the phase matching directions in acentric orthorhombic biaxial crystals,” J. Phys. B 22, 363–376 (1989).
[CrossRef]

F. Bréhat, B. Wyncke, “Calculation of double-refraction walk-off angle along the phase-matching directions in non-linear biaxial crystals,” J. Phys. B 22, 1891–1898 (1989).
[CrossRef]

Carruthers, T. F.

L. Goldberg, M. K. Chun, I. N. Duling, T. F. Carruthers, “Blue light generation by nonlinear mixing of Nd:YAG and GaAlAs laser emission in a KNbO3resonant cavity,” Appl. Phys. Lett. 56, 2071–2073 (1990).
[CrossRef]

Chang, R. S. F.

Chun, M. K.

L. Goldberg, M. K. Chun, I. N. Duling, T. F. Carruthers, “Blue light generation by nonlinear mixing of Nd:YAG and GaAlAs laser emission in a KNbO3resonant cavity,” Appl. Phys. Lett. 56, 2071–2073 (1990).
[CrossRef]

M. K. Chun, L. Goldberg, J. F. Weller, “Second-harmonic generation at 421 nm using injection-locked GaAlAs laser array and KNbO3,” Appl. Phys. Lett. 53, 1170–1171 (1988).
[CrossRef]

Dixon, G. J.

Djeu, N.

Draegert, D. A.

S. Singh, D. A. Draegert, J. E. Geusic, “Optical and ferroelectric properties of barium sodium niobate,” Phys. Rev. B 2, 2709–2724 (1970).
[CrossRef]

Duling, I. N.

L. Goldberg, M. K. Chun, I. N. Duling, T. F. Carruthers, “Blue light generation by nonlinear mixing of Nd:YAG and GaAlAs laser emission in a KNbO3resonant cavity,” Appl. Phys. Lett. 56, 2071–2073 (1990).
[CrossRef]

Fahlen, T. S.

J. Q. Yao, T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

Fay, W. R.

G. C. Mizell, W. R. Fay, Y. Shimoji, “Advances in the production of KNbO3crystals,” in Ceramics and Inorganic Crystals for Optics, Electro-Optics, and Nonlinear Conversion, R. W. Schwartz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.968, 88–92 (1988).
[CrossRef]

Geusic, J. E.

S. Singh, D. A. Draegert, J. E. Geusic, “Optical and ferroelectric properties of barium sodium niobate,” Phys. Rev. B 2, 2709–2724 (1970).
[CrossRef]

Goldberg, L.

L. Goldberg, M. K. Chun, I. N. Duling, T. F. Carruthers, “Blue light generation by nonlinear mixing of Nd:YAG and GaAlAs laser emission in a KNbO3resonant cavity,” Appl. Phys. Lett. 56, 2071–2073 (1990).
[CrossRef]

M. K. Chun, L. Goldberg, J. F. Weller, “Second-harmonic generation at 421 nm using injection-locked GaAlAs laser array and KNbO3,” Appl. Phys. Lett. 53, 1170–1171 (1988).
[CrossRef]

Günter, P.

B. Zysset, I. Biaggio, P. Günter, “Refractive indices of orthorhombic KNbO3. I: Dispersion and temperature dependence,” J. Opt. Soc. Am. B 9, 380–386 (1992).
[CrossRef]

L. S. Wu, H. Looser, P. Günter, “High-efficiency intracavity frequency doubling of Ti:Al2O3lasers with KNbO3crystals,” Appl. Phys. Lett. 56, 2163–2165 (1990).
[CrossRef]

I. Biaggio, H. Looser, P. Günter, “Intracavity frequency doubling of a diode pumped Nd:YAG laser using a KNbO3crystal,” Ferroelectrics 94, 157–161 (1989).
[CrossRef]

J.-C. Baumert, P. Günter, “Noncritically phase-matched sum frequency generation and image up-conversion in KNbO3crystals,” Appl. Phys. Lett. 50, 554–556 (1987).
[CrossRef]

J.-C. Baumert, J. Hoffnagle, P. Günter, “High-efficiency intracavity frequency doubling of a Styril-9 dye laser with KNbO3crystals,” Appl. Opt. 24, 1299–1301 (1985).
[CrossRef]

J.-C. Baumert, P. Günter, H. Melchior, “High-efficiency second-harmonic generation in KNbO3crystals,” Opt. Commun. 48, 215–220 (1983).
[CrossRef]

P. Günter, “Near-infrared noncritically phase matched second-harmonic generation in KNbO3,” Appl. Phys. Lett. 34, 650–652 (1979).
[CrossRef]

J.-C. Baumert, J. Hoffnagle, P. Günter, “Nonlinear optical effects in KNbO3crystals at Alx Ga1−x As, dye, ruby and Nd:YAG laser wavelengths,” in 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374–385 (1984).
[CrossRef]

Hajfler, J.

J. Hajfler, Institute of Quantum Electronics, Swiss Federal Institute of Technology, Zurich, Switzerland (personal communication, 1991).

Hänsch, T. W.

Hemmerich, A.

Hobden, M. V.

M. V. Hobden, “Phase matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38, 4365–4372 (1967).
[CrossRef]

Hoffnagle, J.

J.-C. Baumert, J. Hoffnagle, P. Günter, “High-efficiency intracavity frequency doubling of a Styril-9 dye laser with KNbO3crystals,” Appl. Opt. 24, 1299–1301 (1985).
[CrossRef]

J.-C. Baumert, J. Hoffnagle, P. Günter, “Nonlinear optical effects in KNbO3crystals at Alx Ga1−x As, dye, ruby and Nd:YAG laser wavelengths,” in 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374–385 (1984).
[CrossRef]

Kato, K.

K. Kato, “High-efficiency high-power parametric oscillation in KNbO3,” IEEE J. Quantum Electron. 18, 451–452 (1982).
[CrossRef]

K. Kato, “High-efficiency second-harmonic generation at 4250–4680 Å in KNbO3,” IEEE J. Quantum Electron. QE-15, 410–411 (1979).
[CrossRef]

Kozlovsky, W. J.

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

Latta, E. E.

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

Lenth, W.

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

Looser, H.

L. S. Wu, H. Looser, P. Günter, “High-efficiency intracavity frequency doubling of Ti:Al2O3lasers with KNbO3crystals,” Appl. Phys. Lett. 56, 2163–2165 (1990).
[CrossRef]

I. Biaggio, H. Looser, P. Günter, “Intracavity frequency doubling of a diode pumped Nd:YAG laser using a KNbO3crystal,” Ferroelectrics 94, 157–161 (1989).
[CrossRef]

W. Xing, H. Looser, H. Wüest, H. Arend, “Progress in KNbO3crystal growth,” J. Cryst. Growth 78, 431–437 (1986).
[CrossRef]

McIntyre, D. H.

Melchior, H.

J.-C. Baumert, P. Günter, H. Melchior, “High-efficiency second-harmonic generation in KNbO3crystals,” Opt. Commun. 48, 215–220 (1983).
[CrossRef]

Miller, R. C.

R. C. Miller, “Second harmonic generation with a broadband optical maser,” Phys. Lett. 26A, 177–178 (1968).

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

Mizell, G. C.

G. C. Mizell, W. R. Fay, Y. Shimoji, “Advances in the production of KNbO3crystals,” in Ceramics and Inorganic Crystals for Optics, Electro-Optics, and Nonlinear Conversion, R. W. Schwartz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.968, 88–92 (1988).
[CrossRef]

Moser, A.

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

Shimoji, Y.

G. C. Mizell, W. R. Fay, Y. Shimoji, “Advances in the production of KNbO3crystals,” in Ceramics and Inorganic Crystals for Optics, Electro-Optics, and Nonlinear Conversion, R. W. Schwartz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.968, 88–92 (1988).
[CrossRef]

Singh, S.

S. Singh, D. A. Draegert, J. E. Geusic, “Optical and ferroelectric properties of barium sodium niobate,” Phys. Rev. B 2, 2709–2724 (1970).
[CrossRef]

Uematsu, Y.

Y. Uematsu, “Nonlinear optical properties of KNbO3single crystal in the orthorhombic phase,” Jpn. J. Appl. Phys. 13, 1362–1368 (1974).
[CrossRef]

Weller, J. F.

M. K. Chun, L. Goldberg, J. F. Weller, “Second-harmonic generation at 421 nm using injection-locked GaAlAs laser array and KNbO3,” Appl. Phys. Lett. 53, 1170–1171 (1988).
[CrossRef]

Wu, L. S.

L. S. Wu, H. Looser, P. Günter, “High-efficiency intracavity frequency doubling of Ti:Al2O3lasers with KNbO3crystals,” Appl. Phys. Lett. 56, 2163–2165 (1990).
[CrossRef]

Wüest, H.

W. Xing, H. Looser, H. Wüest, H. Arend, “Progress in KNbO3crystal growth,” J. Cryst. Growth 78, 431–437 (1986).
[CrossRef]

Wyncke, B.

F. Bréhat, B. Wyncke, “Calculation of double-refraction walk-off angle along the phase-matching directions in non-linear biaxial crystals,” J. Phys. B 22, 1891–1898 (1989).
[CrossRef]

B. Wyncke, F. Bréhat, “Calculation of the effective second-order non-linear coefficients along the phase matching directions in acentric orthorhombic biaxial crystals,” J. Phys. B 22, 363–376 (1989).
[CrossRef]

Xing, W.

W. Xing, H. Looser, H. Wüest, H. Arend, “Progress in KNbO3crystal growth,” J. Cryst. Growth 78, 431–437 (1986).
[CrossRef]

Yao, J. Q.

J. Q. Yao, T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

Zhang, Z. M.

Zimmermann, C.

Zysset, B.

Appl. Opt. (1)

Appl. Phys. Lett. (7)

J.-C. Baumert, P. Günter, “Noncritically phase-matched sum frequency generation and image up-conversion in KNbO3crystals,” Appl. Phys. Lett. 50, 554–556 (1987).
[CrossRef]

L. Goldberg, M. K. Chun, I. N. Duling, T. F. Carruthers, “Blue light generation by nonlinear mixing of Nd:YAG and GaAlAs laser emission in a KNbO3resonant cavity,” Appl. Phys. Lett. 56, 2071–2073 (1990).
[CrossRef]

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

M. K. Chun, L. Goldberg, J. F. Weller, “Second-harmonic generation at 421 nm using injection-locked GaAlAs laser array and KNbO3,” Appl. Phys. Lett. 53, 1170–1171 (1988).
[CrossRef]

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

P. Günter, “Near-infrared noncritically phase matched second-harmonic generation in KNbO3,” Appl. Phys. Lett. 34, 650–652 (1979).
[CrossRef]

L. S. Wu, H. Looser, P. Günter, “High-efficiency intracavity frequency doubling of Ti:Al2O3lasers with KNbO3crystals,” Appl. Phys. Lett. 56, 2163–2165 (1990).
[CrossRef]

Ferroelectrics (1)

I. Biaggio, H. Looser, P. Günter, “Intracavity frequency doubling of a diode pumped Nd:YAG laser using a KNbO3crystal,” Ferroelectrics 94, 157–161 (1989).
[CrossRef]

IEEE J. Quantum Electron. (2)

K. Kato, “High-efficiency second-harmonic generation at 4250–4680 Å in KNbO3,” IEEE J. Quantum Electron. QE-15, 410–411 (1979).
[CrossRef]

K. Kato, “High-efficiency high-power parametric oscillation in KNbO3,” IEEE J. Quantum Electron. 18, 451–452 (1982).
[CrossRef]

J. Appl. Phys. (2)

M. V. Hobden, “Phase matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38, 4365–4372 (1967).
[CrossRef]

J. Q. Yao, T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

J. Cryst. Growth (1)

W. Xing, H. Looser, H. Wüest, H. Arend, “Progress in KNbO3crystal growth,” J. Cryst. Growth 78, 431–437 (1986).
[CrossRef]

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

J. Phys. B (2)

F. Bréhat, B. Wyncke, “Calculation of double-refraction walk-off angle along the phase-matching directions in non-linear biaxial crystals,” J. Phys. B 22, 1891–1898 (1989).
[CrossRef]

B. Wyncke, F. Bréhat, “Calculation of the effective second-order non-linear coefficients along the phase matching directions in acentric orthorhombic biaxial crystals,” J. Phys. B 22, 363–376 (1989).
[CrossRef]

Jpn. J. Appl. Phys. (1)

Y. Uematsu, “Nonlinear optical properties of KNbO3single crystal in the orthorhombic phase,” Jpn. J. Appl. Phys. 13, 1362–1368 (1974).
[CrossRef]

Opt. Commun. (1)

J.-C. Baumert, P. Günter, H. Melchior, “High-efficiency second-harmonic generation in KNbO3crystals,” Opt. Commun. 48, 215–220 (1983).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. (1)

R. C. Miller, “Second harmonic generation with a broadband optical maser,” Phys. Lett. 26A, 177–178 (1968).

Phys. Rev. B (1)

S. Singh, D. A. Draegert, J. E. Geusic, “Optical and ferroelectric properties of barium sodium niobate,” Phys. Rev. B 2, 2709–2724 (1970).
[CrossRef]

Other (4)

G. C. Mizell, W. R. Fay, Y. Shimoji, “Advances in the production of KNbO3crystals,” in Ceramics and Inorganic Crystals for Optics, Electro-Optics, and Nonlinear Conversion, R. W. Schwartz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.968, 88–92 (1988).
[CrossRef]

J.-C. Baumert, J. Hoffnagle, P. Günter, “Nonlinear optical effects in KNbO3crystals at Alx Ga1−x As, dye, ruby and Nd:YAG laser wavelengths,” in 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374–385 (1984).
[CrossRef]

J.-C. Baumert, “Nichtlineare optische Eigenschaften und Anwendungen von KNbO3Kristallen,” Ph.D. dissertation ETH 7802 (Swiss Federal Institute of Technology, Zurich, 1985).

J. Hajfler, Institute of Quantum Electronics, Swiss Federal Institute of Technology, Zurich, Switzerland (personal communication, 1991).

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Figures (11)

Fig. 1
Fig. 1

Coordinate system with the main optic axes of KNbO3 and polar angles defining the direction of the wave vector k.

Fig. 2
Fig. 2

Loci of directions of phase matching in KNbO3 for frequency doubling at room temperature and for various wavelengths. Each curve is labeled with the corresponding fundamental wavelength in nanometers. The solid curves refer to type I and the dashed curves to type II phase-matching processes. Circles show the measured directions at 1064 nm. The stereographic projection introduced by Hobden11 is used (nb > na > nc). The lines of longitude give the angle between the a axis and the plane containing the wave vector k and the b axis. The lines of latitude give the angle between the b axis and the wave vector k.

Fig. 3
Fig. 3

Walk-off angle, effective nonlinear-optical coefficient deff, and phase-matching angle Φ between the wave vector and the a axis as a function of the wavelength of the fundamental wave for a beam propagating in the ab plane (Θ = 90°) with second-harmonic polarization along c. The dashed curves are for type II phase matching; in this case deff is zero.

Fig. 4
Fig. 4

Walk-off angle, effective nonlinear-optical coefficient deff, and phase-matching angle Θ between the wave vector and the c axis as a function of the wavelength of the fundamental wave. (a) Φ = 90°. The beam propagates in the bc plane, and the fundamental wave is polarized along a. (b) Φ = 0. The beam propagates in the ac plane, and the fundamental wave is polarized along b. The phase-matching angles for λ = 1064 nm as measured in Ref. 6 (Θ = 46°–48°, Θ = 70°–72°) and in Ref. 7 (Θ = 71° ± 0.2°) are also shown. (The respective calculated values are Θ = 46.4° and Θ = 71.4°.) The dashed curves are for type II phase matching. In this case deff is always zero.

Fig. 5
Fig. 5

Walk-off angles, effective nonlinear-optical coefficients, and phase-matching directions for three different fundamental wavelengths. The directions are given by the polar angle Θ plotted as a function of Φ. deff and the walk-off angles are also plotted for each value of Φ. The dashed curves refer to type II phase matching, the solid curves to type I phase matching. The type II phase-matching deff curves were enlarged for visibility; these values should be divided by 10.

Fig. 6
Fig. 6

Temperature dependence of the wavelengths for noncritical 90° type I phase matching in KNbO3 as calculated from the refractive-index data. The curves shown are least-squares fits to the data calculated by using a second-order polynomial. Extrapolations are shown as dashed curves. Some measured data points are shown: Ref. 22, ▼; Refs. 13 and 18, ○; Ref. 17, ×; Ref. 20, ●; Ref. 17, ■; this study, ◇.

Fig. 7
Fig. 7

Phase-matched, type I SFG or OPO for various propagation directions. The wavelengths λ1 and λ2 (signal and idler) that satisfy Eq. (2) are plotted as a function of λ3 (pump). (a) Configurations with λ3 in the near infrared. The beam is propagating in the bc plane (Φ = 90). (Curves for propagation directions in the ac plane are not shown because in this case the effective nonlinear-optical coefficient is smaller.) (b) Configurations with λ3 in the visible spectral range. The thick curves are for the two noncritical phase-matching configurations with all waves propagating along b (Θ = 90°, Φ = 90°) and all waves propagating along a (Θ = 90°, Φ = 0°).

Fig. 8
Fig. 8

Phase-matching curves for type II SFG or OPO. For completeness, the curves continue in the wavelength regions above 3.5 μm, where they are derived from an extrapolation of the refractive-index data. (a) Beam propagation in the ab plane (Θ = 90°). The dashed curves are for Φ = 0; the solid curves are for Φ = 90°. deff is zero in these configurations. (b) Two propagation directions outside the principal planes of the indicatrix: Φ = 33.4°, Θ = 47.7° (solid curves) and Φ = 40.3°, Θ = 38.0° (dashed curves). The first case corresponds to the direction in Fig. 5, where a maximal deff is reached for type II SHG. The second case is chosen to optimize deff for λ3 = 1064 nm.

Fig. 9
Fig. 9

Phase-matched OPO for some selected pump wavelengths λ3. The wavelengths λ1 and λ2 are given as a function of the propagation direction. The parts of the curves in wavelength regions above 3.5 μm are derived from an extrapolation of the refractive-index data. (a) Propagation direction in the bc plane. Each curve is labeled with the corresponding λ3. Similar curves can be obtained for a smaller Θ in the ac plane, but they are not shown here, because the effective nonlinear-optical coefficient is smaller. (b) Phase-matching curves for λ3 = 1064 nm for propagation directions outside the planes of the indicatrix. Curves for both type I and type II phase matching are shown. The dashed curves are for Φ = 40°, the solid curves for Φ = 60°.

Fig. 10
Fig. 10

Phase matched, noncritical SFG or OPO for various crystal temperatures. The dashed curves are for Θ = 90°, Φ = 90°. The solid curves are for Θ = 90°, Φ = 0°. Each curve is labeled with the corresponding temperature in degrees Celsius.

Fig. 11
Fig. 11

Temperature-tuning curve for the optical parametric oscillator pumped with λ3 = 532 nm. The solid curve is calculated from the refractive-index data. The dots denote measured values.

Tables (2)

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Table 1 Nonzero Nonlinear-Optical Coefficients and Miller Indices for KNbO3 at a Fundamental Wavelength λ = 1064 nma

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Table 2 Wavelengths for 90° Noncritical Type I Phase Matching at Various Temperatures in KNbO3a

Equations (10)

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k 3 = k 1 + k 2 .
n 3 λ 3 = n 1 λ 1 + n 2 λ 2 ,
P i ( ω 3 ) = 0 i j k d i j k ( ω 3 , ω 1 , ω 2 ) E j ( ω 1 ) E k ( ω 2 ) ,
P ( ω 3 ) = 2 0 d eff E ω 1 E ω 2 ,
d eff = i j k d i j k ( ω 3 , ω 1 , ω 2 ) cos ( β i ω 3 ) cos ( β j ω 1 ) cos ( β k ω 2 ) ,
P ( 2 ω ) = 0 d eff E ω 2 ,
d i j k ( λ ) = 0 { [ n i ( 2 ω ) ] 2 - 1 } { [ n j ( ω ) ] 2 - 1 } { [ n k ( ω ) ] 2 - 1 } δ i j k ,
d eff ( λ ) = d 311 ( λ ) cos 2 ( β 1 ω ) + d 322 ( λ ) sin 2 ( β 1 ω ) .
λ PM ( nm ) = a 1 t + a 2 t 2 + a 0 ,
δ λ × L = 1.39 2 π λ ω ( n ω λ ω - 1 2 n 2 ω λ 2 ω ) - 1 , δ T × L = 1.39 2 π λ ω [ T ( n ω - n 2 ω ) ] - 1 , δ α × L 1 / 2 = ( 1.39 λ ω π n j 2 n i 2 - n j 2 n i ) 1 / 2 .

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