Abstract

Phase matching in anisotropic second-order nonlinear optical crystals is studied. All the possible phase matching configurations and existence conditions for general collinear three-wave mixing interactions are derived for propagation within the crystal principal planes. Closed form expressions for the critical phase matching angles are given wherever possible.

© 1990 Optical Society of America

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References

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley & Sons, New York, 1984).
  2. F. A. Hopf, G. I. Stegeman, Applied Classical Electrodynamics, Vol. 1: Linear Optics (Wiley & Sons, New York, 1985); Applied Classical Electrodynamics, Vol. 2: Nonlinear Optics (Wiley & Sons, New York, 1986).
  3. P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
    [CrossRef]
  4. D. A. Kleinman, “Nonlinear Dielectric Polarization in Optical Media,” Phys. Rev. 126, 1977–1979 (1962).
    [CrossRef]
  5. S. Singh, “Nonlinear Optical Properties,” in CRC Handbook of Laser Science and Technology, Vol. VI (CRC Press, Boca Raton, Florida, 1984).
  6. W. S. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, R. S. Craxton, “Demonstration of High Efficiency Third Harmonic Conversion of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 469–473 (1980).
    [CrossRef]
  7. R. S. Craxton, “Theory of High Efficiency Third Harmonic Generation of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 474–478 (1980).
    [CrossRef]
  8. R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Dual-Frequency Nd:YAG Laser for the Study and Application of Nonlinear Optical Crystals,” Opt. Eng. 26, 1240–1244 (1987).
    [CrossRef]
  9. J. C. Baumert, F. M. Schellenberg, W. Lenth, W. P. Risk, G. C. Bjorklund, “Generation of Blue Coherent Radiation by Sum Frequency Mixing in KTiOPO4,” Appl. Phys. Lett. 51, 2192–2194 (1987).
    [CrossRef]
  10. W. P. Risk, J. C. Baumert, G. C. Bjorklund, F. M. Schellenberg, W. Lenth, “Generation of Blue Light by Intracavity Frequency Mixing of the Laser and Pump Radiation of a Miniature Neodymium:Yttrium Aluminum Garnet Laser,” Appl. Phys. Lett. 52, 85–87 (1988).
    [CrossRef]
  11. Lawrence S. Goldberg, “Narrow-Bandwidth Tunable Infrared Difference-Frequency Generation at High Repetition Rates in LilO3,” Appl. Opt. 14, 653–656 (1975); K. Kato, “High Power Difference-Frequency Generation at 4.4–5.7μm in LiIO3,” IEEE J. Quantum Electron. QE-21, 119–120 (1985).
    [CrossRef] [PubMed]
  12. M. Born, E. Wolf, Principles of Optics (Permagon, New York, 1980).
  13. Jean-Claude Baumert, Peter Gtinter, “Noncritically Phase-Matched Sum Frequency Generation and Image Upconversion in KNbO3 Crystals,” Appl. Phys. Lett. 50, 554–556 (1987).
    [CrossRef]
  14. P. Günter, “Near-Infrared Noncritically Phase-Matched Second Harmonic Generation in KNbO3,” Appl. Phys. Lett. 34, 650–652 (1979).
    [CrossRef]
  15. R. A. Stolzenberger, C. C. Hsu, N. Peyghambarian, J. J. E. Reid, R. A. Morgan, “Type II Sum Frequency Generation in Flux and Hydrothermally Grown KTP at 1.319 and 1.338 Microns,” IEEE Photon. Technol. Lett., 1, 446–448 (1989).
    [CrossRef]
  16. Robert A. Morgan, Frederic A. Hopf, “Measurement of the Temperature Tuning Coefficient of Lithium Niobate Using Nonlinear Optical Interferometry,” Appl. Opt. 25, 3011–3013 (1986); Robert A. Morgan, K. I. Kang, C. C. Hsu, Chris L. Koliopoulos, Nasser Peyghamarian, “Measurement of the Thermal Diffusivity of Nonlinear Anisotropic Crystals Using Optical Interferometry,” Appl. Opt. 26, 5266–5271 (1987).
    [CrossRef] [PubMed]
  17. David Eimerl, “Sellmeier Constants and Related Data For KTP,” paper presented at Workshop on Nonlinear Optical Materials, Annapolis, MD, April 28–29, 1986; D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, G. Kennedy, “Deuterated L-Arginine Phosphate: a New Efficient Nonlinear Crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
    [CrossRef]
  18. H. Ito, N. Hatsuhiko, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
    [CrossRef]
  19. F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980–4985 (1976).
    [CrossRef]
  20. R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus/Electro-Opt. 21, 110–124.
  21. R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Three-Wave Mixing Uses of a Novel Dual-Frequency Nd:YAG Laser,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988) paper ThAi.
  22. P. Günter, “Nonlinear Optical Crystals for Frequency Doubling with Laser Diodes,” Proc. Soc. Photo-Opt. Instrum. Eng. 236, 8–18 (1980).
  23. M. V. Hobden, “Phase-Matched Second-Harmonic Generation in Biaxial Crystals,” J. Appl. Phys. 38, 4365–4372 (1967).
    [CrossRef]
  24. 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]

1989 (1)

R. A. Stolzenberger, C. C. Hsu, N. Peyghambarian, J. J. E. Reid, R. A. Morgan, “Type II Sum Frequency Generation in Flux and Hydrothermally Grown KTP at 1.319 and 1.338 Microns,” IEEE Photon. Technol. Lett., 1, 446–448 (1989).
[CrossRef]

1988 (1)

W. P. Risk, J. C. Baumert, G. C. Bjorklund, F. M. Schellenberg, W. Lenth, “Generation of Blue Light by Intracavity Frequency Mixing of the Laser and Pump Radiation of a Miniature Neodymium:Yttrium Aluminum Garnet Laser,” Appl. Phys. Lett. 52, 85–87 (1988).
[CrossRef]

1987 (3)

Jean-Claude Baumert, Peter Gtinter, “Noncritically Phase-Matched Sum Frequency Generation and Image Upconversion in KNbO3 Crystals,” Appl. Phys. Lett. 50, 554–556 (1987).
[CrossRef]

R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Dual-Frequency Nd:YAG Laser for the Study and Application of Nonlinear Optical Crystals,” Opt. Eng. 26, 1240–1244 (1987).
[CrossRef]

J. C. Baumert, F. M. Schellenberg, W. Lenth, W. P. Risk, G. C. Bjorklund, “Generation of Blue Coherent Radiation by Sum Frequency Mixing in KTiOPO4,” Appl. Phys. Lett. 51, 2192–2194 (1987).
[CrossRef]

1986 (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]

1980 (3)

P. Günter, “Nonlinear Optical Crystals for Frequency Doubling with Laser Diodes,” Proc. Soc. Photo-Opt. Instrum. Eng. 236, 8–18 (1980).

W. S. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, R. S. Craxton, “Demonstration of High Efficiency Third Harmonic Conversion of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

R. S. Craxton, “Theory of High Efficiency Third Harmonic Generation of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 474–478 (1980).
[CrossRef]

1979 (1)

P. Günter, “Near-Infrared Noncritically Phase-Matched Second Harmonic Generation in KNbO3,” Appl. Phys. Lett. 34, 650–652 (1979).
[CrossRef]

1976 (1)

F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980–4985 (1976).
[CrossRef]

1975 (2)

1967 (1)

M. V. Hobden, “Phase-Matched Second-Harmonic Generation in Biaxial Crystals,” J. Appl. Phys. 38, 4365–4372 (1967).
[CrossRef]

1962 (1)

D. A. Kleinman, “Nonlinear Dielectric Polarization in Optical Media,” Phys. Rev. 126, 1977–1979 (1962).
[CrossRef]

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Baumert, J. C.

W. P. Risk, J. C. Baumert, G. C. Bjorklund, F. M. Schellenberg, W. Lenth, “Generation of Blue Light by Intracavity Frequency Mixing of the Laser and Pump Radiation of a Miniature Neodymium:Yttrium Aluminum Garnet Laser,” Appl. Phys. Lett. 52, 85–87 (1988).
[CrossRef]

J. C. Baumert, F. M. Schellenberg, W. Lenth, W. P. Risk, G. C. Bjorklund, “Generation of Blue Coherent Radiation by Sum Frequency Mixing in KTiOPO4,” Appl. Phys. Lett. 51, 2192–2194 (1987).
[CrossRef]

Baumert, Jean-Claude

Jean-Claude Baumert, Peter Gtinter, “Noncritically Phase-Matched Sum Frequency Generation and Image Upconversion in KNbO3 Crystals,” Appl. Phys. Lett. 50, 554–556 (1987).
[CrossRef]

Belt, R. F.

R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus/Electro-Opt. 21, 110–124.

Bierlein, J. D.

F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980–4985 (1976).
[CrossRef]

Bjorklund, G. C.

W. P. Risk, J. C. Baumert, G. C. Bjorklund, F. M. Schellenberg, W. Lenth, “Generation of Blue Light by Intracavity Frequency Mixing of the Laser and Pump Radiation of a Miniature Neodymium:Yttrium Aluminum Garnet Laser,” Appl. Phys. Lett. 52, 85–87 (1988).
[CrossRef]

J. C. Baumert, F. M. Schellenberg, W. Lenth, W. P. Risk, G. C. Bjorklund, “Generation of Blue Coherent Radiation by Sum Frequency Mixing in KTiOPO4,” Appl. Phys. Lett. 51, 2192–2194 (1987).
[CrossRef]

Boni, R.

W. S. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, R. S. Craxton, “Demonstration of High Efficiency Third Harmonic Conversion of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Permagon, New York, 1980).

Craxton, R. S.

W. S. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, R. S. Craxton, “Demonstration of High Efficiency Third Harmonic Conversion of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

R. S. Craxton, “Theory of High Efficiency Third Harmonic Generation of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 474–478 (1980).
[CrossRef]

Eimerl, David

David Eimerl, “Sellmeier Constants and Related Data For KTP,” paper presented at Workshop on Nonlinear Optical Materials, Annapolis, MD, April 28–29, 1986; D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, G. Kennedy, “Deuterated L-Arginine Phosphate: a New Efficient Nonlinear Crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
[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]

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Gashurov, G.

R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus/Electro-Opt. 21, 110–124.

Gier, T. E.

F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980–4985 (1976).
[CrossRef]

Goldberg, Lawrence S.

Gtinter, Peter

Jean-Claude Baumert, Peter Gtinter, “Noncritically Phase-Matched Sum Frequency Generation and Image Upconversion in KNbO3 Crystals,” Appl. Phys. Lett. 50, 554–556 (1987).
[CrossRef]

Günter, P.

P. Günter, “Nonlinear Optical Crystals for Frequency Doubling with Laser Diodes,” Proc. Soc. Photo-Opt. Instrum. Eng. 236, 8–18 (1980).

P. Günter, “Near-Infrared Noncritically Phase-Matched Second Harmonic Generation in KNbO3,” Appl. Phys. Lett. 34, 650–652 (1979).
[CrossRef]

Hatsuhiko, N.

H. Ito, N. Hatsuhiko, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
[CrossRef]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Hobden, M. V.

M. V. Hobden, “Phase-Matched Second-Harmonic Generation in Biaxial Crystals,” J. Appl. Phys. 38, 4365–4372 (1967).
[CrossRef]

Hopf, F. A.

R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Dual-Frequency Nd:YAG Laser for the Study and Application of Nonlinear Optical Crystals,” Opt. Eng. 26, 1240–1244 (1987).
[CrossRef]

R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Three-Wave Mixing Uses of a Novel Dual-Frequency Nd:YAG Laser,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988) paper ThAi.

F. A. Hopf, G. I. Stegeman, Applied Classical Electrodynamics, Vol. 1: Linear Optics (Wiley & Sons, New York, 1985); Applied Classical Electrodynamics, Vol. 2: Nonlinear Optics (Wiley & Sons, New York, 1986).

Hopf, Frederic A.

Hsu, C. C.

R. A. Stolzenberger, C. C. Hsu, N. Peyghambarian, J. J. E. Reid, R. A. Morgan, “Type II Sum Frequency Generation in Flux and Hydrothermally Grown KTP at 1.319 and 1.338 Microns,” IEEE Photon. Technol. Lett., 1, 446–448 (1989).
[CrossRef]

Inaba, H.

H. Ito, N. Hatsuhiko, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
[CrossRef]

Ito, H.

H. Ito, N. Hatsuhiko, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
[CrossRef]

Jacobs, S. D.

W. S. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, R. S. Craxton, “Demonstration of High Efficiency Third Harmonic Conversion of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

Kleinman, D. A.

D. A. Kleinman, “Nonlinear Dielectric Polarization in Optical Media,” Phys. Rev. 126, 1977–1979 (1962).
[CrossRef]

Lenth, W.

W. P. Risk, J. C. Baumert, G. C. Bjorklund, F. M. Schellenberg, W. Lenth, “Generation of Blue Light by Intracavity Frequency Mixing of the Laser and Pump Radiation of a Miniature Neodymium:Yttrium Aluminum Garnet Laser,” Appl. Phys. Lett. 52, 85–87 (1988).
[CrossRef]

J. C. Baumert, F. M. Schellenberg, W. Lenth, W. P. Risk, G. C. Bjorklund, “Generation of Blue Coherent Radiation by Sum Frequency Mixing in KTiOPO4,” Appl. Phys. Lett. 51, 2192–2194 (1987).
[CrossRef]

Liu, Y. S.

R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus/Electro-Opt. 21, 110–124.

Morgan, R. A.

R. A. Stolzenberger, C. C. Hsu, N. Peyghambarian, J. J. E. Reid, R. A. Morgan, “Type II Sum Frequency Generation in Flux and Hydrothermally Grown KTP at 1.319 and 1.338 Microns,” IEEE Photon. Technol. Lett., 1, 446–448 (1989).
[CrossRef]

R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Dual-Frequency Nd:YAG Laser for the Study and Application of Nonlinear Optical Crystals,” Opt. Eng. 26, 1240–1244 (1987).
[CrossRef]

R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Three-Wave Mixing Uses of a Novel Dual-Frequency Nd:YAG Laser,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988) paper ThAi.

Morgan, Robert A.

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Peyghambarian, N.

R. A. Stolzenberger, C. C. Hsu, N. Peyghambarian, J. J. E. Reid, R. A. Morgan, “Type II Sum Frequency Generation in Flux and Hydrothermally Grown KTP at 1.319 and 1.338 Microns,” IEEE Photon. Technol. Lett., 1, 446–448 (1989).
[CrossRef]

R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Dual-Frequency Nd:YAG Laser for the Study and Application of Nonlinear Optical Crystals,” Opt. Eng. 26, 1240–1244 (1987).
[CrossRef]

R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Three-Wave Mixing Uses of a Novel Dual-Frequency Nd:YAG Laser,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988) paper ThAi.

Reid, J. J. E.

R. A. Stolzenberger, C. C. Hsu, N. Peyghambarian, J. J. E. Reid, R. A. Morgan, “Type II Sum Frequency Generation in Flux and Hydrothermally Grown KTP at 1.319 and 1.338 Microns,” IEEE Photon. Technol. Lett., 1, 446–448 (1989).
[CrossRef]

Risk, W. P.

W. P. Risk, J. C. Baumert, G. C. Bjorklund, F. M. Schellenberg, W. Lenth, “Generation of Blue Light by Intracavity Frequency Mixing of the Laser and Pump Radiation of a Miniature Neodymium:Yttrium Aluminum Garnet Laser,” Appl. Phys. Lett. 52, 85–87 (1988).
[CrossRef]

J. C. Baumert, F. M. Schellenberg, W. Lenth, W. P. Risk, G. C. Bjorklund, “Generation of Blue Coherent Radiation by Sum Frequency Mixing in KTiOPO4,” Appl. Phys. Lett. 51, 2192–2194 (1987).
[CrossRef]

Rizzo, J. E.

W. S. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, R. S. Craxton, “Demonstration of High Efficiency Third Harmonic Conversion of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

Schellenberg, F. M.

W. P. Risk, J. C. Baumert, G. C. Bjorklund, F. M. Schellenberg, W. Lenth, “Generation of Blue Light by Intracavity Frequency Mixing of the Laser and Pump Radiation of a Miniature Neodymium:Yttrium Aluminum Garnet Laser,” Appl. Phys. Lett. 52, 85–87 (1988).
[CrossRef]

J. C. Baumert, F. M. Schellenberg, W. Lenth, W. P. Risk, G. C. Bjorklund, “Generation of Blue Coherent Radiation by Sum Frequency Mixing in KTiOPO4,” Appl. Phys. Lett. 51, 2192–2194 (1987).
[CrossRef]

Seka, W. S.

W. S. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, R. S. Craxton, “Demonstration of High Efficiency Third Harmonic Conversion of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley & Sons, New York, 1984).

Singh, S.

S. Singh, “Nonlinear Optical Properties,” in CRC Handbook of Laser Science and Technology, Vol. VI (CRC Press, Boca Raton, Florida, 1984).

Stegeman, G. I.

F. A. Hopf, G. I. Stegeman, Applied Classical Electrodynamics, Vol. 1: Linear Optics (Wiley & Sons, New York, 1985); Applied Classical Electrodynamics, Vol. 2: Nonlinear Optics (Wiley & Sons, New York, 1986).

Stolzenberger, R. A.

R. A. Stolzenberger, C. C. Hsu, N. Peyghambarian, J. J. E. Reid, R. A. Morgan, “Type II Sum Frequency Generation in Flux and Hydrothermally Grown KTP at 1.319 and 1.338 Microns,” IEEE Photon. Technol. Lett., 1, 446–448 (1989).
[CrossRef]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Permagon, New York, 1980).

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]

Zumsteg, F. C.

F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980–4985 (1976).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

Jean-Claude Baumert, Peter Gtinter, “Noncritically Phase-Matched Sum Frequency Generation and Image Upconversion in KNbO3 Crystals,” Appl. Phys. Lett. 50, 554–556 (1987).
[CrossRef]

P. Günter, “Near-Infrared Noncritically Phase-Matched Second Harmonic Generation in KNbO3,” Appl. Phys. Lett. 34, 650–652 (1979).
[CrossRef]

J. C. Baumert, F. M. Schellenberg, W. Lenth, W. P. Risk, G. C. Bjorklund, “Generation of Blue Coherent Radiation by Sum Frequency Mixing in KTiOPO4,” Appl. Phys. Lett. 51, 2192–2194 (1987).
[CrossRef]

W. P. Risk, J. C. Baumert, G. C. Bjorklund, F. M. Schellenberg, W. Lenth, “Generation of Blue Light by Intracavity Frequency Mixing of the Laser and Pump Radiation of a Miniature Neodymium:Yttrium Aluminum Garnet Laser,” Appl. Phys. Lett. 52, 85–87 (1988).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. A. Stolzenberger, C. C. Hsu, N. Peyghambarian, J. J. E. Reid, R. A. Morgan, “Type II Sum Frequency Generation in Flux and Hydrothermally Grown KTP at 1.319 and 1.338 Microns,” IEEE Photon. Technol. Lett., 1, 446–448 (1989).
[CrossRef]

J. Appl. Phys. (4)

H. Ito, N. Hatsuhiko, H. Inaba, “Generalized Study on Angular Dependence of Induced Second-Order Nonlinear Optical Polarizations and Phase Matching in Biaxial Crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
[CrossRef]

F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: A New Nonlinear Optical Material,” J. Appl. Phys. 47, 4980–4985 (1976).
[CrossRef]

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]

Laser Focus/Electro-Opt. (1)

R. F. Belt, G. Gashurov, Y. S. Liu, “KTP as a Harmonic Generator for Nd:YAG Lasers,” Laser Focus/Electro-Opt. 21, 110–124.

Opt. Commun. (2)

W. S. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, R. S. Craxton, “Demonstration of High Efficiency Third Harmonic Conversion of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

R. S. Craxton, “Theory of High Efficiency Third Harmonic Generation of High Power Nd-Glass Laser Radiation,” Opt. Commun. 34, 474–478 (1980).
[CrossRef]

Opt. Eng. (1)

R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Dual-Frequency Nd:YAG Laser for the Study and Application of Nonlinear Optical Crystals,” Opt. Eng. 26, 1240–1244 (1987).
[CrossRef]

Phys. Rev. (1)

D. A. Kleinman, “Nonlinear Dielectric Polarization in Optical Media,” Phys. Rev. 126, 1977–1979 (1962).
[CrossRef]

Phys. Rev. Lett. (1)

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

P. Günter, “Nonlinear Optical Crystals for Frequency Doubling with Laser Diodes,” Proc. Soc. Photo-Opt. Instrum. Eng. 236, 8–18 (1980).

Other (6)

M. Born, E. Wolf, Principles of Optics (Permagon, New York, 1980).

R. A. Morgan, F. A. Hopf, N. Peyghambarian, “Three-Wave Mixing Uses of a Novel Dual-Frequency Nd:YAG Laser,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988) paper ThAi.

S. Singh, “Nonlinear Optical Properties,” in CRC Handbook of Laser Science and Technology, Vol. VI (CRC Press, Boca Raton, Florida, 1984).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley & Sons, New York, 1984).

F. A. Hopf, G. I. Stegeman, Applied Classical Electrodynamics, Vol. 1: Linear Optics (Wiley & Sons, New York, 1985); Applied Classical Electrodynamics, Vol. 2: Nonlinear Optics (Wiley & Sons, New York, 1986).

David Eimerl, “Sellmeier Constants and Related Data For KTP,” paper presented at Workshop on Nonlinear Optical Materials, Annapolis, MD, April 28–29, 1986; D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, G. Kennedy, “Deuterated L-Arginine Phosphate: a New Efficient Nonlinear Crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
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Figures (1)

Fig. 1
Fig. 1

Representation of an e-configuration eigenvector in an anisotropic crystal. The principal axes are represented as 1, 2, and 3. The walkoff angle is δ, and the wavevector angle θ is measured according to the RHR (here from the 3-axis) as described in the text. On the same diagram, an o-configuration eigenvector would be polarized along the 2-axis. Its index is independent of θ, and δ = 0. (After Ref. 2.)

Equations (31)

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P i ( E ) = 0 i j χ i j ( 1 ) E j + 0 i j k χ i j k ( 2 ) E j E k + 0 i j k l χ i j k l ( 3 ) E j E k E l + ,
E ( ω a ; z ) z = i ω a d eff n a c E ( ω c ; z ) E * ( ω b ; z ) exp ( i Δ k z ) ,
E ( ω b ; z ) z = i ω b d eff n a c E ( ω c ; z ) E * ( ω a ; z ) exp ( i Δ k z ) ,
E ( ω c ; z ) z = i ω c d eff n c c E ( ω a ; z ) E ( ω b ; z ) exp ( - i Δ k z ) .
ω c = ω b + ω a ;
Δ k = k c - k b - k a 0.
ω c n c ( ω c ) = ω b n b ( ω b ) + ω a n a ( ω a ) ,
n c ( λ c ) λ c = n b ( λ b ) λ b + n a ( λ a ) λ a .
ω c ω b ω a ,
n j ( θ i ) = n i n j ( n j 2 cos 2 θ i + n j 2 sin 2 θ i ) 1 / 2 ,
tan ( δ ) = n 2 ( θ i ) 2 [ 1 n i 2 - 1 n j 2 ] sin ( 2 θ i ) .
η i n ( ω i ) λ i ( i = a , b , c ) .
η e ( ω c ) η o ( ω b ) + η o ( ω a ) sin θ pm = n e ( ω c ) η o ( ω b ) + η o ( ω a ) × { η o 2 ( ω c ) - [ η o ( ω b ) + η o ( ω a ) ] 2 n o 2 ( ω c ) - n e 2 ( ω c ) } 1 / 2 ;
η e ( ω c ) η o ( ω b ) + η e ( ω a ) ;
η e ( ω c ) η e ( ω b ) + η o ( ω a ) .
η o ( ω c ) η e ( ω b ) + η e ( ω a ) ;
η o ( ω c ) η e ( ω b ) + η o ( ω a ) sin θ pm = n e ( ω b ) η o ( ω c ) - η o ( ω a ) × { η o 2 ( ω b ) - [ η o ( ω c ) + η o ( ω a ) ] 2 n o 2 ( ω b ) - n e 2 ( ω b ) } 1 / 2 ;
η o ( ω c ) η o ( ω b ) + η e ( ω a ) sin θ pm = n e ( ω a ) η o ( ω c ) - η o ( ω b ) × { η o 2 ( ω a ) - [ η o ( ω c ) + η o ( ω b ) ] 2 n o 2 ( ω a ) - n e 2 ( ω a ) } 1 / 2 .
n γ n β n a .
η β ( ω c ) η γ ( ω b ) + η γ ( ω a ) and η α ( ω c ) η γ ( ω b ) + η γ ( ω a ) sin θ pm = n α ( ω c ) η γ ( ω b ) + η γ ( ω a ) × { η β 2 ( ω c ) - [ η γ ( ω b ) + η γ ( ω a ) ] 2 n β 2 ( ω c ) - n α 2 ( ω c ) } 1 / 2 ;
η β ( ω c ) η γ ( ω b ) + η β ( ω a ) and η a ( ω c ) η γ ( ω b ) + η α ( ω a ) ;
η β ( ω c ) η β ( ω b ) + η γ ( ω a ) and η a ( ω c ) η α ( ω b ) + η γ ( ω a ) ;
η α ( ω c ) η β ( ω b ) + η β ( ω a ) and η a ( ω c ) η γ ( ω b ) + η γ ( ω a ) ;
η α ( ω c ) η β ( ω b ) + η α ( ω a ) and η α ( ω c ) η γ ( ω b ) + η α ( ω a ) sin θ pm = n β ( ω b ) η α ( ω c ) - η α ( ω a ) × { η γ 2 ( ω b ) - [ η α ( ω c ) - η α ( ω a ) ] 2 n γ 2 ( ω b ) - n β 2 ( ω b ) } 1 / 2 ;
η α ( ω c ) η α ( ω b ) + η β ( ω a ) and η α ( ω c ) η α ( ω b ) + η γ ( ω a ) sin θ pm = n β ( ω a ) η α ( ω c ) - η α ( ω b ) × { η γ 2 ( ω a ) - [ η α ( ω c ) - η α ( ω b ) ] 2 n γ 2 ( ω a ) - n β 2 ( ω a ) } 1 / 2 ;
η α ( ω c ) η β ( ω b ) + η β ( ω a ) sin θ pm = n γ ( ω c ) η β ( ω b ) - η β ( ω a ) × { η α 2 ( ω c ) - [ η β ( ω b ) - η β ( ω a ) ] 2 n α 2 ( ω c ) - n γ 2 ( ω c ) } 1 / 2 ;
η α ( ω c ) η β ( ω b ) + η α ( ω a ) ;
η α ( ω c ) η α ( ω b ) + η β ( ω a ) ;
η β ( ω c ) η γ ( ω b ) + η γ ( ω a ) ;
η β ( ω c ) η γ ( ω b ) + η β ( ω a ) sin θ pm = n γ ( ω b ) η β ( ω c ) - η β ( ω a ) × { η α 2 ( ω b ) - [ η β ( ω c ) - η β ( ω a ) ] 2 n α 2 ( ω b ) - n γ 2 ( ω b ) } 1 / 2 ;
η β ( ω c ) η β ( ω b ) + η γ ( ω a ) sin θ pm = n γ ( ω c ) η β ( ω c ) - η β ( ω b ) × { η α 2 ( ω a ) - [ η β ( ω c ) - η β ( ω b ) ] 2 n α 2 ( ω a ) - n γ 2 ( ω a ) } 1 / 2 .

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