Abstract

Accurate index of refraction measurements have been performed in flux-grown KTiOPO4. These measurements give good agreement between experiment and theory for angle phase matching in Type II second harmonic generation at 1.064 μm. These refractive-index data have allowed us to calculate the propagation angles for second harmonic generation at wavelengths of interest other than 1.064 μm such as 1.34 μm. Type II second harmonic energy conversion efficiency of 1.064 μm of up to 59% in this material has also been demonstrated with higher efficiencies possible. Limits to conversion efficiency are discussed.

© 1987 Optical Society of America

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  1. F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980 (1976).
    [CrossRef]
  2. Y. S. Liu, D. Dentz, R. Belt, “High-Average-Power Intracavity Second-Harmonic Generation Using KTiOPO4 in an Acousto-optically Q-switched Nd:YAG Laser Oscillator at 5 kHz,” Opt. Lett. 9, 76 (1983).
    [CrossRef]
  3. A. M. Johnson, W. M. Simpson, “Continuous-Wave Mode-Locked Nd:YAG-Pumped Subpicosecond Dye Lasers,” Opt. Lett. 8, 554 (1983).
    [CrossRef] [PubMed]
  4. T. S. Fahlen, P. Perkins, “Material and Medical Applications Using a 20-W Frequency-Doubled Nd:YAG Laser,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1984), paper ThC1.
  5. R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus 21(10), 110 (1985).
  6. A. L. Aleksandrovskii, S. A. Akhmanov, V. A. Dyakov, N. I. Zheludev, V. I. Pryalkin, “Efficient Nonlinear Optical Converters made of Potassium Titanyl Phosphate Crystals,” Sov. J. Quantum Electron. 15, 885 (1985).
    [CrossRef]
  7. J. Q. Yao, T. S. Fahlen, “Calculations of Optimal Phase Match Parameters for the Biaxial Crystal KTiOPO4,” J. Appl. Phys. 55, 65 (1984).
    [CrossRef]
  8. T. E. Gier, “Method for Flux Growth of KTiOPO4 and its Analogues,” U.S. Patent4,231,838 (Nov.1980).
  9. C. E. Huang, D. Z. Shen, “The Flux Growth and Characterization of KTiOPO4 Crystals,” J. Synth. Crys. 14, 141 (1985) (in Chinese).
  10. D. F. Cai, C. E. Huang, D. Z. Shen, Z. T. Yang, “On the Microexamination and Structure Analysis of KTiOPO4 Crystals,” J. Chin. Silic. Soc. 14, 257 (1986) (in Chinese).
  11. A. A. Ballman, H. Brown, D. H. Olson, C. E. Rice, “Growth of Potassium Titanyl Phosphate (KTP) from Molten Tungstate Melts,” J. Crys. Growth 75, 390 (1986).
    [CrossRef]
  12. Y. Li, Z. Qin, Z. Zhou, The Measurements of Piezoelectric and Ferroelectric Materials (in Chinese) (Publishing House of Sciences, Beijing, 1984), p. 271.
  13. The refractive indices at 1.064 μm were measured by H. Y. Shen et al., Fujian Institute of Research on the Structure of Matter, Fujian, China.
  14. H. Ito, H. Naito, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992 (1975).
    [CrossRef]
  15. J. D. Bierlein, E. I. du Pont de Nemours et al., Wilmington, DE; private communication.
  16. N. Menyuk, MIT Lincoln Laboratory, Lexington, MA; private communication.
  17. Y. S. Liu, “Spectral Phase-Matching Properties for Second Harmonic Generation in Nonlinear Crystals,” Appl. Phys. Lett. 31, 187 (1977).
    [CrossRef]
  18. S. Velsko, Lawrence Livermore National Laboratory, Livermore, CA; private communication.
  19. R. C. Eckardt, J. Reintjes, “Phase Matching Limitations of High Efficiency Second Harmonic Generation,” IEEE J. Quantum Electron. QE-20, 1178 (1984).
    [CrossRef]

1986 (2)

D. F. Cai, C. E. Huang, D. Z. Shen, Z. T. Yang, “On the Microexamination and Structure Analysis of KTiOPO4 Crystals,” J. Chin. Silic. Soc. 14, 257 (1986) (in Chinese).

A. A. Ballman, H. Brown, D. H. Olson, C. E. Rice, “Growth of Potassium Titanyl Phosphate (KTP) from Molten Tungstate Melts,” J. Crys. Growth 75, 390 (1986).
[CrossRef]

1985 (3)

R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus 21(10), 110 (1985).

A. L. Aleksandrovskii, S. A. Akhmanov, V. A. Dyakov, N. I. Zheludev, V. I. Pryalkin, “Efficient Nonlinear Optical Converters made of Potassium Titanyl Phosphate Crystals,” Sov. J. Quantum Electron. 15, 885 (1985).
[CrossRef]

C. E. Huang, D. Z. Shen, “The Flux Growth and Characterization of KTiOPO4 Crystals,” J. Synth. Crys. 14, 141 (1985) (in Chinese).

1984 (2)

R. C. Eckardt, J. Reintjes, “Phase Matching Limitations of High Efficiency Second Harmonic Generation,” IEEE J. Quantum Electron. QE-20, 1178 (1984).
[CrossRef]

J. Q. Yao, T. S. Fahlen, “Calculations of Optimal Phase Match Parameters for the Biaxial Crystal KTiOPO4,” J. Appl. Phys. 55, 65 (1984).
[CrossRef]

1983 (2)

1977 (1)

Y. S. Liu, “Spectral Phase-Matching Properties for Second Harmonic Generation in Nonlinear Crystals,” Appl. Phys. Lett. 31, 187 (1977).
[CrossRef]

1976 (1)

F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

1975 (1)

H. Ito, H. Naito, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992 (1975).
[CrossRef]

Akhmanov, S. A.

A. L. Aleksandrovskii, S. A. Akhmanov, V. A. Dyakov, N. I. Zheludev, V. I. Pryalkin, “Efficient Nonlinear Optical Converters made of Potassium Titanyl Phosphate Crystals,” Sov. J. Quantum Electron. 15, 885 (1985).
[CrossRef]

Aleksandrovskii, A. L.

A. L. Aleksandrovskii, S. A. Akhmanov, V. A. Dyakov, N. I. Zheludev, V. I. Pryalkin, “Efficient Nonlinear Optical Converters made of Potassium Titanyl Phosphate Crystals,” Sov. J. Quantum Electron. 15, 885 (1985).
[CrossRef]

Ballman, A. A.

A. A. Ballman, H. Brown, D. H. Olson, C. E. Rice, “Growth of Potassium Titanyl Phosphate (KTP) from Molten Tungstate Melts,” J. Crys. Growth 75, 390 (1986).
[CrossRef]

Belt, R.

Belt, R. F.

R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus 21(10), 110 (1985).

Bierlein, J. D.

F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

J. D. Bierlein, E. I. du Pont de Nemours et al., Wilmington, DE; private communication.

Brown, H.

A. A. Ballman, H. Brown, D. H. Olson, C. E. Rice, “Growth of Potassium Titanyl Phosphate (KTP) from Molten Tungstate Melts,” J. Crys. Growth 75, 390 (1986).
[CrossRef]

Cai, D. F.

D. F. Cai, C. E. Huang, D. Z. Shen, Z. T. Yang, “On the Microexamination and Structure Analysis of KTiOPO4 Crystals,” J. Chin. Silic. Soc. 14, 257 (1986) (in Chinese).

Dentz, D.

du Pont de Nemours, E. I.

J. D. Bierlein, E. I. du Pont de Nemours et al., Wilmington, DE; private communication.

Dyakov, V. A.

A. L. Aleksandrovskii, S. A. Akhmanov, V. A. Dyakov, N. I. Zheludev, V. I. Pryalkin, “Efficient Nonlinear Optical Converters made of Potassium Titanyl Phosphate Crystals,” Sov. J. Quantum Electron. 15, 885 (1985).
[CrossRef]

Eckardt, R. C.

R. C. Eckardt, J. Reintjes, “Phase Matching Limitations of High Efficiency Second Harmonic Generation,” IEEE J. Quantum Electron. QE-20, 1178 (1984).
[CrossRef]

Fahlen, T. S.

J. Q. Yao, T. S. Fahlen, “Calculations of Optimal Phase Match Parameters for the Biaxial Crystal KTiOPO4,” J. Appl. Phys. 55, 65 (1984).
[CrossRef]

T. S. Fahlen, P. Perkins, “Material and Medical Applications Using a 20-W Frequency-Doubled Nd:YAG Laser,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1984), paper ThC1.

Gashurov, G.

R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus 21(10), 110 (1985).

Gier, T. E.

F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

T. E. Gier, “Method for Flux Growth of KTiOPO4 and its Analogues,” U.S. Patent4,231,838 (Nov.1980).

Huang, C. E.

D. F. Cai, C. E. Huang, D. Z. Shen, Z. T. Yang, “On the Microexamination and Structure Analysis of KTiOPO4 Crystals,” J. Chin. Silic. Soc. 14, 257 (1986) (in Chinese).

C. E. Huang, D. Z. Shen, “The Flux Growth and Characterization of KTiOPO4 Crystals,” J. Synth. Crys. 14, 141 (1985) (in Chinese).

Inaba, H.

H. Ito, H. Naito, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992 (1975).
[CrossRef]

Ito, H.

H. Ito, H. Naito, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992 (1975).
[CrossRef]

Johnson, A. M.

Li, Y.

Y. Li, Z. Qin, Z. Zhou, The Measurements of Piezoelectric and Ferroelectric Materials (in Chinese) (Publishing House of Sciences, Beijing, 1984), p. 271.

Liu, Y. S.

R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus 21(10), 110 (1985).

Y. S. Liu, D. Dentz, R. Belt, “High-Average-Power Intracavity Second-Harmonic Generation Using KTiOPO4 in an Acousto-optically Q-switched Nd:YAG Laser Oscillator at 5 kHz,” Opt. Lett. 9, 76 (1983).
[CrossRef]

Y. S. Liu, “Spectral Phase-Matching Properties for Second Harmonic Generation in Nonlinear Crystals,” Appl. Phys. Lett. 31, 187 (1977).
[CrossRef]

Menyuk, N.

N. Menyuk, MIT Lincoln Laboratory, Lexington, MA; private communication.

Naito, H.

H. Ito, H. Naito, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992 (1975).
[CrossRef]

Olson, D. H.

A. A. Ballman, H. Brown, D. H. Olson, C. E. Rice, “Growth of Potassium Titanyl Phosphate (KTP) from Molten Tungstate Melts,” J. Crys. Growth 75, 390 (1986).
[CrossRef]

Perkins, P.

T. S. Fahlen, P. Perkins, “Material and Medical Applications Using a 20-W Frequency-Doubled Nd:YAG Laser,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1984), paper ThC1.

Pryalkin, V. I.

A. L. Aleksandrovskii, S. A. Akhmanov, V. A. Dyakov, N. I. Zheludev, V. I. Pryalkin, “Efficient Nonlinear Optical Converters made of Potassium Titanyl Phosphate Crystals,” Sov. J. Quantum Electron. 15, 885 (1985).
[CrossRef]

Qin, Z.

Y. Li, Z. Qin, Z. Zhou, The Measurements of Piezoelectric and Ferroelectric Materials (in Chinese) (Publishing House of Sciences, Beijing, 1984), p. 271.

Reintjes, J.

R. C. Eckardt, J. Reintjes, “Phase Matching Limitations of High Efficiency Second Harmonic Generation,” IEEE J. Quantum Electron. QE-20, 1178 (1984).
[CrossRef]

Rice, C. E.

A. A. Ballman, H. Brown, D. H. Olson, C. E. Rice, “Growth of Potassium Titanyl Phosphate (KTP) from Molten Tungstate Melts,” J. Crys. Growth 75, 390 (1986).
[CrossRef]

Shen, D. Z.

D. F. Cai, C. E. Huang, D. Z. Shen, Z. T. Yang, “On the Microexamination and Structure Analysis of KTiOPO4 Crystals,” J. Chin. Silic. Soc. 14, 257 (1986) (in Chinese).

C. E. Huang, D. Z. Shen, “The Flux Growth and Characterization of KTiOPO4 Crystals,” J. Synth. Crys. 14, 141 (1985) (in Chinese).

Shen, H. Y.

The refractive indices at 1.064 μm were measured by H. Y. Shen et al., Fujian Institute of Research on the Structure of Matter, Fujian, China.

Simpson, W. M.

Velsko, S.

S. Velsko, Lawrence Livermore National Laboratory, Livermore, CA; private communication.

Yang, Z. T.

D. F. Cai, C. E. Huang, D. Z. Shen, Z. T. Yang, “On the Microexamination and Structure Analysis of KTiOPO4 Crystals,” J. Chin. Silic. Soc. 14, 257 (1986) (in Chinese).

Yao, J. Q.

J. Q. Yao, T. S. Fahlen, “Calculations of Optimal Phase Match Parameters for the Biaxial Crystal KTiOPO4,” J. Appl. Phys. 55, 65 (1984).
[CrossRef]

Zheludev, N. I.

A. L. Aleksandrovskii, S. A. Akhmanov, V. A. Dyakov, N. I. Zheludev, V. I. Pryalkin, “Efficient Nonlinear Optical Converters made of Potassium Titanyl Phosphate Crystals,” Sov. J. Quantum Electron. 15, 885 (1985).
[CrossRef]

Zhou, Z.

Y. Li, Z. Qin, Z. Zhou, The Measurements of Piezoelectric and Ferroelectric Materials (in Chinese) (Publishing House of Sciences, Beijing, 1984), p. 271.

Zumsteg, F. C.

F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

Appl. Phys. Lett. (1)

Y. S. Liu, “Spectral Phase-Matching Properties for Second Harmonic Generation in Nonlinear Crystals,” Appl. Phys. Lett. 31, 187 (1977).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. C. Eckardt, J. Reintjes, “Phase Matching Limitations of High Efficiency Second Harmonic Generation,” IEEE J. Quantum Electron. QE-20, 1178 (1984).
[CrossRef]

J. Appl. Phys. (3)

F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

H. Ito, H. Naito, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992 (1975).
[CrossRef]

J. Q. Yao, T. S. Fahlen, “Calculations of Optimal Phase Match Parameters for the Biaxial Crystal KTiOPO4,” J. Appl. Phys. 55, 65 (1984).
[CrossRef]

J. Chin. Silic. Soc. (1)

D. F. Cai, C. E. Huang, D. Z. Shen, Z. T. Yang, “On the Microexamination and Structure Analysis of KTiOPO4 Crystals,” J. Chin. Silic. Soc. 14, 257 (1986) (in Chinese).

J. Crys. Growth (1)

A. A. Ballman, H. Brown, D. H. Olson, C. E. Rice, “Growth of Potassium Titanyl Phosphate (KTP) from Molten Tungstate Melts,” J. Crys. Growth 75, 390 (1986).
[CrossRef]

J. Synth. Crys. (1)

C. E. Huang, D. Z. Shen, “The Flux Growth and Characterization of KTiOPO4 Crystals,” J. Synth. Crys. 14, 141 (1985) (in Chinese).

Laser Focus (1)

R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus 21(10), 110 (1985).

Opt. Lett. (2)

Sov. J. Quantum Electron. (1)

A. L. Aleksandrovskii, S. A. Akhmanov, V. A. Dyakov, N. I. Zheludev, V. I. Pryalkin, “Efficient Nonlinear Optical Converters made of Potassium Titanyl Phosphate Crystals,” Sov. J. Quantum Electron. 15, 885 (1985).
[CrossRef]

Other (7)

T. E. Gier, “Method for Flux Growth of KTiOPO4 and its Analogues,” U.S. Patent4,231,838 (Nov.1980).

Y. Li, Z. Qin, Z. Zhou, The Measurements of Piezoelectric and Ferroelectric Materials (in Chinese) (Publishing House of Sciences, Beijing, 1984), p. 271.

The refractive indices at 1.064 μm were measured by H. Y. Shen et al., Fujian Institute of Research on the Structure of Matter, Fujian, China.

T. S. Fahlen, P. Perkins, “Material and Medical Applications Using a 20-W Frequency-Doubled Nd:YAG Laser,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1984), paper ThC1.

J. D. Bierlein, E. I. du Pont de Nemours et al., Wilmington, DE; private communication.

N. Menyuk, MIT Lincoln Laboratory, Lexington, MA; private communication.

S. Velsko, Lawrence Livermore National Laboratory, Livermore, CA; private communication.

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Figures (4)

Fig. 1
Fig. 1

Angle of propagation relative to the z axis θ as a function of angle of propagation relative to the x axis in the x-y plane ϕ for SHG phase matching and the magnitude of the effective nonlinear coefficients deff as a function of ϕ. The phase matching curves are solid lines, and the deff are the dashed lines. I and II denote Types I and II interactions, respectively: (a) 1.064 μm; (b) 1.34 μm.

Fig. 2
Fig. 2

Angle phase matching for the ϕ direction at 1.064 μm about ϕ = 23.2°. The bar indicates the predicted value for the acceptance angle.

Fig. 3
Fig. 3

Angle phase matching for the θ direction at 1.064 μm about θ = 90°. The bar indicates the predicted value for angular acceptance.

Fig. 4
Fig. 4

SHG energy conversion efficiency as a function of peak incident intensity at 1.064 μm.

Tables (2)

Tables Icon

Table I Sellmeier Equation Coefficients

Tables Icon

Table II Experimental and Fitted Values for the Indices of Refraction

Equations (11)

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

n 2 = A + B 1 - C λ - 2 - D λ 2 .
d eff ( Type I ) = ½ ( d 15 - d 24 ) sin 2 θ sin 2 ϕ ,
d eff ( Type II ) = ( d 24 - d 15 ) sin 2 θ sin 2 ϕ - ( d 15 sin 2 ϕ + d 24 cos 2 ϕ ) sin θ .
k 2 ω ( ϕ ) = k ω ( ϕ ) + k ω , z ,
2 n 2 ω ( ϕ ) = n ω ( ϕ ) + n ω , z ,
1 n 2 ( ϕ ) = cos 2 ϕ n y 2 + sin 2 ϕ n x 2 .
Δ k = Δ k ( ϕ = ϕ m ) + ( Δ k ϕ ) ϕ = ϕ m ( δ ϕ ) + 1 2 ( Δ k 2 2 ϕ ) ϕ = ϕ m ( δ ϕ ) 2 + ,
Δ k ϕ = ϕ k 2 ω ( ϕ ) - ϕ k ω ( ϕ ) = 2 π λ ω [ 2 ϕ n 2 ω ( ϕ ) - ϕ n ω ( ϕ ) ] ,
2 Δ k θ 2 2 π λ ω n ω , z 3 ( 1 n ω , x y 2 - 1 n ω , z 2 ) ,
δ θ ext n eff δ θ n eff ( 2 λ ω n ω , z 3 l 1 n ω , x y - 2 - n ω , z - 2 ) 1 / 2 .
v p = 2 k 2 ω ( ϕ ) ω - k ω ( ϕ ) ω - k ω , z ω

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